Metadata-Version: 2.4
Name: u-Protrude3D
Version: 0.1.0
Summary: 3D cell protrusion segmentation, benchmarking, and volumization
Author-email: "Felix Y. Zhou" <felixzhou1@gmail.com>
License:                     GNU GENERAL PUBLIC LICENSE
                               Version 3, 29 June 2007
        
         Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
         Everyone is permitted to copy and distribute verbatim copies
         of this license document, but changing it is not allowed.
        
                                    Preamble
        
          The GNU General Public License is a free, copyleft license for
        software and other kinds of works.
        
          The licenses for most software and other practical works are designed
        to take away your freedom to share and change the works.  By contrast,
        the GNU General Public License is intended to guarantee your freedom to
        share and change all versions of a program--to make sure it remains free
        software for all its users.  We, the Free Software Foundation, use the
        GNU General Public License for most of our software; it applies also to
        any other work released this way by its authors.  You can apply it to
        your programs, too.
        
          When we speak of free software, we are referring to freedom, not
        price.  Our General Public Licenses are designed to make sure that you
        have the freedom to distribute copies of free software (and charge for
        them if you wish), that you receive source code or can get it if you
        want it, that you can change the software or use pieces of it in new
        free programs, and that you know you can do these things.
        
          To protect your rights, we need to prevent others from denying you
        these rights or asking you to surrender the rights.  Therefore, you have
        certain responsibilities if you distribute copies of the software, or if
        you modify it: responsibilities to respect the freedom of others.
        
          For example, if you distribute copies of such a program, whether
        gratis or for a fee, you must pass on to the recipients the same
        freedoms that you received.  You must make sure that they, too, receive
        or can get the source code.  And you must show them these terms so they
        know their rights.
        
          Developers that use the GNU GPL protect your rights with two steps:
        (1) assert copyright on the software, and (2) offer you this License
        giving you legal permission to copy, distribute and/or modify it.
        
          For the developers' and authors' protection, the GPL clearly explains
        that there is no warranty for this free software.  For both users' and
        authors' sake, the GPL requires that modified versions be marked as
        changed, so that their problems will not be attributed erroneously to
        authors of previous versions.
        
          Some devices are designed to deny users access to install or run
        modified versions of the software inside them, although the manufacturer
        can do so.  This is fundamentally incompatible with the aim of
        protecting users' freedom to change the software.  The systematic
        pattern of such abuse occurs in the area of products for individuals to
        use, which is precisely where it is most unacceptable.  Therefore, we
        have designed this version of the GPL to prohibit the practice for those
        products.  If such problems arise substantially in other domains, we
        stand ready to extend this provision to those domains in future versions
        of the GPL, as needed to protect the freedom of users.
        
          Finally, every program is threatened constantly by software patents.
        States should not allow patents to restrict development and use of
        software on general-purpose computers, but in those that do, we wish to
        avoid the special danger that patents applied to a free program could
        make it effectively proprietary.  To prevent this, the GPL assures that
        patents cannot be used to render the program non-free.
        
          The precise terms and conditions for copying, distribution and
        modification follow.
        
                               TERMS AND CONDITIONS
        
          0. Definitions.
        
          "This License" refers to version 3 of the GNU General Public License.
        
          "Copyright" also means copyright-like laws that apply to other kinds of
        works, such as semiconductor masks.
        
          "The Program" refers to any copyrightable work licensed under this
        License.  Each licensee is addressed as "you".  "Licensees" and
        "recipients" may be individuals or organizations.
        
          To "modify" a work means to copy from or adapt all or part of the work
        in a fashion requiring copyright permission, other than the making of an
        exact copy.  The resulting work is called a "modified version" of the
        earlier work or a work "based on" the earlier work.
        
          A "covered work" means either the unmodified Program or a work based
        on the Program.
        
          To "propagate" a work means to do anything with it that, without
        permission, would make you directly or secondarily liable for
        infringement under applicable copyright law, except executing it on a
        computer or modifying a private copy.  Propagation includes copying,
        distribution (with or without modification), making available to the
        public, and in some countries other activities as well.
        
          To "convey" a work means any kind of propagation that enables other
        parties to make or receive copies.  Mere interaction with a user through
        a computer network, with no transfer of a copy, is not conveying.
        
          An interactive user interface displays "Appropriate Legal Notices"
        to the extent that it includes a convenient and prominently visible
        feature that (1) displays an appropriate copyright notice, and (2)
        tells the user that there is no warranty for the work (except to the
        extent that warranties are provided), that licensees may convey the
        work under this License, and how to view a copy of this License.  If
        the interface presents a list of user commands or options, such as a
        menu, a prominent item in the list meets this criterion.
        
          1. Source Code.
        
          The "source code" for a work means the preferred form of the work
        for making modifications to it.  "Object code" means any non-source
        form of a work.
        
          A "Standard Interface" means an interface that either is an official
        standard defined by a recognized standards body, or, in the case of
        interfaces specified for a particular programming language, one that
        is widely used among developers working in that language.
        
          The "System Libraries" of an executable work include anything, other
        than the work as a whole, that (a) is included in the normal form of
        packaging a Major Component, but which is not part of that Major
        Component, and (b) serves only to enable use of the work with that
        Major Component, or to implement a Standard Interface for which an
        implementation is available to the public in source code form.  A
        "Major Component", in this context, means a major essential component
        (kernel, window system, and so on) of the specific operating system
        (if any) on which the executable work runs, or a compiler used to
        produce the work, or an object code interpreter used to run it.
        
          The "Corresponding Source" for a work in object code form means all
        the source code needed to generate, install, and (for an executable
        work) run the object code and to modify the work, including scripts to
        control those activities.  However, it does not include the work's
        System Libraries, or general-purpose tools or generally available free
        programs which are used unmodified in performing those activities but
        which are not part of the work.  For example, Corresponding Source
        includes interface definition files associated with source files for
        the work, and the source code for shared libraries and dynamically
        linked subprograms that the work is specifically designed to require,
        such as by intimate data communication or control flow between those
        subprograms and other parts of the work.
        
          The Corresponding Source need not include anything that users
        can regenerate automatically from other parts of the Corresponding
        Source.
        
          The Corresponding Source for a work in source code form is that
        same work.
        
          2. Basic Permissions.
        
          All rights granted under this License are granted for the term of
        copyright on the Program, and are irrevocable provided the stated
        conditions are met.  This License explicitly affirms your unlimited
        permission to run the unmodified Program.  The output from running a
        covered work is covered by this License only if the output, given its
        content, constitutes a covered work.  This License acknowledges your
        rights of fair use or other equivalent, as provided by copyright law.
        
          You may make, run and propagate covered works that you do not
        convey, without conditions so long as your license otherwise remains
        in force.  You may convey covered works to others for the sole purpose
        of having them make modifications exclusively for you, or provide you
        with facilities for running those works, provided that you comply with
        the terms of this License in conveying all material for which you do
        not control copyright.  Those thus making or running the covered works
        for you must do so exclusively on your behalf, under your direction
        and control, on terms that prohibit them from making any copies of
        your copyrighted material outside their relationship with you.
        
          Conveying under any other circumstances is permitted solely under
        the conditions stated below.  Sublicensing is not allowed; section 10
        makes it unnecessary.
        
          3. Protecting Users' Legal Rights From Anti-Circumvention Law.
        
          No covered work shall be deemed part of an effective technological
        measure under any applicable law fulfilling obligations under article
        11 of the WIPO copyright treaty adopted on 20 December 1996, or
        similar laws prohibiting or restricting circumvention of such
        measures.
        
          When you convey a covered work, you waive any legal power to forbid
        circumvention of technological measures to the extent such circumvention
        is effected by exercising rights under this License with respect to
        the covered work, and you disclaim any intention to limit operation or
        modification of the work as a means of enforcing, against the work's
        users, your or third parties' legal rights to forbid circumvention of
        technological measures.
        
          4. Conveying Verbatim Copies.
        
          You may convey verbatim copies of the Program's source code as you
        receive it, in any medium, provided that you conspicuously and
        appropriately publish on each copy an appropriate copyright notice;
        keep intact all notices stating that this License and any
        non-permissive terms added in accord with section 7 apply to the code;
        keep intact all notices of the absence of any warranty; and give all
        recipients a copy of this License along with the Program.
        
          You may charge any price or no price for each copy that you convey,
        and you may offer support or warranty protection for a fee.
        
          5. Conveying Modified Source Versions.
        
          You may convey a work based on the Program, or the modifications to
        produce it from the Program, in the form of source code under the
        terms of section 4, provided that you also meet all of these conditions:
        
            a) The work must carry prominent notices stating that you modified
            it, and giving a relevant date.
        
            b) The work must carry prominent notices stating that it is
            released under this License and any conditions added under section
            7.  This requirement modifies the requirement in section 4 to
            "keep intact all notices".
        
            c) You must license the entire work, as a whole, under this
            License to anyone who comes into possession of a copy.  This
            License will therefore apply, along with any applicable section 7
            additional terms, to the whole of the work, and all its parts,
            regardless of how they are packaged.  This License gives no
            permission to license the work in any other way, but it does not
            invalidate such permission if you have separately received it.
        
            d) If the work has interactive user interfaces, each must display
            Appropriate Legal Notices; however, if the Program has interactive
            interfaces that do not display Appropriate Legal Notices, your
            work need not make them do so.
        
          A compilation of a covered work with other separate and independent
        works, which are not by their nature extensions of the covered work,
        and which are not combined with it such as to form a larger program,
        in or on a volume of a storage or distribution medium, is called an
        "aggregate" if the compilation and its resulting copyright are not
        used to limit the access or legal rights of the compilation's users
        beyond what the individual works permit.  Inclusion of a covered work
        in an aggregate does not cause this License to apply to the other
        parts of the aggregate.
        
          6. Conveying Non-Source Forms.
        
          You may convey a covered work in object code form under the terms
        of sections 4 and 5, provided that you also convey the
        machine-readable Corresponding Source under the terms of this License,
        in one of these ways:
        
            a) Convey the object code in, or embodied in, a physical product
            (including a physical distribution medium), accompanied by the
            Corresponding Source fixed on a durable physical medium
            customarily used for software interchange.
        
            b) Convey the object code in, or embodied in, a physical product
            (including a physical distribution medium), accompanied by a
            written offer, valid for at least three years and valid for as
            long as you offer spare parts or customer support for that product
            model, to give anyone who possesses the object code either (1) a
            copy of the Corresponding Source for all the software in the
            product that is covered by this License, on a durable physical
            medium customarily used for software interchange, for a price no
            more than your reasonable cost of physically performing this
            conveying of source, or (2) access to copy the
            Corresponding Source from a network server at no charge.
        
            c) Convey individual copies of the object code with a copy of the
            written offer to provide the Corresponding Source.  This
            alternative is allowed only occasionally and noncommercially, and
            only if you received the object code with such an offer, in accord
            with subsection 6b.
        
            d) Convey the object code by offering access from a designated
            place (gratis or for a charge), and offer equivalent access to the
            Corresponding Source in the same way through the same place at no
            further charge.  You need not require recipients to copy the
            Corresponding Source along with the object code.  If the place to
            copy the object code is a network server, the Corresponding Source
            may be on a different server (operated by you or a third party)
            that supports equivalent copying facilities, provided you maintain
            clear directions next to the object code saying where to find the
            Corresponding Source.  Regardless of what server hosts the
            Corresponding Source, you remain obligated to ensure that it is
            available for as long as needed to satisfy these requirements.
        
            e) Convey the object code using peer-to-peer transmission, provided
            you inform other peers where the object code and Corresponding
            Source of the work are being offered to the general public at no
            charge under subsection 6d.
        
          A separable portion of the object code, whose source code is excluded
        from the Corresponding Source as a System Library, need not be
        included in conveying the object code work.
        
          A "User Product" is either (1) a "consumer product", which means any
        tangible personal property which is normally used for personal, family,
        or household purposes, or (2) anything designed or sold for incorporation
        into a dwelling.  In determining whether a product is a consumer product,
        doubtful cases shall be resolved in favor of coverage.  For a particular
        product received by a particular user, "normally used" refers to a
        typical or common use of that class of product, regardless of the status
        of the particular user or of the way in which the particular user
        actually uses, or expects or is expected to use, the product.  A product
        is a consumer product regardless of whether the product has substantial
        commercial, industrial or non-consumer uses, unless such uses represent
        the only significant mode of use of the product.
        
          "Installation Information" for a User Product means any methods,
        procedures, authorization keys, or other information required to install
        and execute modified versions of a covered work in that User Product from
        a modified version of its Corresponding Source.  The information must
        suffice to ensure that the continued functioning of the modified object
        code is in no case prevented or interfered with solely because
        modification has been made.
        
          If you convey an object code work under this section in, or with, or
        specifically for use in, a User Product, and the conveying occurs as
        part of a transaction in which the right of possession and use of the
        User Product is transferred to the recipient in perpetuity or for a
        fixed term (regardless of how the transaction is characterized), the
        Corresponding Source conveyed under this section must be accompanied
        by the Installation Information.  But this requirement does not apply
        if neither you nor any third party retains the ability to install
        modified object code on the User Product (for example, the work has
        been installed in ROM).
        
          The requirement to provide Installation Information does not include a
        requirement to continue to provide support service, warranty, or updates
        for a work that has been modified or installed by the recipient, or for
        the User Product in which it has been modified or installed.  Access to a
        network may be denied when the modification itself materially and
        adversely affects the operation of the network or violates the rules and
        protocols for communication across the network.
        
          Corresponding Source conveyed, and Installation Information provided,
        in accord with this section must be in a format that is publicly
        documented (and with an implementation available to the public in
        source code form), and must require no special password or key for
        unpacking, reading or copying.
        
          7. Additional Terms.
        
          "Additional permissions" are terms that supplement the terms of this
        License by making exceptions from one or more of its conditions.
        Additional permissions that are applicable to the entire Program shall
        be treated as though they were included in this License, to the extent
        that they are valid under applicable law.  If additional permissions
        apply only to part of the Program, that part may be used separately
        under those permissions, but the entire Program remains governed by
        this License without regard to the additional permissions.
        
          When you convey a copy of a covered work, you may at your option
        remove any additional permissions from that copy, or from any part of
        it.  (Additional permissions may be written to require their own
        removal in certain cases when you modify the work.)  You may place
        additional permissions on material, added by you to a covered work,
        for which you have or can give appropriate copyright permission.
        
          Notwithstanding any other provision of this License, for material you
        add to a covered work, you may (if authorized by the copyright holders of
        that material) supplement the terms of this License with terms:
        
            a) Disclaiming warranty or limiting liability differently from the
            terms of sections 15 and 16 of this License; or
        
            b) Requiring preservation of specified reasonable legal notices or
            author attributions in that material or in the Appropriate Legal
            Notices displayed by works containing it; or
        
            c) Prohibiting misrepresentation of the origin of that material, or
            requiring that modified versions of such material be marked in
            reasonable ways as different from the original version; or
        
            d) Limiting the use for publicity purposes of names of licensors or
            authors of the material; or
        
            e) Declining to grant rights under trademark law for use of some
            trade names, trademarks, or service marks; or
        
            f) Requiring indemnification of licensors and authors of that
            material by anyone who conveys the material (or modified versions of
            it) with contractual assumptions of liability to the recipient, for
            any liability that these contractual assumptions directly impose on
            those licensors and authors.
        
          All other non-permissive additional terms are considered "further
        restrictions" within the meaning of section 10.  If the Program as you
        received it, or any part of it, contains a notice stating that it is
        governed by this License along with a term that is a further
        restriction, you may remove that term.  If a license document contains
        a further restriction but permits relicensing or conveying under this
        License, you may add to a covered work material governed by the terms
        of that license document, provided that the further restriction does
        not survive such relicensing or conveying.
        
          If you add terms to a covered work in accord with this section, you
        must place, in the relevant source files, a statement of the
        additional terms that apply to those files, or a notice indicating
        where to find the applicable terms.
        
          Additional terms, permissive or non-permissive, may be stated in the
        form of a separately written license, or stated as exceptions;
        the above requirements apply either way.
        
          8. Termination.
        
          You may not propagate or modify a covered work except as expressly
        provided under this License.  Any attempt otherwise to propagate or
        modify it is void, and will automatically terminate your rights under
        this License (including any patent licenses granted under the third
        paragraph of section 11).
        
          However, if you cease all violation of this License, then your
        license from a particular copyright holder is reinstated (a)
        provisionally, unless and until the copyright holder explicitly and
        finally terminates your license, and (b) permanently, if the copyright
        holder fails to notify you of the violation by some reasonable means
        prior to 60 days after the cessation.
        
          Moreover, your license from a particular copyright holder is
        reinstated permanently if the copyright holder notifies you of the
        violation by some reasonable means, this is the first time you have
        received notice of violation of this License (for any work) from that
        copyright holder, and you cure the violation prior to 30 days after
        your receipt of the notice.
        
          Termination of your rights under this section does not terminate the
        licenses of parties who have received copies or rights from you under
        this License.  If your rights have been terminated and not permanently
        reinstated, you do not qualify to receive new licenses for the same
        material under section 10.
        
          9. Acceptance Not Required for Having Copies.
        
          You are not required to accept this License in order to receive or
        run a copy of the Program.  Ancillary propagation of a covered work
        occurring solely as a consequence of using peer-to-peer transmission
        to receive a copy likewise does not require acceptance.  However,
        nothing other than this License grants you permission to propagate or
        modify any covered work.  These actions infringe copyright if you do
        not accept this License.  Therefore, by modifying or propagating a
        covered work, you indicate your acceptance of this License to do so.
        
          10. Automatic Licensing of Downstream Recipients.
        
          Each time you convey a covered work, the recipient automatically
        receives a license from the original licensors, to run, modify and
        propagate that work, subject to this License.  You are not responsible
        for enforcing compliance by third parties with this License.
        
          An "entity transaction" is a transaction transferring control of an
        organization, or substantially all assets of one, or subdividing an
        organization, or merging organizations.  If propagation of a covered
        work results from an entity transaction, each party to that
        transaction who receives a copy of the work also receives whatever
        licenses to the work the party's predecessor in interest had or could
        give under the previous paragraph, plus a right to possession of the
        Corresponding Source of the work from the predecessor in interest, if
        the predecessor has it or can get it with reasonable efforts.
        
          You may not impose any further restrictions on the exercise of the
        rights granted or affirmed under this License.  For example, you may
        not impose a license fee, royalty, or other charge for exercise of
        rights granted under this License, and you may not initiate litigation
        (including a cross-claim or counterclaim in a lawsuit) alleging that
        any patent claim is infringed by making, using, selling, offering for
        sale, or importing the Program or any portion of it.
        
          11. Patents.
        
          A "contributor" is a copyright holder who authorizes use under this
        License of the Program or a work on which the Program is based.  The
        work thus licensed is called the contributor's "contributor version".
        
          A contributor's "essential patent claims" are all patent claims
        owned or controlled by the contributor, whether already acquired or
        hereafter acquired, that would be infringed by some manner, permitted
        by this License, of making, using, or selling its contributor version,
        but do not include claims that would be infringed only as a
        consequence of further modification of the contributor version.  For
        purposes of this definition, "control" includes the right to grant
        patent sublicenses in a manner consistent with the requirements of
        this License.
        
          Each contributor grants you a non-exclusive, worldwide, royalty-free
        patent license under the contributor's essential patent claims, to
        make, use, sell, offer for sale, import and otherwise run, modify and
        propagate the contents of its contributor version.
        
          In the following three paragraphs, a "patent license" is any express
        agreement or commitment, however denominated, not to enforce a patent
        (such as an express permission to practice a patent or covenant not to
        sue for patent infringement).  To "grant" such a patent license to a
        party means to make such an agreement or commitment not to enforce a
        patent against the party.
        
          If you convey a covered work, knowingly relying on a patent license,
        and the Corresponding Source of the work is not available for anyone
        to copy, free of charge and under the terms of this License, through a
        publicly available network server or other readily accessible means,
        then you must either (1) cause the Corresponding Source to be so
        available, or (2) arrange to deprive yourself of the benefit of the
        patent license for this particular work, or (3) arrange, in a manner
        consistent with the requirements of this License, to extend the patent
        license to downstream recipients.  "Knowingly relying" means you have
        actual knowledge that, but for the patent license, your conveying the
        covered work in a country, or your recipient's use of the covered work
        in a country, would infringe one or more identifiable patents in that
        country that you have reason to believe are valid.
        
          If, pursuant to or in connection with a single transaction or
        arrangement, you convey, or propagate by procuring conveyance of, a
        covered work, and grant a patent license to some of the parties
        receiving the covered work authorizing them to use, propagate, modify
        or convey a specific copy of the covered work, then the patent license
        you grant is automatically extended to all recipients of the covered
        work and works based on it.
        
          A patent license is "discriminatory" if it does not include within
        the scope of its coverage, prohibits the exercise of, or is
        conditioned on the non-exercise of one or more of the rights that are
        specifically granted under this License.  You may not convey a covered
        work if you are a party to an arrangement with a third party that is
        in the business of distributing software, under which you make payment
        to the third party based on the extent of your activity of conveying
        the work, and under which the third party grants, to any of the
        parties who would receive the covered work from you, a discriminatory
        patent license (a) in connection with copies of the covered work
        conveyed by you (or copies made from those copies), or (b) primarily
        for and in connection with specific products or compilations that
        contain the covered work, unless you entered into that arrangement,
        or that patent license was granted, prior to 28 March 2007.
        
          Nothing in this License shall be construed as excluding or limiting
        any implied license or other defenses to infringement that may
        otherwise be available to you under applicable patent law.
        
          12. No Surrender of Others' Freedom.
        
          If conditions are imposed on you (whether by court order, agreement or
        otherwise) that contradict the conditions of this License, they do not
        excuse you from the conditions of this License.  If you cannot convey a
        covered work so as to satisfy simultaneously your obligations under this
        License and any other pertinent obligations, then as a consequence you may
        not convey it at all.  For example, if you agree to terms that obligate you
        to collect a royalty for further conveying from those to whom you convey
        the Program, the only way you could satisfy both those terms and this
        License would be to refrain entirely from conveying the Program.
        
          13. Use with the GNU Affero General Public License.
        
          Notwithstanding any other provision of this License, you have
        permission to link or combine any covered work with a work licensed
        under version 3 of the GNU Affero General Public License into a single
        combined work, and to convey the resulting work.  The terms of this
        License will continue to apply to the part which is the covered work,
        but the special requirements of the GNU Affero General Public License,
        section 13, concerning interaction through a network will apply to the
        combination as such.
        
          14. Revised Versions of this License.
        
          The Free Software Foundation may publish revised and/or new versions of
        the GNU General Public License from time to time.  Such new versions will
        be similar in spirit to the present version, but may differ in detail to
        address new problems or concerns.
        
          Each version is given a distinguishing version number.  If the
        Program specifies that a certain numbered version of the GNU General
        Public License "or any later version" applies to it, you have the
        option of following the terms and conditions either of that numbered
        version or of any later version published by the Free Software
        Foundation.  If the Program does not specify a version number of the
        GNU General Public License, you may choose any version ever published
        by the Free Software Foundation.
        
          If the Program specifies that a proxy can decide which future
        versions of the GNU General Public License can be used, that proxy's
        public statement of acceptance of a version permanently authorizes you
        to choose that version for the Program.
        
          Later license versions may give you additional or different
        permissions.  However, no additional obligations are imposed on any
        author or copyright holder as a result of your choosing to follow a
        later version.
        
          15. Disclaimer of Warranty.
        
          THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
        APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
        HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
        OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
        THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
        PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
        IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
        ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
        
          16. Limitation of Liability.
        
          IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
        WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
        THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
        GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
        USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
        DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
        PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
        EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
        SUCH DAMAGES.
        
          17. Interpretation of Sections 15 and 16.
        
          If the disclaimer of warranty and limitation of liability provided
        above cannot be given local legal effect according to their terms,
        reviewing courts shall apply local law that most closely approximates
        an absolute waiver of all civil liability in connection with the
        Program, unless a warranty or assumption of liability accompanies a
        copy of the Program in return for a fee.
        
                             END OF TERMS AND CONDITIONS
        
                    How to Apply These Terms to Your New Programs
        
          If you develop a new program, and you want it to be of the greatest
        possible use to the public, the best way to achieve this is to make it
        free software which everyone can redistribute and change under these terms.
        
          To do so, attach the following notices to the program.  It is safest
        to attach them to the start of each source file to most effectively
        state the exclusion of warranty; and each file should have at least
        the "copyright" line and a pointer to where the full notice is found.
        
            <one line to give the program's name and a brief idea of what it does.>
            Copyright (C) <year>  <name of author>
        
            This program is free software: you can redistribute it and/or modify
            it under the terms of the GNU General Public License as published by
            the Free Software Foundation, either version 3 of the License, or
            (at your option) any later version.
        
            This program is distributed in the hope that it will be useful,
            but WITHOUT ANY WARRANTY; without even the implied warranty of
            MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
            GNU General Public License for more details.
        
            You should have received a copy of the GNU General Public License
            along with this program.  If not, see <https://www.gnu.org/licenses/>.
        
        Also add information on how to contact you by electronic and paper mail.
        
          If the program does terminal interaction, make it output a short
        notice like this when it starts in an interactive mode:
        
            <program>  Copyright (C) <year>  <name of author>
            This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
            This is free software, and you are welcome to redistribute it
            under certain conditions; type `show c' for details.
        
        The hypothetical commands `show w' and `show c' should show the appropriate
        parts of the General Public License.  Of course, your program's commands
        might be different; for a GUI interface, you would use an "about box".
        
          You should also get your employer (if you work as a programmer) or school,
        if any, to sign a "copyright disclaimer" for the program, if necessary.
        For more information on this, and how to apply and follow the GNU GPL, see
        <https://www.gnu.org/licenses/>.
        
          The GNU General Public License does not permit incorporating your program
        into proprietary programs.  If your program is a subroutine library, you
        may consider it more useful to permit linking proprietary applications with
        the library.  If this is what you want to do, use the GNU Lesser General
        Public License instead of this License.  But first, please read
        <https://www.gnu.org/licenses/why-not-lgpl.html>.
        
Keywords: cell biology,mesh segmentation,protrusion,filopodia,lamellipodia
Classifier: Programming Language :: Python :: 3
Classifier: Topic :: Scientific/Engineering :: Bio-Informatics
Classifier: Intended Audience :: Developers
Classifier: Operating System :: POSIX :: Linux
Classifier: Operating System :: MacOS :: MacOS X
Classifier: Operating System :: Microsoft :: Windows
Classifier: Programming Language :: Python :: 3.9
Classifier: Programming Language :: Python :: 3.10
Classifier: Programming Language :: Python :: 3.11
Classifier: Programming Language :: Python :: 3.12
Requires-Python: <3.13,>=3.9
Description-Content-Type: text/markdown
License-File: LICENSE
Requires-Dist: u-Unwrap3D
Requires-Dist: h5py
Requires-Dist: seaborn
Provides-Extra: dev
Requires-Dist: pytest>=7; extra == "dev"
Requires-Dist: pytest-cov; extra == "dev"
Requires-Dist: black; extra == "dev"
Requires-Dist: ruff; extra == "dev"
Dynamic: license-file

# u-Protrude3D

<p align="center">
  <img src="docs/imgs/summary_figure.png" width="800"/>
</p>

**3D cell protrusion segmentation, benchmarking, and volumization for fluorescence microscopy derived meshes.**

`u-Protrude3D` takes a triangulated cell surface mesh and automatically detects, and labels individual protrusions (e.g. blebs, filopodia, microvilli, lamellipodia) by inferring an optimal basal reference surface. It can optionally benchmark predictions against ground-truth labels and volumize surface labels into 3-D voxel volumes. The latter effectively decomposes the cell volume = protrusion volumes + basal volume.    

---

## Installation

```bash
pip install u-Protrude3D
```

> **Solver note.** The default sparse solver is `pardiso` (Intel MKL). If you do not have MKL installed, change `cfg.cmcf.solver` to `'scipy'` (slower but dependency-free).

Pre-compile the numba JIT functions once before your first run to avoid a 10–30 s delay on the first call:

```python
import u_protrude3d
u_protrude3d.warmup()
```

---

## Quick-start

Use the script in `example_scripts` folder which performs the detection, benchmarking and voxelization decomposition on synthetic generated cell surface mesh to quickly get started. Further example real segmented cell meshes for testing are provided in the `example_data` folder. Note: only the synthetic cell surfaces have ground truth vertex labels and should be run with benchmarking script. Detection and voxelization does not require ground truth labels. 

```python
import u_protrude3d as up3d

# 1. Segment protrusions using scale-invariant Shape Index (recommended)
result = up3d.segment_protrusions_invariant(
    mesh_path="data/cell01.obj",
    save_dir="output/cell01/",
)
print(result.vertex_labels)   # integer label per vertex (0 = background)

# 2. Benchmark predicted labels against ground truth
bench = up3d.benchmark_segmentation(
    pred_dirs=["output/cell01/", "output/cell02/"],
    gt_dirs=["gt/cell01/",       "gt/cell02/"],
    save_dir="output/benchmark/",
)
print(bench.ap)  # shape (n_cells, n_thresholds)

# 3. Volumize: map surface labels into a 3-D voxel array
vol = up3d.volumize_protrusions(
    mesh_path="data/cell01.obj",
    protrusion_labels=result.vertex_labels,
    tif_path="data/cell01.tif",
    save_dir="output/cell01_vol/",
)
print(vol.volume_labels.shape)  # (Z, Y, X)
```

---

## Segment protrusions (scale-invariant, recommended)

`segment_protrusions_invariant` is the recommended segmentation path. It detects protrusions using the **Koenderink Shape Index (SI)** — a dimensionless curvature character measure that ranges from −1 (concavity/cup) through 0 (cylindrical ridge) to +1 (spherical dome). Because SI is normalised by cell surface area it works without retuning across different cell sizes, voxel sizes, or microscope resolutions.

### Pipeline overview

1. Load and optionally remesh the surface.
2. Compute per-vertex principal curvatures → Shape Index, ridgeness, height field via cMCF inflation.
3. Smooth all scalar fields; compute eight scale-invariant descriptors; export coloured `.obj` files for visual inspection.
4. Binarise the height field → initial connected-component (CC) patches.
5. **Per-patch SI labelling** — for each patch, Otsu-threshold face-level SI to find dome-like (high-SI) regions; propagate those seed labels to all patch faces by geometric-affinity diffusion. Patches with no high-SI region receive a single label.
6. **Adaptive saddle merge** *(optional, recommended)* — merge adjacent label pairs that are spurious over-splits, using a criterion that depends on the shape type of each label (compact bleb vs. elongated ridge).
7. Apply basal mask; remove small isolated fragments; save outputs.

### Full example

```python
import u_protrude3d as up3d

cfg = up3d.SegmentConfig()

# Core geometry parameters
cfg.voxel_size    = 0.160   # physical voxel size (µm)
cfg.cmcf.n_iters  = 20      # cMCF inflation steps — more → smoother basal reference

# ── Initial height binarization (critical — tune this first) ──────────────────
# This step determines which surface regions are candidates for protrusions.
# The threshold method and prop_iters are strongly coupled — see parameter table.
#
# Option A: mean threshold (default, inclusive, good starting point)
cfg.initial_height.use_mean             = True
cfg.initial_height.use_otsu             = False
cfg.initial_height.prop_iters           = 1     # 1 diffusion step is usually enough

# Option B: conservative 3-level Otsu (only protrusion tips initially; needs more diffusion)
# cfg.initial_height.use_mean           = False
# cfg.initial_height.use_otsu           = True
# cfg.initial_height.otsu_n_levels      = 3     # three height classes: low / mid / high
# cfg.initial_height.otsu_level         = -1    # use the highest threshold (tips only)
# cfg.initial_height.prop_iters         = 5     # more diffusion to recover full protrusion extent
# cfg.initial_height.prop_rebinarize    = 0.25  # keep vertices with propagated prob > this
# ─────────────────────────────────────────────────────────────────────────────

# Per-patch SI labelling
cfg.invariant.si_segment_method        = 'multiotsu'   # how to threshold SI within each patch
cfg.invariant.si_segment_otsu_n_levels = 2             # number of Otsu classes
cfg.invariant.n_diffusion_iters        = 5             # label-spreading iterations

# Adaptive saddle merge (on by default)
cfg.invariant.ws_saddle_merge          = True
cfg.invariant.ws_saddle_criterion      = 'adaptive'    # recommended: bleb vs. ridge-aware
cfg.invariant.ws_saddle_ar_threshold   = 0.5    # mean SI > this → compact/bleb; ≤ → elongated/ridge
cfg.invariant.ws_saddle_si_threshold   = 0.5    # compact pairs: merge if mean(SI at boundary) > this
cfg.invariant.ws_saddle_depth_threshold = 0.2   # elongated pairs: merge if valley depth < this

result = up3d.segment_protrusions_invariant(
    mesh_path="data/cell01.obj",
    save_dir="output/cell01/",
    cfg=cfg,
)

# Result fields
result.vertex_labels      # (N,) int  — per-vertex instance labels (0 = background)
result.vertex_labels_cc   # (N,) int  — initial CC labels before per-patch SI splitting
result.basal_binary       # (N,) bool — protrusion-permissive binary mask
result.height             # (N,) float — smoothed cMCF displacement height
result.shape_index        # (N,) float — Koenderink SI ∈ [−1, +1]
result.curvedness_norm    # (N,) float — sqrt((k1²+k2²)/2) · sqrt(A)
result.ridgeness_norm     # (N,) float — ridgeness · sqrt(A)
result.H_mean_norm        # (N,) float — H_mean · sqrt(A)  (signed)
result.K_norm             # (N,) float — k1·k2 · A          (signed)
result.curv_anisotropy    # (N,) float — (|k_max|−|k_min|)/(|k_max|+|k_min|) ∈ [0, 1]
result.principal_ratio    # (N,) float — |k_min|/|k_max| ∈ [0, 1]
result.total_surface_area # float — total mesh area in mesh-unit²
result.output_paths       # dict of Path objects for every saved file
```

### Output files

| File | Contents |
|---|---|
| `raw_surface_stats.mat` | Pre-smoothing curvatures, height field, and raw scale-invariant metrics |
| `smooth_surface_stats.mat` | Smoothed curvatures, height field, and smoothed scale-invariant metrics |
| `initial_patch_areas.svg` | Bar chart of initial CC areas with large-patch threshold line |
| `external_MCF_iteration_determination.svg` | cMCF Gaussian curvature trace with selected reference iteration marked |
| `instance_protrusion_segmentation_stats.mat` | Final instance labels, initial CC labels, height field, curvatures, basal binary |
| `inv_shape_index.obj`, `inv_curvedness_norm.obj`, … | Per-measure coloured mesh exports (coolwarm colormap) |
| `inv_height_binary.obj`, `inv_basal_binary.obj` | Binary mesh exports (red = foreground, gray = background) |
| `inv_final_labels.obj` | Final per-instance coloured mesh |

### Adaptive saddle merge — how it works

After per-patch SI labelling, adjacent label pairs within each patch are evaluated. Each label is first classified by its **mean Shape Index**:

- **Compact** (mean SI > `ws_saddle_ar_threshold`) — bleb-like dome.
- **Elongated** (mean SI ≤ threshold) — ridge/lamellipodia-like.

The merge criterion then depends on the pair's types:

| Pair type | Criterion | Merge if… |
|---|---|---|
| Both compact | SI boundary | mean(SI at shared boundary) > `ws_saddle_si_threshold` |
| Both elongated | Height depth | (h_lower − h_saddle) / h_lower < `ws_saddle_depth_threshold` |
| Mixed (bleb + ridge) | — | Never merged — genuine bleb–ridge junction |

This prevents merging blebs with filopodia (which would produce physically nonsensical labels) while correctly collapsing over-segmented dome fragments and shallow ridge splits.

### Chaining into volumize

```python
result = up3d.segment_protrusions_invariant(
    "data/cell01.obj", "output/cell01/", cfg=cfg
)

vol = up3d.volumize_protrusions(
    mesh_path="data/cell01.obj",
    protrusion_labels=result.vertex_labels,
    tif_path="data/cell01.tif",
    save_dir="output/cell01_vol/",
)
```

---

## Segment protrusions (curvature-based, classic)

`segment_protrusions` is the original pipeline. It classifies each candidate patch as bleb-like or ridge-like using a ratiometric curvature threshold and applies separate segmentation strategies for each type.

### Full example

```python
import u_protrude3d as up3d

cfg = up3d.SegmentConfig()

cfg.voxel_size   = 0.160   # physical voxel size of the microscope (µm)
cfg.cmcf.n_iters = 25      # more iterations → smoother basal reference

# ── Initial height binarization (critical — tune this first) ──────────────────
cfg.initial_height.use_mean          = True   # threshold at mean height (default, inclusive)
cfg.initial_height.prop_iters        = 1      # diffusion steps to grow binary outward
cfg.initial_height.prop_rebinarize   = 0.25   # keep vertices with propagated prob > this

# For a more conservative threshold (protrusion tips only), use 3-level Otsu + more diffusion:
# cfg.initial_height.use_mean        = False
# cfg.initial_height.use_otsu        = True
# cfg.initial_height.otsu_n_levels   = 3
# cfg.initial_height.otsu_level      = -1    # highest threshold class
# cfg.initial_height.prop_iters      = 5
# ─────────────────────────────────────────────────────────────────────────────

cfg.std_patch.curv_ridge_ratio_threshold = 0.35   # more aggressive filopodium detection

result = up3d.segment_protrusions(
    mesh_path="data/cell01.obj",
    save_dir="output/cell01/",
    cfg=cfg,
    tif_path="data/cell01.tif",       # optional: needed for SDF-based binary
    gt_label_path="gt/cell01.tif",    # optional: compute inline AP score
)

# Result fields
result.vertex_labels   # (N,) int — 0 = background, 1..K = protrusion instances
result.cMCF_steps      # (N, 3, T) float — mesh vertex positions at each cMCF step
result.basal_binary    # (N,) bool — vertices classified as basal (non-protrusion)
result.dists           # (N,) float — signed-distance height field
result.H               # (N,) float — mean curvature at each vertex
result.output_paths    # dict of Path objects for every saved file
result.ap              # AP scores (only if gt_label_path was provided)
```

### Chaining into volumize

```python
result = up3d.segment_protrusions("data/cell01.obj", "output/cell01/", cfg=cfg)

vol = up3d.volumize_protrusions(
    mesh_path="data/cell01.obj",
    protrusion_labels=result.vertex_labels,
    tif_path="data/cell01.tif",
    save_dir="output/cell01_vol/",
    cMCF_steps=result.cMCF_steps,
)
```

---

## Benchmark segmentation

### Full example

```python
import glob
import u_protrude3d as up3d

pred_dirs = sorted(glob.glob("output/cell*/"))
gt_dirs   = sorted(glob.glob("gt/cell*/"))

cfg = up3d.BenchmarkConfig()
cfg.figure_format = "png"   # change output format
cfg.figure_dpi    = 300

bench = up3d.benchmark_segmentation(
    pred_dirs=pred_dirs,
    gt_dirs=gt_dirs,
    save_dir="output/benchmark/",
    cfg=cfg,
)

# Result fields
bench.ap               # (n_cells, n_thresholds) average precision
bench.tp               # (n_cells, n_thresholds) true positives
bench.fp               # (n_cells, n_thresholds) false positives
bench.fn               # (n_cells, n_thresholds) false negatives
bench.iou_thresholds   # (n_thresholds,) the IoU cutoffs used
bench.per_cell_names   # list of folder names, one per cell
bench.figures          # dict of matplotlib Figure objects
bench.output_paths     # dict of saved file paths
```

The `.mat` files inside each `pred_dir` must contain the key `protrusion_labels` (per-vertex integer array). Ground-truth `.mat` files must contain the key `protrude_labels`.

**When pred and GT labels live on different meshes** (e.g. the prediction was computed on a remeshed surface), supply the mesh filenames so the GT labels can be transferred onto the prediction mesh before comparison:

```python
bench = up3d.benchmark_segmentation(
    pred_dirs=pred_dirs,
    gt_dirs=gt_dirs,
    pred_mesh_filename="mesh.obj",     # mesh inside each pred_dir
    gt_mesh_filename="gt_mesh.obj",    # mesh inside each gt_dir
    save_dir="output/benchmark/",
    cfg=cfg,
)
```

If `pred_mesh_filename` and `gt_mesh_filename` are the same, only one argument is needed. The transfer uses barycentric interpolation (`meshtools.transfer_mesh_measurements`) and runs automatically only when the vertex counts differ.

---

## Volumize protrusions

### Full example

```python
import numpy as np
import u_protrude3d as up3d

cfg = up3d.VolumeConfig()
cfg.voxel_size          = 0.160   # must match the acquisition voxel size (µm)
cfg.total_shrinkwrap_iters = 120  # more iterations → tighter basal fit
cfg.gvf_iters           = 20      # more GVF smoothing → cleaner force field

vol = up3d.volumize_protrusions(
    mesh_path="data/cell01.obj",
    protrusion_labels=np.load("labels.npy"),   # (N_vertices,) int
    tif_path="data/cell01.tif",
    save_dir="output/cell01_vol/",
    cfg=cfg,
)

# Result fields
vol.volume_labels   # (Z, Y, X) int16 — voxel-space protrusion labels
vol.cell_binary     # (Z, Y, X) bool  — voxel cell mask
vol.basal_binary    # (Z, Y, X) bool  — voxel basal region mask
vol.surface_labels  # (N,) int        — final per-vertex labels after refinement
vol.output_paths    # dict of saved file paths
```

---

## Interactive GUI

Open a point-and-click parameter editor that returns the updated config objects:

```python
import u_protrude3d as up3d

# Launch with defaults
seg_cfg, bench_cfg, vol_cfg = up3d.launch_config_gui()

# Or pre-populate from existing configs
seg_cfg, bench_cfg, vol_cfg = up3d.launch_config_gui(
    cfg_segment=seg_cfg,
    cfg_benchmark=bench_cfg,
    cfg_volume=vol_cfg,
)

# Use the edited configs immediately
result = up3d.segment_protrusions("data/cell01.obj", "output/", cfg=seg_cfg)
```

The GUI window has three tabs (Segment / Benchmark / Volume). Click **Apply** to validate and commit values, **Export JSON** to save a config file, and **Load JSON** to restore one.

---

## Parameter reference

### SegmentConfig — general pipeline settings

| Parameter | Default | Explanation |
|---|---|---|
| `voxel_size` | `0.160` | Physical size of one voxel in micrometers. Must match your microscope acquisition settings. Used when converting the mesh into a signed-distance height field. |
| `n_smooth_scalar_fn_iters` | `50` | How many Laplacian smoothing passes are applied to the height-field scalar before thresholding. More passes reduce noise but may blur sharp protrusion boundaries. |
| `offset_ref_ind` | `0` | Which cMCF iteration is used as the "reference" flat baseline for height calculation. Increase if the very first inflation step produces a noisy reference. |
| `min_size_comps_initial` | `20` | Minimum number of vertices a connected region must have to survive the initial foreground detection. Smaller values keep more detail; larger values discard more noise. |
| `min_size_comps_protrude_patch` | `5` | Same size filter applied to sub-patches inside each candidate protrusion region. |
| `sdf_binary_dilate_ksize` | `2` | Dilation radius (in voxels) applied to the binary cell mask before computing the height field. Increase if protrusion bases are getting clipped. |
| `sdf_binary_erode_ksize` | `1` | Erosion radius after dilation. Balances out the dilation to avoid inflating the mask. |
| `curvature_radius` | `5` | Neighbourhood radius (in mesh hops) used when computing principal curvatures. Larger values smooth the curvature estimate and are better for coarse meshes; smaller values preserve local detail. |
| `n_protrude_colors` | `24` | Size of the colour palette used when saving coloured `.obj` visualisation files. Increase if you have more than 24 protrusions per cell. |
| `random_seed` | `1232` | Seeds the random-colour palette so colours are reproducible across runs. |
| `debug_viz` | `False` | When `True`, saves extra intermediate visualisations. Useful for diagnosing segmentation failures but produces many files. |

---

### cMCFConfig — basal-surface extraction

The pipeline "inflates" the mesh inward using conformal Mean Curvature Flow (cMCF) to find the smooth, protrusion-free basal surface. The height of each vertex above this inflated reference is the main signal used for protrusion detection.

| Parameter | Default | Explanation |
|---|---|---|
| `n_iters` | `20` | Number of inflation steps. More iterations → a smoother, more convex basal reference. Increase for highly irregular or spiky cells; decrease if the reference over-smooths and loses anatomically relevant curvature. |
| `step_size` | `0.25` | How far the mesh moves per inflation step (as a fraction of the Laplacian update). Larger values converge faster but can cause mesh tangling. |
| `extra_smooth` | `False` | Apply a small amount of Laplacian mesh smoothing between each cMCF step. Helps stabilise convergence on meshes with very irregular triangles. |
| `deltaL_smooth` | `5e-5` | Strength of the inter-step Laplacian smoothing (only used when `extra_smooth=True`). Very small by default to avoid distorting the mesh. |
| `deltaL` | `5e-4` | Laplacian step size multiplier for the cMCF update itself. Rarely needs changing; reduce if you see mesh instability. |
| `mollify_factor` | `1e-5` | Regularisation constant for the robust Laplacian, which guards against numerical errors in near-degenerate triangles. Only needs increasing if you see linear-algebra warnings. |
| `solver` | `'pardiso'` | Sparse linear solver used at each cMCF step. `'pardiso'` (Intel MKL) is fastest. Use `'scipy'` if MKL is not available. |

---

### InitialHeightConfig — protrusion binary mask

> **This is one of the most critical settings in the pipeline.** The initial height binarization defines which surface regions are treated as protrusions for both the classical (`segment_protrusions`) and invariant (`segment_protrusions_invariant`) pipelines. An overly tight threshold will miss real protrusions; an overly loose one will bleed into the cell body. Getting this right — and pairing the threshold with an appropriate `prop_iters` — has a large effect on downstream segmentation quality.

After computing the height field, these settings control how it is binarised into "protrusion" vs. "background".

| Parameter | Default | Explanation |
|---|---|---|
| `use_auto` | `True` | Automatically select a threshold from the height-field distribution. Set to `False` to use `manual_threshold` instead. |
| `use_mean` | `True` | When `use_auto=True`, threshold at the mean height value. Simple and robust for most cells. |
| `use_otsu` | `False` | When `use_auto=True`, use multi-class Otsu's method instead of the mean. More adaptive but can be fooled by bimodal distributions. Only one of `use_mean` / `use_otsu` should be `True`. |
| `otsu_n_levels` | `3` | Number of classes for multi-class Otsu when `use_otsu=True`. `3` levels gives low / mid / high height classes; the selected class is controlled by `otsu_level`. |
| `otsu_level` | `-1` | Which Otsu class to use as the protrusion threshold. `-1` = the highest threshold (most conservative — only the tallest protrusions); `0` = the lowest threshold (most inclusive). Use `-1` with 3-level Otsu for conservative binarization, `0` for inclusive. |
| `manual_threshold` | `3.0` | Height value (in µm) used as the threshold when `use_auto=False`. Increase to be more conservative (fewer, larger protrusions detected). |
| `prop_iters` | `1` | How many label-diffusion steps are applied to the binary mask after thresholding. More iterations grow the binary region outward, filling in gaps and extending protrusion boundaries further down the flanks. **This should be tuned alongside the threshold method** — see guidance below. |
| `prop_rebinarize` | `0.25` | After diffusion, vertices whose propagated probability exceeds this value are kept as foreground. Lower = more inclusive boundary. |

#### Threshold method and `prop_iters` — recommended pairings

The threshold method and `prop_iters` are strongly coupled. A high threshold produces a tight binary that sits near protrusion tips only; diffusion is needed to grow it back down to the flanks. A low threshold already includes the flanks and needs little or no diffusion.

| Threshold setting | Typical behaviour | Recommended `prop_iters` |
|---|---|---|
| `use_mean=True` | Moderate threshold; includes most of each protrusion | `1` (default) |
| `use_otsu=True`, `otsu_n_levels=2`, `otsu_level=-1` | Similar to mean; two-class split | `1` |
| `use_otsu=True`, `otsu_n_levels=3`, `otsu_level=-1` | High threshold — only protrusion tips initially labelled | `5` — more diffusion needed to recover the full protrusion extent |
| `use_otsu=True`, `otsu_n_levels=3`, `otsu_level=0` | Low threshold — inclusive, similar to mean | `1` |
| `use_auto=False`, high `manual_threshold` | Very conservative | `3–5` depending on threshold |

In general: **the higher (more conservative) the threshold, the more `prop_iters` are needed** to grow the binary back out to a biologically meaningful extent. Too few iterations with a high threshold will under-label protrusions; too many with a low threshold will bleed the mask into the cell body.

---

### InvariantConfig — SI-based segmentation and saddle merge

These parameters control `segment_protrusions_invariant`. They live under `cfg.invariant`.

#### Per-patch Shape Index labelling

| Parameter | Default | Explanation |
|---|---|---|
| `si_segment_method` | `'multiotsu'` | How to binarise Shape Index within each patch to find dome-like (high-SI) seed regions. `'multiotsu'` uses Otsu's multi-class method; `'mean'` thresholds at the patch mean. |
| `si_segment_otsu_n_levels` | `2` | Number of Otsu classes when `si_segment_method='multiotsu'`. `2` = one threshold (foreground/background); `3` = two thresholds. |
| `si_segment_otsu_level` | `-1` | Which Otsu threshold to use, with Python negative indexing: `-1` = highest (most selective — fewer seeds). Raise to `-2` to be more inclusive. |
| `n_diffusion_iters` | `5` | How many geometric-affinity label-spreading steps propagate the seed labels to the rest of the patch. More iterations fill larger patches but can blur boundaries between adjacent instances. |

#### Watershed seeding (alternative to SI threshold)

These parameters are only relevant when `watershed_seeding` is set to `'height'` or `'shape_index'`. The default (`None`) uses the SI binarisation path above.

| Parameter | Default | Explanation |
|---|---|---|
| `watershed_seeding` | `None` | Seeding strategy. `None` = SI threshold + label diffusion (recommended). `'height'` = seed geodesic watershed from local height maxima. `'shape_index'` = seed from local SI maxima. |
| `ws_min_peak_dist` | `3` | Minimum graph-hop distance between kept peaks during non-maximum suppression. Prevents two seeds from being placed on the same dome summit. |
| `ws_smooth_iters` | `10` | Smoothing passes applied to the seed scalar field before peak finding. `0` = skip. |
| `ws_peak_eps` | `0.0` | Plateau tolerance for peak finding. `0` = strict local maximum; `>0` allows plateau vertices to qualify as peaks (useful for flat SI domes). |

#### Adaptive saddle merge

| Parameter | Default | Explanation |
|---|---|---|
| `ws_saddle_merge` | `True` | Enable the saddle merge step. Applies to all seeding paths. Set to `False` to keep the raw per-patch labels without merging. |
| `ws_saddle_criterion` | `'height'` | Which criterion governs merging. `'adaptive'` (recommended): classify each label as compact or elongated by its mean SI, then apply the appropriate criterion. `'height'`: use the valley-depth criterion for all pairs. `'shape_index'`: use the SI boundary criterion for all pairs. |
| `ws_saddle_ar_threshold` | `0.5` | **Adaptive criterion only.** Labels whose mean Shape Index exceeds this value are classified as compact (bleb-like, use the SI boundary criterion); labels at or below it are classified as elongated (ridge-like, use the height-depth criterion). Adjust if blebs and ridges in your data are not well separated at 0.5. |
| `ws_saddle_si_threshold` | `0.5` | **Compact–compact pairs.** Two compact labels are merged when the mean SI of their shared boundary vertices exceeds this value. A high-SI boundary means the contact region is itself dome-like — the two labels are the same protrusion. Lower to merge more aggressively; raise to be more conservative. |
| `ws_saddle_depth_threshold` | `0.2` | **Elongated–elongated pairs.** Two elongated labels are merged when `(h_lower − h_saddle) / h_lower < threshold`, where `h_saddle` is the mean height on the shared boundary and `h_lower` is the mean height of the shallower label. A small value means the boundary sits almost as high as the protrusion tip — a shallow ridge with no real valley between segments. Raise to merge more aggressively. |

---

### LargePatchConfig — oversized patch handling

Patches larger than `min_max_area` faces are treated differently because they often represent lamellipodia or other flat, broad structures rather than discrete protrusions.

| Parameter | Default | Explanation |
|---|---|---|
| `min_max_area` | `10000` | Face count above which a candidate patch is classified as "large". Increase if you want the algorithm to treat more patches as discrete protrusions rather than large flat structures. |
| `max_area_thresh_factor` | `0.0` | Adds `factor × median_patch_area` to `min_max_area` as an adaptive component. Useful when patch sizes vary widely across cells. |
| `curv_ridge_ratio_threshold` | `0.5` | Fraction `ridgeness / (ridgeness + |curvature|)` for the patch, in [0, 1]. Below this fraction the patch is classified as bleb-like (dome, segmented by curvature); above it, ridge-like (filopodium/lamellipodium edge, segmented by ridgeness). Because curvature and ridgeness share units, this ratio is dimensionless and doesn't need retuning across voxel sizes, unlike a raw ridgeness threshold. |
| `occ_threshold` | `0.4` | If the fraction of the patch that is "occupied" by the primary binary mask exceeds this value, a simpler single-step segmentation is used; otherwise a two-step approach is applied. |
| `H_segment_method` | `'mean'` | How to threshold mean curvature within a bleb-like large patch. `'mean'` = threshold at the mean value; `'multiotsu'` = use Otsu multi-class thresholding for a more data-driven cut. |
| `H_segment_otsu_n_levels` | `3` | Number of Otsu classes when `H_segment_method='multiotsu'`. More classes = finer curvature bins. |
| `H_segment_otsu_level` | `-1` | Which Otsu threshold to use, with Python negative indexing: `-1` = highest (most conservative), `-2` = second-highest (more inclusive). |
| `second_seg_H_method` | `'multiotsu'` | Method for the second-pass H segmentation (applied to complex patches that the first pass could not cleanly resolve). |
| `second_seg_H_otsu_n_levels` | `2` | Otsu levels for the second-pass segmentation. |
| `second_seg_H_otsu_level` | `-1` | Which Otsu threshold for the second pass. |
| `ridge_segment_method` | `'mean'` | How to threshold ridgeness within a ridge-like large patch. |
| `ridge_otsu_n_levels` | `3` | Otsu levels for ridge segmentation. |
| `ridge_otsu_level` | `-1` | Which Otsu threshold for ridge segmentation. |

---

### StdPatchConfig — standard patch classification

Standard-sized patches (below `LargePatchConfig.min_max_area`) go through a more detailed classification pipeline that separates blebs (dome-shaped), filopodia (thin ridges), and lamellipodia (flat sheets).

#### Protrusion-type thresholds

| Parameter | Default | Explanation |
|---|---|---|
| `curv_ridge_ratio_threshold` | `0.5` | Fraction `ridgeness / (ridgeness + |curvature|)` for the patch, in [0, 1]. Below this fraction the patch is classified as bleb-like (curvature-dominated, feeds the multi-bleb check); above it, ridge-like (ridgeness-dominated, segmented by ridgeness). Being a dimensionless ratio of two curvature quantities, it doesn't need retuning across voxel sizes. |

#### Mean-curvature (H) segmentation

These parameters control how the height within each patch is binarised using mean curvature.

| Parameter | Default | Explanation |
|---|---|---|
| `H_segment_method` | `'multiotsu'` | `'mean'`: threshold at the patch mean — fast but less adaptive. `'multiotsu'`: data-driven threshold using Otsu classes — better when curvature is bimodal. |
| `H_segment_otsu_n_levels` | `2` | Number of Otsu classes. `2` = one threshold (foreground/background). `3` = two thresholds (add an intermediate class). |
| `H_segment_otsu_level` | `-1` | Which threshold to use. `-1` = highest (most conservative, fewest foreground vertices). |
| `H_segment_erode_steps` | `2` | Number of morphological erosion passes applied to the H binary on the mesh. Erosion shrinks the foreground, removing thin connections and isolated specks. |
| `H_segment_use_local_adaptive` | `True` | Compute the H threshold locally (per-patch adaptive baseline) rather than globally. Recommended: handles illumination or curvature gradients across the cell surface. |
| `H_local_adaptive_smooth_iters` | `50` | Number of Laplacian smoothing steps used to estimate the local H baseline. More iterations → a smoother, more global baseline. |
| `apply_power_H_correct` | `True` | Apply a power-law correction (`H^power_H_correct`) before thresholding. This compresses the high end of the curvature range, which can make thresholding more robust when a few vertices have extreme values. |
| `power_H_correct` | `0.5` | Exponent for the power correction (default `0.5` = square-root). Values < 1 compress the high end; values > 1 amplify it. |

#### Ridgeness segmentation

The same structure as H segmentation but applied to the ridgeness scalar field, which is high along the crests of narrow protrusions.

| Parameter | Default | Explanation |
|---|---|---|
| `ridge_segment_method` | `'multiotsu'` | Threshold method for ridgeness. Same options as `H_segment_method`. |
| `ridge_otsu_n_levels` | `3` | Otsu classes for ridgeness. |
| `ridge_otsu_level` | `-1` | Which Otsu threshold to use. |
| `ridge_segment_erode_steps` | `1` | Erosion passes on the ridge binary. |
| `ridge_use_local_adaptive` | `True` | Use a per-patch adaptive ridgeness baseline. |
| `ridge_local_adaptive_smooth_iters` | `50` | Smoothing iterations for the local ridge baseline. |
| `apply_power_ridge_correct` | `False` | Apply power correction to ridgeness before thresholding. Disabled by default because ridgeness is already well-scaled. |
| `power_ridge_correct` | `0.5` | Exponent if power correction is enabled. |

#### Planarity test (filopodium detection)

| Parameter | Default | Explanation |
|---|---|---|
| `planarity_check_frac` | `1.0` | Maximum fraction of interior vertices allowed to lie *outside* the projected boundary hull for the patch to be considered planar (filopodium-like). `1.0` = any planarity passes; lower values enforce stricter planarity. |
| `planarity_check_dilate_binary` | `2` | Dilation radius (pixels) used when rasterising the boundary for the planarity test. Increase for coarser meshes where boundaries look jagged in projection. |

#### Multi-bleb splitting

If a single large foreground region contains multiple dome-shaped sub-structures, these parameters control whether it is split into separate bleb labels.

| Parameter | Default | Explanation |
|---|---|---|
| `multibleb_min_recovered_frac` | `0.4` | Watershed must recover at least this fraction of the region area for splitting to proceed. Prevents over-splitting of noisy, heterogeneous patches. |
| `multibleb_min_occ_area_fraction` | `0.1` | Each candidate sub-bleb must occupy at least this fraction of the total patch area. Eliminates very small fragments. |
| `multibleb_max_mean_aspect_ratio` | `2.0` | Sub-blebs whose average aspect ratio exceeds this value are rejected (too elongated to be a bleb — likely a filopodium). |
| `multibleb_check_neck_neg_curvature` | `False` | Additionally require negative curvature at the boundary between sub-blebs (a "neck"). Stricter splitting criterion; rarely needed. |
| `multibleb_neck_neg_curvature_thresh` | `-0.05` | Curvature value that counts as a neck when `multibleb_check_neck_neg_curvature=True`. More negative = stricter. |

---

### BenchmarkConfig

| Parameter | Default | Explanation |
|---|---|---|
| `iou_thresholds` | `linspace(0, 1, 21)` | List of IoU cutoffs at which AP/TP/FP/FN are evaluated. The default gives a sweep from 0 to 1 in steps of 0.05. Narrow to `[0.5, 0.75]` for a COCO-style summary. |
| `save_figures` | `True` | Save mean-AP and median-AP curve figures alongside the summary `.mat` file. |
| `figure_dpi` | `600` | Resolution of saved figures in dots-per-inch. Use `300` for drafts, `600` for publication. |
| `figure_format` | `'svg'` | Output format: `'svg'` (lossless, scalable), `'pdf'`, or `'png'`. |

---

### VolumeConfig — volumization

| Parameter | Default | Explanation |
|---|---|---|
| `voxel_size` | `0.160` | Physical voxel size (µm). Must match `SegmentConfig.voxel_size` and your acquisition settings. |
| `gvf_mu` | `0.01` | Diffusion coefficient for the Gradient Vector Field (GVF). GVF is a smoothed version of the signed-distance gradient used to guide the inward mesh advection. Larger `mu` → more diffusion, which helps the force field reach into deep concavities but blurs boundaries. |
| `gvf_iters` | `15` | Number of GVF diffusion iterations. More iterations → a smoother force field that extends further from the original gradient. Only active when `use_mesh_based_shrinkwrap=False` (non-default). |
| `total_shrinkwrap_iters` | `100` | Total number of steps the basal surface mesh takes as it shrinks inward to fit the cell body. More iterations → tighter basal fit, but also more computation time. |
| `use_mesh_based_shrinkwrap` | `False` | **Work in progress — keep at `False`.** Use mesh-based shrinkwrap instead of GVF. Uses direct BVH closest-point queries at every step and constrained Laplacian force diffusion — no voxelization required. Although faster for large meshes, the mesh-based path does not yet reliably form a closed meniscus over protrusion openings and may produce incorrect basal volumes. The GVF voxelization path (`False`) is slower but robust and should always be used in practice. |
| `mesh_sw_anchor_factor` | `3.0` | Anchor radius for mesh-based force diffusion, expressed as a multiple of the average edge length. Vertices closer than this become Dirichlet anchors that pull far vertices into concavities. |
| `mesh_sw_concavity_boost` | `1.0` | Extra force multiplier at vertices approaching the target from the concave side. Set to `0` to disable. Higher values help the wrap mesh enter deep pockets. |
| `mesh_sw_force_sigma` | `5.0` | Distance scale for tanh force attenuation (mesh units). Forces taper to zero as the wrap mesh approaches the target surface, preventing overshoot. |
| `mesh_sw_convergence_sq_dist` | `0.5` | Early-stop threshold: iterations halt when the 90th-percentile squared closest-point distance drops below this value. Lower → tighter convergence but more iterations. |
| `mesh_sw_topology_repair_alpha_frac` | `0.05` | Alpha fraction of mean mesh extent used to repair the genus-0 topology (via alpha-wrap) whenever it is lost during mesh-based iteration. |
| `mesh_sw_genus0_alpha_auto` | `False` | When `True`, the alpha value for genus-0 repair is chosen automatically to be the smallest value that fits the mesh without degenerating into a shell. Keep `False` when the target mesh has large flat regions where auto-alpha tends to produce thin shells. |
| `mesh_sw_min_size` | `10000` | Target vertex count after internal remeshing inside each shrinkwrap step. Larger values preserve more surface detail but increase computation time. |
| `mesh_sw_vfc_sigma` | `0.0` | Gaussian sigma for the VFC (Vector Field Convolution) field. `0` disables VFC (default). Set to e.g. `1.0` to enable: VFC precomputes a volumetric inward-normal field convolved with a Gaussian, which helps pull the wrap mesh into deep concavities that direct closest-point forces miss. |
| `mesh_sw_vfc_blend` | `0.5` | Blend weight between direct closest-point forces and VFC forces. `0` = pure VFC, `1` = pure direct force. Only active when `mesh_sw_vfc_sigma > 0`. |
| `mesh_sw_smooth_iters` | `0` | Post-force Laplacian smoothing passes per shrinkwrap step. `0` = disabled. Small values (2–5) can stabilise convergence on noisy meshes. |
| `mesh_sw_balloon_factor` | `0.0` | Outward balloon force added at each step. `0` = disabled. A small positive value (e.g. `0.05`) prevents premature collapse of the wrap mesh in very concave regions. |
| `shrinkwrap_iter_select` | `'last'` | Which iteration to use as the final basal mesh. `'last'` uses the final iteration (most tightly fitted; default). `'min_loss'` picks the iteration minimising a 0.5 × chamfer + 0.5 × |Gaussian curvature| combined loss (both normalised to [0, 1]) — more conservative, avoids over-tightening on concave cells. |
| `n_punchout_refinements` | `2` | Number of topology-repair passes after shrinkwrapping. Each pass removes mesh self-intersections ("punch-outs"). Rarely needs changing. |
| `decay_rate` | `0.75` | Rate at which the shrinkwrap step size decays each iteration. Values closer to 1 maintain a larger step size for longer (faster but less stable); values closer to 0 slow down more aggressively. |
| `min_lr` | `0.24` | Minimum step size floor for shrinkwrapping. Prevents the step size from decaying to near zero before convergence. |
| `voxelize_dilate_ksize` | `2` | Morphological dilation kernel size applied to the voxelised cell binary. Closes small holes in the voxel mask. |
| `voxelize_erode_ksize` | `2` | Erosion after dilation, restoring the boundary while keeping the interior filled. |
| `voxelize_padsize` | `50` | Zero-padding (in voxels) added around the cell binary before volumizing. Ensures the mesh does not intersect the array boundary. |
| `extra_pad` | `25` | Additional padding for numerical stability in the GVF computation. |
| `label_erosion_rings` | `1` | Number of erosion rings applied to the basal label before inpainting. Prevents basal labels from bleeding into protrusion bases. |
| `min_size_comps` | `20` | Minimum voxel count for a connected component in the volume labels. Removes isolated specks. |
| `n_smooth_iters` | `50` | Laplacian smoothing passes on the volumized label surfaces. Produces cleaner isosurfaces for visualisation. |
| `random_seed` | `1232` | Reproducibility seed for random operations inside the volumization. |
| `n_protrude_colors` | `24` | Colour palette size for volumized `.obj` visualisation files. |

#### Spherical mapping (advanced)

These parameters control the internal quasi-conformal parameterization used to build the GVF reference sphere. They rarely need adjustment.

| Parameter | Default | Explanation |
|---|---|---|
| `spherical_map_delta` | `5e-3` | Step size for the iterative spherical map solver. Reduce if the solver diverges. |
| `spherical_map_min_iter` | `10` | Minimum solver iterations even if convergence is reached earlier. |
| `spherical_map_max_iter` | `25` | Maximum solver iterations. Increase for very complex mesh topologies. |
| `spherical_map_mollify_factor` | `1e-5` | Robust Laplacian regularisation for the spherical solver. Matches `cMCFConfig.mollify_factor`. |

---

## Tips and common adjustments

### Scale-invariant pipeline (`segment_protrusions_invariant`)

**Too many fragments — blebs are being over-split.** The adaptive merge is not firing. Check that `ws_saddle_criterion='adaptive'` and `ws_saddle_merge=True`. If bleb labels have mean SI < `ws_saddle_ar_threshold` (which can happen when a fragment is a thin rim rather than a dome), try lowering `ws_saddle_ar_threshold` from `0.5` to `0.3` so more labels are classified as compact and use the SI boundary criterion.

**Distinct blebs are being merged together.** Raise `ws_saddle_si_threshold` (e.g. to `0.7`) so the shared boundary must have a higher, more spherical SI to trigger a merge. Alternatively raise `ws_saddle_ar_threshold` to make the compact classification stricter.

**Ridges are over-split along their length.** Lower `ws_saddle_depth_threshold` (e.g. to `0.1`) to merge even shallower valleys between adjacent elongated-label pairs.

**Nothing is being segmented / all patches return a single label.** The Otsu threshold on SI may be finding no high-SI faces within each patch. Inspect `smooth_surface_stats.mat` — if `smooth_shape_index` values are all below 0.5 across the cell, the surface may be too smooth or the cell type has low SI contrast. Try lowering `si_segment_otsu_level` to `-2` for a more inclusive seed region, or switch `si_segment_method='mean'`.

**Inspect the scale-invariant measures before committing.** The exported `inv_*.obj` files (coolwarm colourmap) and the `.mat` files let you visualise each descriptor in a mesh viewer. Check `inv_shape_index.obj` first: dome-like protrusions should be red (SI ≈ +1) and flat or concave regions should be blue (SI ≈ −1 to 0).

### Classic pipeline (`segment_protrusions`)

**Fewer false-positive protrusions.** Raise `std_patch.curv_ridge_ratio_threshold` (e.g. to `0.65`) so fewer patches are treated as ridge-like, and raise `min_size_comps_initial` to filter more small patches.

**Blebs are being split into multiple fragments.** Reduce `cmcf.n_iters` to keep the basal reference closer to the original shape, or lower `std_patch.H_segment_erode_steps` to prevent over-erosion.

**Filopodia are not being detected.** Lower `std_patch.curv_ridge_ratio_threshold` (e.g. to `0.35`) so more patches are treated as ridge-like. If they are thin, also check that `std_patch.planarity_check_frac` is set to `1.0` (permissive).

### General

**Pardiso not available.** Set `cfg.cmcf.solver = 'scipy'`. Expect a 3–5× slowdown per cell.

**Consistent colours across cells.** Keep `random_seed` the same value in both `SegmentConfig` and `VolumeConfig`, and do not change `n_protrude_colors` mid-dataset.

**Batch processing a folder of cells.**
```python
import glob
from pathlib import Path
import u_protrude3d as up3d

cfg = up3d.SegmentConfig()
cfg.voxel_size = 0.160

for mesh_path in sorted(glob.glob("data/*.obj")):
    name = Path(mesh_path).stem
    result = up3d.segment_protrusions_invariant(
        mesh_path=mesh_path,
        save_dir=f"output/{name}/",
        cfg=cfg,
    )
    print(f"{name}: {result.vertex_labels.max()} protrusions found")
```
