deformation op• Data kinds: image → image
• Call: fullseye.apply(img, "deform_ffd", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])
Cubic B-spline free-form deformation (Rueckert et al., IEEE TMI 1999).
A coarse control lattice of `n x n spans (n = 2 + int(6b)`, one padding
ring on each side) carries a deterministic smooth displacement pattern
`phi[i,j] = amp * [sin(2 pi j/n), cos(2 pi i/n)]`; the dense displacement
at a pixel is the tensor product of the four uniform cubic B-spline basis
functions of its span coordinate with the surrounding 4x4 control
displacements, so a control point only ever moves the 4 spans it supports.
That field is used as the backward map and the image is bilinearly resampled.
`a sets the amplitude amp = 0.45*a*min(sy,sx)` -- kept under the
`0.48*spacing` injectivity bound of Choi & Lee (2000), so the deformation
stays a fold-free bijection -- and `b the lattice resolution. a = 0`
gives a zero lattice, hence the identity (up to sub-pixel resampling error).
• gallery2d_geometry family guide
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• gallery2d_geometry — py -3.11 examples/gallery2d_geometry.py
image as input)identity · gaussian · mean_box · bilateral · unsharp · median · min_filter · max_filter
deformation)*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.