deform_ffd — 2D deformation op

Data kinds: imageimage

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])

Usage

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).

Detailed usage guide

gallery2d_geometry family guide

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

gallery2d_geometrypy -3.11 examples/gallery2d_geometry.py

Ops the type connects to (they accept image as input)

identity · gaussian · mean_box · bilateral · unsharp · median · min_filter · max_filter

Same category (deformation)

deform_tps · deform_mls


*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.