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])
*The figure is the real output on a synthetic 128×128 input. Left: input, right: output (a non-image return value is shown as the value itself).*
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.
The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.
deform_ffd 0.50 0.50
▸ Load this pipeline · Load & run
• 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.