deform_mls — 2D deformation op

Data kinds: imageimage

Call: fullseye.apply(img, "deform_mls", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

Usage

Moving-least-squares image deformation, affine variant (Schaefer 2006).

A 5x5 grid of control points `p_i` is displaced to

`q_i = p_i + amp*[sin(2 pi gx), cos(2 pi gy)]` (gy, gx = normalised

control coordinates). For every destination pixel the weighted

least-squares affine map is re-solved with the weights

`w_i = 1/|p_i - v|^(2 alpha)`, so the warp is a *different* affine at every

pixel -- smooth, interpolating at the control points, and exact on affine

data. The backward map is obtained by solving the same MLS problem with the

roles of `p and q` swapped (the resampling formulation of the paper's

section 4), which is the exact inverse whenever the control data is affine

and a smooth approximation of it otherwise. `a` sets the amplitude

`amp = 0.12*a*min(H,W), b the falloff alpha = 0.5 + 1.5b` (large

alpha = tightly local deformation). `a = 0 gives q = p`, 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_ffd


*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.