deform_tps — 2D `deformation` op

• Data kinds: image → image

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

deform_tps: 入力 → 出力

*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).*

Usage

Thin-plate-spline warp over a 5x5 control grid (Bookstein, TPAMI 1989).

The 3x3 interior control points are displaced by the deterministic smooth

field `d = amp * [sin(2 pi f gx), cos(2 pi f gy)]` (gy, gx = the control

point's normalised coordinates), the 16 border control points are pinned so

the frame stays anchored. The backward map is the TPS interpolant fitted

from the *displaced* control points back to the original ones -- the unique

minimum-bending-energy interpolant, i.e. the surface a thin metal plate

would take -- and it is evaluated at every destination pixel before bilinear

resampling. `a sets the amplitude amp = 0.15*a*min(H,W), b` the

spatial frequency `f = 0.5 + 1.5b. a = 0` leaves the control points

where they are, so the solved map is 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.

Try it in Studio

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_tps 0.50 0.50

▸ Load this pipeline · Load & run

Runnable examples (verified samples that actually call this op)

• gallery2d_geometry — py -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_ffd · deform_mls

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

deform_tps — 2D deformation op