complex_steerable_decompose — MOTIONMAG `decompose` op

• Data kinds: image2d → table

• Call: import motionmag; motionmag.complex_steerable_decompose(image, scales: 'int' = 4, orientations: 'int' = 4) -> 'dict' (or opsmotionmag.get("complex_steerable_decompose"))

Usage

Complex oriented sub-band decomposition of one frame -> `dict`.

Splits the image into `scales * orientations` analytic sub-bands plus

three residuals (low-pass, high-pass and a small symmetric completion band).

Each sub-band is a full-resolution `(H, W)` complex array whose modulus is

the local contrast of that scale/orientation and whose argument is the local

phase — the quantity a translation shifts linearly, which is what the

rest of this module is built on. There is no spatial decimation: keeping

every band at full resolution costs memory but makes the frame exactly

invertible, and exactness is the point.

Returns ``{"bands": [complex (H, W), ...], "kinds": [...],

"centre_cycles_per_px": [...], "orientation_rad": [...], "shape": (H, W),

"scales": s, "orientations": k}`. kinds[j] is "band"` for an oriented

sub-band and `"lowpass" / "highpass" / "residual"` otherwise;

`centre_cycles_per_px and orientation_rad are None` for residuals,

which have no orientation and no single centre frequency.

Feed the whole dict back to :func:complex_steerable_reconstruct. Round trip

error, measured on a 64x64 random frame with the defaults, is

`max|out - in| = 6.66e-16`; on a 31x37 (odd, non-square) frame 7.22e-16;

and the worst over every `scales` in 1..8 crossed with every

`orientations` in 1..16 on 32x32 is 7.77e-16 — the tight-frame construction

is exact, not approximate (see the notes on the self-conjugate grid points

in :func:_filter_bank).

References: Freeman & Adelson, IEEE PAMI 1991; Simoncelli & Freeman,

ICIP 1995; Portilla & Simoncelli, IJCV 2000.

Detailed usage guide

• motion_magnification 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)

• motion_magnification — py -3.11 examples/motion_magnification.py

Ops the type connects to (they accept `table` as input)

complex_steerable_reconstruct

Same category (`decompose`)

complex_steerable_reconstruct

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

complex_steerable_decompose — MOTIONMAG decompose op