xg_eccentricity — 2D `xldgeom` op

• Data kinds: contour → feature

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

• HALCON equivalent: eccentricity_points_xld (the HALCON reference is a useful guide to its meaning and parameters)

xg_eccentricity: input → output

*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*

*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*

*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*

Stages (the ops that come before → this op, left to right):

▸ xg_eccentricity: stages (docs site)

Usage

Eccentricity sqrt(1 - lambda_min/lambda_max) from the point covariance.

> The detailed description below is the original text — the summary and the headings are translated.

輪郭辞書 `{"shape", "cs"}` の全輪郭の点を 1 つの点集合にまとめ、その

(row, col) 座標の母共分散行列の固有値 `λ_min <= λ_max` から離心率

`e = sqrt(1 - λ_min/λ_max)` を返す。閉輪郭の重複した終点(先頭と同じ点)は

数えない。`a, b` は未使用。

返り値は `numpy.float64` で [0, 1]。真円・正方形など等方な点配置で 0、

一直線上の点(`λ_min = 0)で 1。点が 2 個未満、または λ_max <= 1e-12`

(全点同一)なら 0.0。輪郭が複数あればそれらをまとめた分布の離心率になり、

個々の輪郭の形ではなく配置の広がりも混ざる(輪郭ごとに評価したいなら先に

`select_contours_xld` などで 1 本に絞る)。輪郭点の密度に依存する(点が

密な部分が重く効く)点は面積ベースの指標と異なる。軸比そのものは

`xg_elliptic_axis、主軸の向きは xg_orientation`。

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.

threshold 0.50 0.50
sk_find_contours 0.50 0.50
xg_eccentricity 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 `feature` as input)

identity · feature_to_img

Same category (`xldgeom`)

xg_moments · xg_area_center · xg_orientation · xg_elliptic_axis · xg_height_width_ratio · xg_regress_contours · xg_clip_contours · xg_gen_polygons

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

xg_eccentricity — 2D xldgeom op