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| """Polygon-based morphometric traits for a single segmented tuber. | |
| The width and height used by downstream stages are the extents of the | |
| polygon bounding box. The aspect_ratio field is bbox max/min and is not | |
| used as the published axis-ratio; a PCA-based ratio is derived from | |
| eccentricity in the modeling stage. | |
| """ | |
| from __future__ import annotations | |
| import numpy as np | |
| def close_polygon(x: np.ndarray, y: np.ndarray) -> tuple[np.ndarray, np.ndarray]: | |
| if x.size == 0 or y.size == 0: | |
| return x, y | |
| if x[0] != x[-1] or y[0] != y[-1]: | |
| x = np.concatenate([x, x[:1]]) | |
| y = np.concatenate([y, y[:1]]) | |
| return x, y | |
| def polygon_area_px(x: np.ndarray, y: np.ndarray) -> float: | |
| """Shoelace formula. Eq. (2) in the paper.""" | |
| x, y = close_polygon(x, y) | |
| if x.size < 3: | |
| return float("nan") | |
| area = 0.0 | |
| for i in range(len(x) - 1): | |
| area += x[i] * y[i + 1] - x[i + 1] * y[i] | |
| return abs(area) / 2.0 | |
| def polygon_perimeter_px(x: np.ndarray, y: np.ndarray) -> float: | |
| """Sum of Euclidean distances between consecutive vertices. Eq. (1) in the paper.""" | |
| x, y = close_polygon(x, y) | |
| if x.size < 2: | |
| return float("nan") | |
| dx = np.diff(x) | |
| dy = np.diff(y) | |
| return float(np.sqrt(dx**2 + dy**2).sum()) | |
| def polygon_circularity(x: np.ndarray, y: np.ndarray) -> float: | |
| """4路蟺路A / P虏.""" | |
| A = polygon_area_px(x, y) | |
| P = polygon_perimeter_px(x, y) | |
| if not np.isfinite(A) or not np.isfinite(P) or P <= 0: | |
| return float("nan") | |
| return float(4.0 * np.pi * A / (P**2)) | |
| def polygon_eccentricity(x: np.ndarray, y: np.ndarray) -> float: | |
| """sqrt(1 - 位_min / 位_max) of the polygon-vertex covariance matrix.""" | |
| if len(x) < 3: | |
| return float("nan") | |
| coords = np.column_stack([x, y]) | |
| coords_centered = coords - coords.mean(axis=0, keepdims=True) | |
| cov_mat = np.cov(coords_centered, rowvar=False) | |
| eigvals = np.linalg.eigvalsh(cov_mat) | |
| eigvals = np.sort(eigvals)[::-1] | |
| if eigvals.size < 2 or eigvals[0] <= 0: | |
| return float("nan") | |
| return float(np.sqrt(1.0 - eigvals[1] / eigvals[0])) | |
| def aspect_ratio_bbox(width: float, height: float) -> float: | |
| if width <= 0 or height <= 0: | |
| return float("nan") | |
| return float(max(width, height) / min(width, height)) | |
| def roundness_bbox(width: float, height: float) -> float: | |
| if width <= 0 or height <= 0: | |
| return float("nan") | |
| area_bbox = width * height | |
| max_dim = max(width, height) | |
| return float(4.0 * area_bbox / (np.pi * max_dim**2)) | |
| def polygon_shape_metrics(x: np.ndarray, y: np.ndarray) -> dict[str, float]: | |
| """All per-tuber pixel-space metrics in a single call. | |
| Returns: area_poly_px, perimeter_px, circularity, eccentricity, | |
| width_px, height_px, aspect_ratio, roundness_bbox. | |
| """ | |
| area_px = polygon_area_px(x, y) | |
| perim_px = polygon_perimeter_px(x, y) | |
| circ = polygon_circularity(x, y) | |
| ecc = polygon_eccentricity(x, y) | |
| width_px = float(x.max() - x.min()) if x.size > 0 else float("nan") | |
| height_px = float(y.max() - y.min()) if y.size > 0 else float("nan") | |
| ar = aspect_ratio_bbox(width_px, height_px) | |
| rb = roundness_bbox(width_px, height_px) | |
| return { | |
| "area_poly_px": area_px, | |
| "perimeter_px": perim_px, | |
| "circularity": circ, | |
| "eccentricity": ecc, | |
| "width_px": width_px, | |
| "height_px": height_px, | |
| "aspect_ratio": ar, | |
| "roundness_bbox": rb, | |
| } | |