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A computational approach to edge detection
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Image segmentation using topological persistence
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Edge detection produces a set of points that are likely to lie on discontinuities between objects within an image. We consider faces of the Gabriel graph of these points, a sub-graph of the Delaunay triangulation. Features are extracted by merging these faces using size, shape and color cues. We measure regional properties of faces using a novel shapeadaptive sampling method that overcomes undesirable sampling bias of the Delaunay triangles. Instead, sampling is biased so as to smooth regional statistics within the detected object boundaries, and this smoothing adapts to local geometric features of the shape such as curvature, thickness and straightness. We further identify within the Gabriel graph regions having uniform thickness and orientation which are grouped into directional features for subsequent hierarchical region merging.