Hierarchical Image Segmentation—Part I: Detection of Regular Curves in a Vector Graph

The problem of edge detection is viewed as a hierarchy of detection problems where the geometric objects to be detected (e.g., edge points, curves, regions) have increasing complexity and spatial extent. An early stage of the proposed hierarchy consists in detecting the regular portions of the visible edges. The input to this stage is given by a graph whose vertices are tangent vectors representing local and uncertain information about the edges. A model relating the input vector graph to the curves to be detected is proposed. An algorithm with linear time complexity is described which solves the corresponding detection problem in a worst-case scenario. The stability of curve reconstruction in the presence of uncertain information and multiple responses to the same edge is analyzed and addressed explicitly by the proposed algorithm.

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