Curve skeletonization using minimum-cost path

Abstract Skeletonization produces a compact representation of an object that reduces its dimensionality by one. In three dimensions, skeletons include both surface and curve structures. However, depending upon the primary aim of an application, especially those involving elongated objects, often, mere curve structures are sufficient to represent essential geometric and topologic features in an object. A skeleton that includes only curve structures is referred to as a curve skeletonization. This chapter reviews various definitions of a curve skeleton and different computational approaches. Conventional curve skeletonization algorithms using the principle of Blum's grassfire transform, often, produce unwanted spurious branches caused by boundary irregularities, digital effects, and other artifacts. Besides reviewing definitions and algorithms of curve skeletonization, a comprehensive solution using a minimum-cost path approach is described, and various important and related issues, e.g., centeredness of minimum-cost paths, collision impact, skeletal branch significance, etc. are discussed. A practical and efficient algorithm for the minimum-cost path based curve skeletonization is presented, and several applications are discussed.

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