Incremental bit-quads count in component trees: Theory, algorithms, and optimization

Abstract Component tree is a full image representation which encodes all connected components from upper (resp. lower) level sets of a given image through the inclusion relation. Information from this representation can be used in many image processing and computational vision applications, e.g. connected filtering, image segmentation, feature extraction, among others. In general, each node of a component tree represents a connected component of a level set and stores attributes which describes features of this connected component. This paper presents a review of a previously published method to compute attributes such as area, perimeter, and number of Euler by incrementally counting patterns while traversing nodes of a component tree. This method foundation is further detailed in this paper by presenting a novel theoretical background and algorithm correctness intuition. We also present a novel approach for this algorithm showing improvements for run-time execution and precision analysis.