A topology-based approach to computing neighborhood-of-interest points using the Morse complex

• The work proposes a novel topological operator, called the Local Morse Context.
• It explores structural information in images through neighborhoods of interest points.
• The strategy avoids incorrect correspondences in high similarity images.
• The approach is designed and tested for the correspondence of stereo image pairs.
• Data sets with synthetic and real images are used in the evaluation of the method.

A central problem in image processing and computer vision is the computation of corresponding interest points in a given set of images. Usually, interest points are considered as independent elements described by some local information. Due to the limitations of such an approach, many incorrect correspondences can be obtained. A specific contribution of this paper is the proposition of a topological operator, called Local Morse Context (LMC), computed over Morse complexes, introduced as a way of efficiently computing neighborhoods of interest points to explore the structural information in images. The LMC is used in the development of a matching algorithm, that helps reducing the number of incorrect matches, and obtaining a confidence measure of whether a correspondence is correct or incorrect. The approach is designed and tested for the correspondence of narrow-baseline synthetic and specially challenging underwater stereo pairs of images, for which traditional methods present difficulties for finding correct correspondences.