Graph-based image segmentation with shape priors and Local Band constraints - Braz, Caio de Moraes (2023)
The goal of this work is to describe an efficient algorithm for finding a binary segmentation of an image such that: the indicated object satisfies a novel high-level prior, called Local Band, LB, constraint; the returned segmentation is optimal, with respect to an appropriate graph cut measure, among all segmentations satisfying the given LB constraint. The new algorithm has two stages: expanding the number of arcs of a standard edge-weighted graph of an image; applying to this new weighted graph an algorithm known as an Oriented Image Foresting Transform, OIFT. In our theoretical investigations, we discuss the theoretical relationships of LB with other shape constraints and prove that OIFT algorithm belongs to a class of General Fuzzy Connectedness algorithms and so, has several good theoretical properties, like robustness for seed placement. The extension of the graph constructed in the first stage ensures, as we prove, that the resulted object indeed satisfies the given LB constraint. For purposes of computational efficiency, we consider the least number of arcs needed to guarantee the constraint. This graph construction is flexible enough to allow combining it with other high-level constraints. For the particular case of LB with infinite radius, this case called Band constraint, we also present an efficient algorithm, with proof of correctness, which can be applied directly to the original image graph. Finally, we experimentally demonstrate that the LB constraint gives competitive results as compared to Geodesic Star Convexity, Boundary Band, and Hedgehog Shape Prior, all implemented within OIFT framework and applied to various scenarios involving natural and medical images.