On the Graph Laplacian for Spectral Image Segmentation and Energy Minimization on Graphs

Abstract

Image segmentation is an indispensable tool to enhance the ability of computer systems to perform elementary cognitive tasks such as recognition and tracking. In particular, graph-based algorithms have gained a lot of attention lately, specially due to their good performance in clustering complex images and easy usability. However, most traditional approaches rely on sophisticated mathematical tools whose effectiveness strongly depends on how good the boundaries reflect the partitions of the image. In fact, sharp adherence to the contours of image segments, uniqueness of solution, high computational burden, and extensive user intervention are some of the weaknesses of most representative techniques. In this work we proposed two novel graph-based image segmentation techniques that sort out the issues discussed above. The proposed methods rely on Laplace operators, spectral graph theory, and optimization approaches towards enabling highly accurate segmentation tools which demand a small amount of user involvement while still being mathematically easy-to-handle and computationally efficient. The effectiveness of our segmentation algorithms is attested by a comprehensive set of comparisons against state-of-the-art methods. As additional contribution, we have also proposed two new techniques for image inpainting and photo colorization, both of which rely on the accuracy of our segmentation apparatus.