Some Mathematical Models for Computer Vision Problems

Abstract:  In this talk, I will show how different mathematical models can be used to solve typical problems in computer vision. Three very different problems in this domain, namely:

i) scalable video summarization [1], ii) non-rigid registration of Zebra Fish larval images [2] and iii) pulmonary nodule segmentation [3] will be addressed. The problem of scalable video summarization will be modelled as a problem of scalable graph clustering. I will demonstrate how a combination of Minimum Spanning Tree and Random Walks can yield a computationally efficient yet accurate clustering solution for this problem. Non-rigid registration of Zebra Fish larval images will be presented as the next problem.

I will discuss how a coarse-to-fine strategy involving L-BFGS algorithm, diffeomorphic demons and bipartite graph matching can generate superior results than the existing ViBE-Z software. The third and final problem will be on the segmentation of lung nodules in CT images. A synergistic combination of deep learning and shape driven level sets will be shown to outperform several state-of-the-art solutions.