# Image Matching Using Convex Optimization

Arvind Bhusnurmath and I have been working on approaches to recasting many classic image matching problems including, stereopsis, motion estimation, image registration and 3D volumetric matching as convex optimization problems that can be solved effectively using the Interior Point method. More specifically we proceed by constructing piecewise linear convex approximations of the original image matching functions and then reformulate the matching problems as linear programs. Importantly, in each case we are able to exploit the structure of the resulting linear program to develop efficient algorithms which allow us to solve optimization problems involving hundreds of thousands of variables more efficiently than standard codes like TOMLAB and MOSEK.

# Related Publications

• Solving Image Registration Problems Using Interior Point Methods

European Conference on Computer Vision, October 2008
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• Graph Cuts via $\ell_1$ Norm Minimization

IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol: 30, No: 10, Pgs: 1866-1871, October 2008
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• Solving Stereo Matching Problems Using Interior Point Methods

Fourth International Symposium on 3D Data Processing, Visualization and Transmission, 3DPVT, Pgs: 321-329, June 2008
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• Applying Convex Optimization Techniques to Energy Minimization Problems in Computer Vision

PhD Thesis, Computer and Information Science Department, University of Pennsylvania, 2008
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