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ConvexVision

Principal Investigator

Prof. Dr. Daniel Cremers
Technische Universität München
Fakultät für Informatik
Lehrstuhl für Computer Vision and Pattern Recognition
Boltzmannstraße 3
85748 Garching

 

Abstract

Optimization methods have become an established paradigm to address many Computer Vision challenges such as the reconstruction of three-dimensional objects from multiple images, or the tracking of a deformable shape over time. Yet, it has been largely overlooked that optimization approaches are practically useless if there exist no efficient algorithms to compute minimizers of respective energies. Most existing formulations give rise to non-convex energies. As a consequence, solutions highly depend on the choice of minimization scheme and implementational (initialization, time step sizes, etc.), with little or no guarantees regarding the quality of computed solutions and their robustness to perturbations of the input data.

In the proposed research project, we plan to address this important shortcoming by developing optimization methods for Computer Vision which allow to efficiently compute globally optimal solutions. Preliminary results indicate that this will substantially leverage the power of optimization methods and their applicability in a substantially broader context. Specifically we will focus on three lines of research:

1) We will develop convex formulations for a variety of challenges such as 3D reconstruction from multiple views, tracking of deformable objects, and object recognition. While convex formulations are currently being developed for low-level problems such as image segmentation, our main effort will focus on carrying convex optimization to higher level problems of image understanding and scene interpretation.

2) We will investigate alternative strategies of global optimization by means of discrete graph theoretic methods. We will characterize advantages and drawbacks of continuous and discrete methods and thereby develop novel algorithms combining the advantages of both approaches.

3) We will go beyond convex formulations. This is an important challenge since many realworld problems cannot be expressed in terms of convex functionals. By developing nonconvex programming methods we intend to substantially enlarge the class of tractable problems and compute high quality solutions that lie within a bound of the optimal energy. We plan to study their relation to discrete polynomial time approximation schemes (PTAS).

Advancing the state of the art in optimization methods will have a profound impact well beyond Computer Vision. We strongly believe that we have the necessary competence to pursue this project. Preliminary results have been well received by the community.

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