Fast Convex Relaxations using Graph Discretizations
This work addresses computational bottlenecks for practitioners in computer vision applications like multi-label segmentation and stereo estimation, offering a significant speed-up with minimal loss in accuracy.
The paper tackles the high computational cost of convex lifting approaches for non-convex energy minimization problems in computer vision by proposing a graph discretization method using super-pixel graphs, which reduces runtime and memory consumption by up to a factor of 10 while maintaining near-globally optimal energy values.
Matching and partitioning problems are fundamentals of computer vision applications with examples in multilabel segmentation, stereo estimation and optical-flow computation. These tasks can be posed as non-convex energy minimization problems and solved near-globally optimal by recent convex lifting approaches. Yet, applying these techniques comes with a significant computational effort, reducing their feasibility in practical applications. We discuss spatial discretization of continuous partitioning problems into a graph structure, generalizing discretization onto a Cartesian grid. This setup allows us to faithfully work on super-pixel graphs constructed by SLIC or Cut-Pursuit, massively decreasing the computational effort for lifted partitioning problems compared to a Cartesian grid, while optimal energy values remain similar: The global matching is still solved near-globally optimal. We discuss this methodology in detail and show examples in multi-label segmentation by minimal partitions and stereo estimation, where we demonstrate that the proposed graph discretization can reduce runtime as well as memory consumption of convex relaxations of matching problems by up to a factor of 10.