Abstract

We develop new algorithms to analyze and exploit the joint subspace structure of a set of related images to facilitate the process of concurrent segmentation of a large set of images. Most existing ap- proaches for this problem are either limited to extracting a single similar ob ject across the given image set or do not scale well to a large number of images containing multiple ob jects varying at different scales. One of the goals of this paper is to show that various desirable properties of such an algorithm (ability to handle multiple images with multiple ob- jects showing arbitary scale variations) can be cast elegantly using simple constructs from linear algebra: this significantly extends the operating range of such methods. While intuitive, this formulation leads to a hard optimization problem where one must perform the image segmentation task together with appropriate constraints which enforce desired alge- braic regularity (e.g., common subspace structure). We propose efficient iterative algorithms (with small computational requirements) whose key steps reduce to ob jective functions solvable by max-flow and/or nearly closed form identities. We study the qualitative, theoretical, and empiri- cal properties of the method, and present results on benchmark datasets.