A Topological Approach to Hierarchical Segmentation Using Mean Shift
Mean shift is a popular method to segment images and videos. Pixels are represented by feature points, and the segmentation is driven by the point density in feature space. In this paper, we introduce the use of Morse theory to interpret mean shift as a topological decomposition of the feature space into density modes. This allows us to build on the watershed technique and design a new algorithm to compute mean-shift segmentations of images and videos. In addition, we introduce the use of topological persistence to create a segmentation hierarchy. We validated our method by clustering images using color cues. In this context, our technique runs faster than previous work, especially on videos and large images.

Motion Magnification
We present motion magnification, a technique that acts like a microscope for visual motion. It can amplify subtle motions in a video sequence, allowing for visualization of deformations that would otherwise be invisible. To achieve motion magnification, we need to accurately measure visual motions, and group the pixels to be modified. After an initial image registration step, we measure motion by a robust analysis of feature point trajectories, and segment pixels based on similarity of position, color, and motion. A novel measure of motion similarity groups even very small motions according to correlation over time, which often relates to physical cause.