Shock-based Reaction-diiusion Bubbles for Image Segmentation

Figure-Ground segmentation is a fundamental problem in computer vision. The main diiculty is the integration of low-level, pixel-based local image features to obtain global object-based descriptions. Active contours in the form of snakes, balloons, and level-set modeling techniques have been proposed that satisfactorily address this question for certain applications. However, these methods require manual initializa-tion, do not always perform well near sharp protrusions or indentations, or often cross gaps. We propose an approach inspired by these methods and a shock-based representation of shape in terms of parts, protrusions, and bends. In this representation parts are related to fourth order shocks. Since initially it is not clear where the objects or their parts are, parts are hypothesized in the form of fourth order shocks randomly initialized in homogeneous areas of images. These shocks then form evolving contours, or bubbles, which grow, shrink, merge, split and disappear to capture the objects in the image. In the homogeneous areas of the image bubbles deform by a reaction-diiusion process. In the inhomogeneous areas, indicated by diierential properties computed from low-level processes such as edge-detection, texture, optical-ow and stereo, etc. , bubbles do not deform. As such, the randomly initialized bubbles integrate low-level information , and in the process segment gures from ground. The bubble technique does not require manual initialization, integrates a variety of visual information, and deals with gaps of information to capture objects in an image, as illustrated on several synthetic images as well as medical MRI images, in two-dimensions as well as in three-dimensions.