Active Contour Models for Manifold Valued Image Segmentation

Abstract

Image segmentation is the process of partitioning an image into different regions or groups based on some characteristics like color, texture, motion, or shape etc. Active contours are a popular variational method for object segmentation in images, in which the user initializes a contour which evolves in order to optimize an objective function designed such that the desired object boundary is the optimal solution. Recently, imaging modalities that produce Manifold-valued images are frequently used, for example, DT-MRI images, vector fields. The traditional active contour model does not work on such images. In this paper, we generalize the active contour model to work on Manifold-valued images. As expected, our algorithm detects regions with similar Manifold values in the image. Our algorithm also produces expected results on usual gray-scale images, since these are nothing but trivial examples of Manifold-valued images. As another application of our general active contour model, we perform texture segmentation on gray-scale images by first creating an appropriate Manifold-valued image. We demonstrate segmentation results for manifold-valued images and texture images.