Abstract:
This paper addresses the problem of image segmentation and suggests that a number of interesting visual features can be specified as the boundaries of segments. It proposes a segmentation strategy that utilizes the local homogeneity of local image structure. Stable differential measurements are made via a variable-conductance diffusion process, sometimes called anisotropic diffusion. Anisotropic diffusion has been shown to preserve important image structure while reducing unwanted noise.
A multi-scale approach to variable-conductance diffusion is described. This technique combines information at a range of scales and provides a means of obtaining precise boundaries of ``large-scale'' objects in the presence of noise. These ideas generalize to incorporate multi-valued images and higher-order geometric structure. The result is a framework for constructing image segmentations based on the homogeneity of a set of descriptors. When applied to local image geometry, this method offers a means of breaking images into geometric patches that have interesting visual features as boundaries.
Several examples of this framework are presented. While the diffusion of intensity provides a means of detecting edges, the diffusion of first-order information produces ridges and valleys. A combination of of first- and second-order information provides a means of detecting the ``middles'' as well as the edges of objects. A proof of the geometric invariance under orthogonal group transformations is given. These same methods generalize to include systems of frequency-sensitive diffusion processes. These systems are useful for characterizing patches based on texture.
An empirical investigation of these nonlinear diffusion processes shows they are stable in the presence of noise and offer distinct advantages over conventional linear smoothing. This analysis derives from a novel method for evaluating low-level computer-vision algorithms. The method uses ensembles of stochastically generated images to compute a set of statistical metrics which quantify the accuracy and reliability of a process. This evaluation offers a means of comparing different algorithms and exploring the space of free parameters associated with a single algorithm.