Can the Use of nonlinear Color Metrics systematically improve Segmentation?

Image segmentation is a procedure where an image is split into its constituent parts, according to some criterion. In the literature, there are different well-known approaches for segmentation, such as clustering, thresholding, graph theory and region growing. Such approaches, additionally, can be combined with color distance metrics, playing an important role for color similarity computation. Aiming to investigate general approaches able to enhance the performance of segmentation methods, this work presents an empirical study of the effect of a nonlinear color metric on segmentation procedures. For this purpose, three algorithms were  chosen: Mumford-Shah, Color Structure Code and Felzenszwalb and Huttenlocher Segmentation. The color similarity metric employed by these algorithms (L2-norm) was replaced by the Polynomial Mahalanobis Distance. This metric is an extension of the statistical Mahalanobis Distance used to measure the distance between coordinates and distribution centers. An evaluation based upon automated comparison of segmentation results against ground truths from the Berkeley Dataset was performed. All three segmentation approaches were compared to their traditional implementations, against each other and also to a large set of other segmentation methods. The statistical analysis performed has indicated a systematic improvement of segmentation results for all three segmentation approaches when the nonlinear metric was employed.