The Scale-Curvature Connection and its Application to Texture Segmentation

In this work we establish a theoretical relation between the notions of scale and a discrete Finsler-Haantjes curvature. Based on this connection we demonstrate the applicability of the interpretation of scale in terms of curvature, to signal processing in the context of analysis and segmentation of textures in images. The outcome of this procedure is a novel scheme for texture segmentation that is based on scaled metric curvature. The presented method proves itself to be efficient even when the multiscale analysis is done up to scales of 19 and more. Our main conclusions are that the discrete curvature calculated on sampled images can give us an indication on the local scale within the image, and therefore can be used for many additional tasks in image analysis.