Quaternary Crack-Edge Representation for Lossless Contour Compression

We present a method for lossless compression of contours in images using a specific crack-edge representation, where each horizontal binary crack-edge is bundled together with a vertical binary crack-edge in a new symbol, having four possible values. One can represent all contours in an image using an auxiliary quaternary image, which has bundled at each pixel the value of the north and west crack-edges. We use context coding for the quaternary image with the coding tree optimally pruned to obtain the most relevant bi-dimensional contexts. The coding using bi-dimensional contexts of the crack-edge information contrasts with the coding using chain codes, where the contours are represented by one-dimensional sequences of (differential) angles, telling how one can travel from starting points towards ending points in the bi-dimensional image grid. The code length for encoding the starting and ending points (which are referred to as anchors) is large when the contours are very dense, because the representation with chain codes needs specifying many anchor points, while the newly proposed bi-dimensional context coding does not need such information. In the case of images with very dense contours the quaternary representation can be efficiently encoded by context coding. We present experiments with depth images, where using various quantization steps one can obtain a multitude of images of geodesic contours, having a decreasing density of contour links as the quantization step increases. We illustrate the two coding methods for encoding the contours in fractal images, showing a better performance of the quaternary representation as compared to chain code representation.