The chordlet transform with an application to shape compression

Due to their abilities to succinctly capture features at different scales and directions, wavelet-based decomposition or representation methods have found wide use in image analysis, restoration, and compression. While there has been a drive to increase the representation ability of these methods via directional filters or elongated basis functions, they still have been focused on essentially piecewise linear representation of curves in images. We propose to extend the line-based dictionary of the beamlet framework to one that includes sets of arcs that are quantized in height. The proposed chordlet dictionary has elements that are constrained at their endpoints and limited in curvature by system rate or distortion constraints. This provides a more visually natural representation of curves in images and, furthermore, it is shown that for a class of images the chordlet representation is more efficient than the beamlet representation under tight distortion constraints. A data structure, the fat quadtree and an algorithm for determining an optimal chordlet representation of an image are proposed. Codecs have been implemented to illustrate applications to both lossy and lossless low bitrate compressions of binary edge images, and better rate or rate–distortion performance over the JBIG2 standard and a beamlet-based compression method are demonstrated. & 2011 Elsevier B.V. All rights reserved.