Morphological Image Coding Based on a Geometric Sampling Theorem and a Modified Skeleton Representation

Abstract

A new approach for gray-level image coding using binary morphological operations on the image bit-planes is presented. This approach is based on a Geometric Sampling Theorem (GST), and on a modified morphological skeleton. The theorem, which is proved in this paper, states conditions for the reconstruction of the boundary of a continuous two level image from a unique subset of points of its skeleton representation. This set of points, referred to as essential points, is found to play an important role in the skeleton representation of discrete binary images as well. The modified morphological skeleton (MMS) uses an exponentially increasing in size structuring element. The computational advantage of this representation was previously reported. A new approach to its development is presented here, and its advantage in image coding is demonstrated. The coding scheme consists of the following steps: First, the image is preprocessed by an error-diffusion technique in order to reduce the number of bit-planes from 8 to 4 without significant quality degradation. The pixel values are subsequently converted to Gray-code. The bit-planes are represented by the MMS. Redundancy in this representation is reduced using an algorithm motivated by the GST. These reduced modified morphological skeletons are coded with an entropy coding scheme particularly devised for efficient skeleton coding. The possibility of the introduction of geometric errors to reduce the bit-rate is also discussed. Compression ratios of up to 11:1 were obtained for satellite images.