3D binary morphological operations using run-length representation

Abstract

In this paper, we propose fast three-dimensional (3D) dilation and erosion methods using run-length encoding (RLE). RLE is an alternative way of representing a binary image using a run, which is a sequence of 'one' pixels. We extend the principle of two-dimensional (2D) RLE to 3D RLE and show that the proposed RLE-based 3D morphological operations can save a considerable amount of computation time. From our analysis, we found that the proposed method reduces computation time by more than 30% over voxel-wise processing. This reduction in computational time and complexity increases as more voxels, and consequently more operations, are processed. We describe a complete and detailed set of procedures for deriving the proposed 3D dilation and erosion. Since a morphological operator is a widely accepted tool for various applications, we believe that the proposed 3D morphological methods will reduce the processing time and increase the performance efficiency of these popular filters. (C) 2008 Elsevier B.V. All rights reserved.