3D binary morphological operations using run-length representation

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.