Efficient Strategies for Computing Euler Number of a 3D Binary Image

Abstract

As an important topological property for a 3D binary image, the Euler number can be computed by finding specific a voxel block with 2 × 2 × 2 voxels, named the voxel pattern, in the image. In this paper, we introduce three strategies for enhancing the efficiency of a voxel-pattern-based Euler number computing algorithm used for 3D binary images. The first strategy is taking advantage of the voxel information acquired during computation to avoid accessing voxels repeatedly. This can reduce the average number of accessed voxels from 8 to 4 for processing a voxel pattern. Therefore, the efficiency of computation will be improved. The second strategy is scanning every two rows and processing two voxel patterns simultaneously in each scan. In this strategy, only three voxels need to be accessed when a voxel pattern is processed. The last strategy is determining the voxel accessing order in the processing voxel pattern and unifying the processing of the voxel patterns that have identical Euler number increments to one group in the computation. Although this strategy can theoretically reduce the average number of voxels accessed from 8 to 4.25 for processing a voxel pattern, it is more efficient than the above two strategies for moderate- and high-density 3D binary images. Experimental results demonstrated that the three algorithms with each of our proposed three strategies exhibit greater efficiency compared to the conventional Euler number computing algorithm based on finding specific voxel patterns in the image.