The Euler number of a binary image is an important topological property for pattern recognition, image analysis, and computer vision. A famous method for computing the Euler number of a binary image is by counting certain patterns of bit-quads in the image, which has been improved by scanning three rows once to process two bit-quads simultaneously. This paper studies the bit-quad-based Euler number computing problem. We show that for a bit-quad-based Euler number computing algorithm, with the increase of the number of bit-quads being processed simultaneously, on the one hand, the average number of pixels to be checked for processing a bit-quad will decrease in theory, and on the other hand, the length of the codes for implementing the algorithm will increase, which will make the algorithm less efficient in practice. Experimental results on various types of images demonstrated that scanning five rows once and processing four bit-quads simultaneously is the optimal tradeoff, and that the optimal bit-quad-based Euler number computing algorithm is more efficient than other Euler number computing algorithms.

The Euler number is an important topological property in a binary image, and it can be computed by counting certain bit-quads in the binary image. This paper proposes a further improved bit-quad-based algorithm for computing the Euler number. By scanning image rows two by two and utilizing the information obtained while processing the previous pixels, the number of pixels to be checked for processing a bit-quad can be decreased from 2 to 1.5. Experimental results demonstrated that our proposed algorithm significantly outperforms conventional Euler number computing algorithms.