A Review for the Euler Number Computing Problem

In a binary image, the Euler number is a crucial topological feature that holds immense significance in image understanding and image analysis owing to its invariance under scaling, rotation, or any arbitrary rubber-sheet transformation of images. This paper focuses on the Euler number computing problem in a binary image. The state-of-the-art Euler number computing algorithms are reviewed, which obtain the Euler number through different techniques, such as definition, features of binary images, and special data structures representing forms of binary images, and we explain the main principles and strategies of the algorithms in detail. Afterwards, we present the experimental results to bring order of the prevailing Euler number computing algorithms in 8-connectivity cases. Then, we discuss both the parallel implementation and the hardware implementation of algorithms for calculating the Euler number and present the algorithm extension for 3D image Euler number computation. Lastly, we aim to outline forthcoming efforts concerning the computation of the Euler number.