Indexing topological numbers on images by transferring chiral magnetic textures*

Topological analysis finds extensive application across diverse research domains, unveiling intricate features and structural relationships inherent in geometric objects. Specifically, within the realm of data analysis, the exploration of the topological properties of various images yields rich insights into the underlying geometric information they encapsulate. This research introduces a novel approach for investiigating the topological properties of arbitrary grayscale images. The method leverages a straightforward procedure borrowed from two-dimensional magnetism studies to compute topological numbers. Machine learning techniques are employed to imprint chiral magnetic textures onto the images, followed by the direct computation of the topological number. Computation of topological number is achieved by integrating the solid angles formed by adjacent spin vectors within the converted images. Our method successfully and consistently identifies the topological numbers of various grayscale images, exhibiting robust performance even in the presence of minor noise. Moreover, we underscore the method's efficacy and potential applications by applying it to an analysis of the topological characteristics present in handwritten digits within the MNIST dataset.