Remote sensing image segmentation by combining manifold projection and persistent homology

•An image segmentation algorithm by combining Manifold Projection and Persistent Homology is proposed.•The correlation between pixels is defined by combining homology generators and the Riemannian manifold.•The differences between different classes are described from three aspects: geometry, statistics and topology. This paper presents an image segmentation algorithm by combining Manifold Projection and Persistent Homology (MP_PH). First, for a given image, the spectral measures of each pixel and its neighbor pixels are modeled with Gaussian Probability Distribution Function (GPDF) in an exponential family fashion. The Riemannian manifold, i.e. the data sub-manifold for the pixel, is built by taking the parameters of the GPDF exponential family model as its coordinates to depict the statistical characteristics of the original image. By Legendre transformation, the data sub-manifold is transformed into a parameter sub-manifold to depict all possible segmentation results. Only points representing classes of current segmentation results are activated on the parameter sub-manifold. Then, simplicial complexes constructed from the original image are used to compute persistent homology. The optimal scale can be obtained from persistent homology to compute the optimal homology group generated by homology generators which are referred to some pixels belonging to the same class. Finally, the segmentation is performed by projecting points of the data sub-manifold belonging to the same homology generator to the nearest activated point of the parameter sub-manifold, and updating all the activated points according to the projection results. As a result, all the activated points tend to be optimal segmentation. The experiments for synthetic and real images show that the proposed algorithm has high segmentation accuracy.