Reproducible kernel Hilbert space based global and local image segmentation

Image segmentation is the task of partitioning an image into individual objects, and has many important applications in a wide range of fields. The majority of segmentation methods rely on image intensity gradient to define edges between objects. However, intensity gradient fails to identify edges when the contrast between two objects is low. In this paper we aim to introduce methods to make such weak edges more prominent in order to improve segmentation results of objects of low contrast. This is done for two kinds of segmentation models: global and local. We use a combination of a reproducing kernel Hilbert space and approximated Heaviside functions to decompose an image and then show how this decomposition can be applied to a segmentation model. We show some results and robustness to noise, as well as demonstrating that we can combine the reconstruction and segmentation model together, allowing us to obtain both the decomposition and segmentation simultaneously.