Multiphase Segmentation For Simultaneously Homogeneous and Textural Images
This work addresses segmentation challenges for natural images with mixed homogeneous and textural content, which is a common issue in image processing, but it appears incremental as it builds on existing models with refinements.
The paper tackles the problem of segmenting images that contain both homogeneous and textured regions, which existing models often fail to handle, by introducing a bi-level constrained minimization model and demonstrating its effectiveness on natural images with theoretical results.
Segmentation remains an important problem in image processing. For homogeneous (piecewise smooth) images, a number of important models have been developed and refined over the past several decades. However, these models often fail when applied to the substantially larger class of natural images that simultaneously contain regions of both texture and homogeneity. This work introduces a bi-level constrained minimization model for simultaneous multiphase segmentation of images containing both homogeneous and textural regions. We develop novel norms defined in different functional Banach spaces for the segmentation which results in a non-convex minimization. Finally, we develop a generalized notion of segmentation delving into approximation theory and demonstrating that a more refined decomposition of these images results in multiple meaningful components. Both theoretical results and demonstrations on natural images are provided.