Robust Matrix Decomposition for Image Segmentation under Heavy Noises and Uneven Background Intensities

This paper presents a robust matrix decomposition approach that automatically segments a binary image to foreground regions and background regions under high observation noise levels and uneven background intensities. The work is motivated by the need of identifying foreground objects in a noisy electron microscopic image, but the method can be extended for a general binary classification problem. The proposed method models an input image as a matrix of image pixel values, and the matrix is represented by a mixture of three component matrices of the same size, background, foreground and noise matrices. We propose a robust matrix decomposition approach to separate the input matrix into the three components, based on robust singular value decomposition. The proposed approach is more robust to high image noises and uneven background than the existing matrix-based approaches, which is numerically shown using simulated images and eight electron microscope images with manually achieved ground truth