Image segmentation with background correction using a multiplicative smoothing-spline model

This paper presents an image-segmentation method which compensates multiplicative distortions based on smooth regularity assumptions. In this work, we generalize the original Chan-Vese functional to handle a continuous multiplicative bias. In the derivation of our model, we show that the optimal correction function is necessarily a spline, which we express in terms of discrete coefficients. Following an iterative technique, we propose to find the solution by an alternate optimization of this map and of the segmented domains. In order to maximize the overall efficiency, graph cuts are combined with a specifically designed multigrid algorithm. Our experiments demonstrate the relevance of our approach for biomedical data.