In many algorithms for background modeling, a distribution over feature values is modeled at each pixel. These models, however, do not account for the dependencies that may exist among nearby pixels. The joint domain-range kernel density estimate (KDE) model by Sheikh and Shah [7], which is not a pixel-wise model, represents the background and foreground processes by combining the three color d...

The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented regi...

In this work, we approach the classic Mumford-Shah problem from a curve evolution perspective. In particular, we let a given family of curves define the boundaries between regions in an image within which the data are modeled by piecewise smooth functions plus noise as in the standard Mumford-Shah functional. The gradient descent equation of this functional is then used to evolve the curve. Eac...

Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber’s Law. The current paper develops a new segmentation model based on the integration of both Weber’s Law and the celebrated M...

In this paper a novel region-merging image segmentation approach is presented. This approach is based on a two-step procedure: a distance metric is learned from some features on the image, then a piecewise approximation function for the Mumford-Shah model is optimized by this metric. The global optimum of the approximation function is inductively achieved under high polynomial terms of the Maha...