On image segmentation using information theoretic criteria

Image segmentation is a long-studied and important problem in image processing. Different solutions have been proposed, many of which follow the information theoretic paradigm. While these information theoretic segmentation methods often produce excellent empirical results, their theoretical properties are still largely unknown. The main goal of this paper is to conduct a rigorous theoretical study into the statistical consistency properties of such methods. To be more specific, this paper investigates if these methods can accurately recover the true number of segments together with their true boundaries in the image as the number of pixels tends to infinity. Our theoretical results show that both the Bayesian information criterion (BIC) and the minimum description length (MDL) principle can be applied to derive statistically consistent segmentation methods, while the same is not true for the Akaike information criterion (AIC). Numerical experiments were conducted to illustrate and support our theoretical findings.Comment: Published in at http://dx.doi.org/10.1214/11-AOS925 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Detecting abrupt changes in the spectra of high-energy astrophysical sources

Variable-intensity astronomical sources are the result of complex and often extreme physical processes. Abrupt changes in source intensity are typically accompanied by equally sudden spectral shifts, that is, sudden changes in the wavelength distribution of the emission. This article develops a method for modeling photon counts collected from observation of such sources. We embed change points into a marked Poisson process, where photon wavelengths are regarded as marks and both the Poisson intensity parameter and the distribution of the marks are allowed to change. To the best of our knowledge, this is the first effort to embed change points into a marked Poisson process. Between the change points, the spectrum is modeled nonparametrically using a mixture of a smooth radial basis expansion and a number of local deviations from the smooth term representing spectral emission lines. Because the model is over-parameterized, we employ an ℓ1ℓ1 penalty. The tuning parameter in the penalty and the number of change points are determined via the minimum description length principle. Our method is validated via a series of simulation studies and its practical utility is illustrated in the analysis of the ultra-fast rotating yellow giant star known as FK Com

An Automatic Level Set Based Liver Segmentation from MRI Data Sets

A fast and accurate liver segmentation method is a challenging work in medical image analysis area. Liver segmentation is an important process for computer-assisted diagnosis, pre-evaluation of liver transplantation and therapy planning of liver tumors. There are several advantages of magnetic resonance imaging such as free form ionizing radiation and good contrast visualization of soft tissue. Also, innovations in recent technology and image acquisition techniques have made magnetic resonance imaging a major tool in modern medicine. However, the use of magnetic resonance images for liver segmentation has been slow when we compare applications with the central nervous systems and musculoskeletal. The reasons are irregular shape, size and position of the liver, contrast agent effects and similarities of the gray values of neighbor organs. Therefore, in this study, we present a fully automatic liver segmentation method by using an approximation of the level set based contour evolution from T2 weighted magnetic resonance data sets. The method avoids solving partial differential equations and applies only integer operations with a two-cycle segmentation algorithm. The efficiency of the proposed approach is achieved by applying the algorithm to all slices with a constant number of iteration and performing the contour evolution without any user defined initial contour. The obtained results are evaluated with four different similarity measures and they show that the automatic segmentation approach gives successful results