Variational Image Segmentation Model Coupled with Image Restoration Achievements

Image segmentation and image restoration are two important topics in image processing with great achievements. In this paper, we propose a new multiphase segmentation model by combining image restoration and image segmentation models. Utilizing image restoration aspects, the proposed segmentation model can effectively and robustly tackle high noisy images, blurry images, images with missing pixels, and vector-valued images. In particular, one of the most important segmentation models, the piecewise constant Mumford-Shah model, can be extended easily in this way to segment gray and vector-valued images corrupted for example by noise, blur or missing pixels after coupling a new data fidelity term which comes from image restoration topics. It can be solved efficiently using the alternating minimization algorithm, and we prove the convergence of this algorithm with three variables under mild condition. Experiments on many synthetic and real-world images demonstrate that our method gives better segmentation results in comparison to others state-of-the-art segmentation models especially for blurry images and images with missing pixels values.Comment: 23 page

Time series segmentation by Cusum, AutoSLEX and AutoPARM methods

Time series segmentation has many applications in several disciplines as neurology, cardiology, speech, geology and others. Many time series in this fields do not behave as stationary and the usual transformations to linearity cannot be used. This paper describes and evaluates different methods for segmenting non-stationary time series. We propose a modification of the algorithm in Lee et al. (2003) which is designed to searching for a unique change in the parameters of a time series, in order to find more than one change using an iterative procedure. We evaluate the performance of three approaches for segmenting time series: AutoSLEX (Ombao et al., 2002), AutoPARM (Davis et al., 2006) and the iterative cusum method mentioned above and referred as ICM. The evaluation of each methodology consists of two steps. First, we compute how many times each procedure fails in segmenting stationary processes properly. Second, we analyze the effect of different change patterns by counting how many times the corresponding methodology correctly segments a piecewise stationary process. ICM method has a better performance than AutoSLEX for piecewise stationary processes. AutoPARM presents a very satisfactory behaviour. The performance of the three methods is illustrated with time series datasets of neurology and speechTime series segmentation, AutoSLEX, AutoPARM, Cusum Methods

Results on principal component filter banks: colored noise suppression and existence issues

We have made explicit the precise connection between the optimization of orthonormal filter banks (FBs) and the principal component property: the principal component filter bank (PCFB) is optimal whenever the minimization objective is a concave function of the subband variances of the FB. This explains PCFB optimality for compression, progressive transmission, and various hitherto unnoticed white-noise, suppression applications such as subband Wiener filtering. The present work examines the nature of the FB optimization problems for such schemes when PCFBs do not exist. Using the geometry of the optimization search spaces, we explain exactly why these problems are usually analytically intractable. We show the relation between compaction filter design (i.e., variance maximization) and optimum FBs. A sequential maximization of subband variances produces a PCFB if one exists, but is otherwise suboptimal for several concave objectives. We then study PCFB optimality for colored noise suppression. Unlike the case when the noise is white, here the minimization objective is a function of both the signal and the noise subband variances. We show that for the transform coder class, if a common signal and noise PCFB (KLT) exists, it is, optimal for a large class of concave objectives. Common PCFBs for general FB classes have a considerably more restricted optimality, as we show using the class of unconstrained orthonormal FBs. For this class, we also show how to find an optimum FB when the signal and noise spectra are both piecewise constant with all discontinuities at rational multiples of π

Joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a Bayesian sampling approach

International audienceWe propose a joint segmentation algorithm for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors allow to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology yields improved segmentation results when compared to parallel and independent individual signal segmentations. The initial algorithm is derived for piecewise constant AR processes whose orders are fixed on each segment. However, an extension to models with unknown model orders is also discussed. Theoretical results are illustrated by many simulations conducted with synthetic signals and real arc-tracking and speech signals

Multiscale statistical methods for the segmentation of signals and images

Includes bibliographical references (p. 29-30).Supported by a National Science Foundation Graduate Fellowship, and by ONR. N00014-91-J-1004 Supported by AFOSR. F49620-95-1-0083 Supported by Boston University. GC123919NGN Supported by NIH. NINDS 1 R01 NS34189M.K. Schneider ... [et al.]

Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures

1 Indirect estimation of signal-dependent noise with non-adaptive heterogeneous samples

Abstract—We consider the estimation of signal-dependent noise from a single image. Unlike conventional algorithms that build a scatterplot of local mean-variance pairs from either small or adaptively selected homogeneous data samples, our proposed approach relies on arbitrarily large patches of heterogeneous data extracted at random from the image. We demonstrate the feasibility of our approach through an extensive theoretical analysis based on mixture of Gaussian distributions. A prototype algorithm is also developed in order to validate the approach on simulated data as well as on real camera raw images. Index Terms—Noise estimation, signal-dependent noise, Poisson noise