Ilya Pollak

Segmentation of dermatoscopic images by stabilized inverse diffusion equations

Several segmentation techniques were evaluated for their effectiveness in distinguishing lesion from background in dermatoscopic images of pigmented lesions (moles and melanomas). These included 5 techniques previously used for segmentation of pigmented lesions, and several new techniques based on stabilized inverse diffusion equations (SIDE) and Markov random fields (MRF). Novel multiresolution implementations of the SIDE and MRF algorithms were created for this work. Techniques based on the SIDE and MRF algorithms produced the most accurate segmentations.

Hierarchical Stochastic Image Grammars for Classification and Segmentation

We develop a new class of hierarchical stochastic image models called spatial random trees (SRTs) which admit polynomial-complexity exact inference algorithms. Our framework of multitree dictionaries is the starting point for this construction. SRTs are stochastic hidden tree models whose leaves are associated with image data. The states at the tree nodes are random variables, and, in addition, the structure of the tree is random and is generated by a probabilistic grammar. We describe an efficient recursive algorithm for obtaining the maximum a posteriori estimate of both the tree structure and the tree states given an image. We also develop an efficient procedure for performing one iteration of the expectation-maximization algorithm and use it to estimate the model parameters from a set of training images. We address other inference problems arising in applications such as maximization of posterior marginals and hypothesis testing. Our models and algorithms are illustrated through several image classification and segmentation experiments, ranging from the segmentation of synthetic images to the classification of natural photographs and the segmentation of scanned documents. In each case, we show that our method substantially improves accuracy over a variety of existing methods

Nonlinear evolution equations as fast and exact solvers of estimation problems

We develop computationally efficient procedures for solving certain restoration problems in one dimension, including the one-dimensional (1-D) discrete versions of the total variation regularized problem introduced by Sauer and Bouman and the constrained total variation minimization problem introduced by Rudin et al. The procedures are exact and have time complexity O(NlogN) and space complexity O(N), where N is the number of data samples. They are based on a simple nonlinear diffusion equation proposed by Pollak et al. and related to the Perona-Malik equation. A probabilistic interpretation for this diffusion equation in 1-D is provided by showing that it produces optimal solutions to a sequence of estimation problems. We extend our methods to two dimensions, where they no longer have similar optimality properties; however, we experimentally demonstrate their effectiveness for image restoration.

Fast search for best representations in multitree dictionaries

We address the best basis problem - or, more generally, the best representation problem: Given a signal, a dictionary of representations, and an additive cost function, the aim is to select the representation from the dictionary which minimizes the cost for the given signal. We develop a new framework of multitree dictionaries, which includes some previously proposed dictionaries as special cases. We show how to efficiently find the best representation in a multitree dictionary using a recursive tree-pruning algorithm. We illustrate our framework through several examples, including a novel block image coder, which significantly outperforms both the standard JPEG and quadtree-based methods and is comparable to embedded coders such as JPEG2000 and SPIHT.

Spatial Random Tree Grammars for Modeling Hierarchal Structure in Images with Regions of Arbitrary Shape

We present a novel probabilistic model for the hierarchical structure of an image and its regions. We call this model spatial random tree grammars (SRTGs). We develop algorithms for the exact computation of likelihood and maximum a posteriori (MAP) estimates and the exact expectation-maximization (EM) updates for model-parameter estimation. We collectively call these algorithms the center-surround algorithm. We use the center-surround algorithm to automatically estimate the maximum likelihood (ML) parameters of SRTGs and classify images based on their likelihood and based on the MAP estimate of the associated hierarchical structure. We apply our method to the task of classifying natural images and demonstrate that the addition of hierarchical structure significantly improves upon the performance of a baseline model that lacks such structure.

Nonlinear multiscale filtering

In this article, we give an overview of scale-spaces and their application to noise suppression and segmentation of 1-D signals and 2-D images. Several prototypical problems serve as our motivation. We review several scale-spaces (linear Gaussian, Perona-Malik, and SIDE-stabilized inverse diffusion equation) and discuss their advantages and shortcomings. We describe our previous work and argue that a very simple nonlinear scale-space leads to a fast estimation algorithm which produces accurate segmentations and estimates of signals and images.

Multiscale segmentation with vector-valued nonlinear diffusions on arbitrary graphs

We propose a novel family of nonlinear diffusion equations and apply it to the problem of segmentation of multivalued images. We show that this family can be viewed as an extension of stabilized inverse diffusion equations (SIDEs) which were proposed for restoration, enhancement, and segmentation of scalar-valued signals and images in . Our new diffusion equations can process vector-valued images defined on arbitrary graphs which makes them well suited for segmentation. In addition, we introduce novel ways of utilizing the shape information during the diffusion process. We demonstrate the effectiveness of our methods on a large number of segmentation tasks.

Scale Space Analysis by Stabilized Inverse Diffusion Equations

We introduce a family of first-order multi-dimensional ordinary differential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations “stabilized inverse diffusion equations” (“SIDEs”). A SIDE in one spatial dimension may be interpreted as a limiting case of a semi-discretized Perona-Malik equation [3, 4]. In an experimental section, SIDEs are shown to suppress noise while sharpening edges present in the input signal. Their application to image segmentation is demonstrated.

A Document Image Model and Estimation Algorithm for Optimized JPEG Decompression

The JPEG standard is one of the most prevalent image compression schemes in use today. While JPEG was designed for use with natural images, it is also widely used for the encoding of raster documents. Unfortunately, JPEGs characteristic blocking and ringing artifacts can severely degrade the quality of text and graphics in complex documents. We propose a JPEG decompression algorithm which is designed to produce substantially higher quality images from the same standard JPEG encodings. The method works by incorporating a document image model into the decoding process which accounts for the wide variety of content in modern complex color documents. The method works by first segmenting the JPEG encoded document into regions corresponding to background, text, and picture content. The regions corresponding to text and background are then decoded using maximum a posteriori (MAP) estimation. Most importantly, the MAP reconstruction of the text regions uses a model which accounts for the spatial characteristics of text and graphics. Our experimental comparisons to the baseline JPEG decoding as well as to three other decoding schemes, demonstrate that our method substantially improves the quality of decoded images, both visually and as measured by PSNR.

New algorithms for best local cosine basis search

We propose a best basis search algorithm for local cosine dictionaries. We improve upon the classical best local cosine basis selection based on a dyadic tree (Coifman, R.R. and Wickerhauser, M.V., IEEE Trans. Inf. Th., vol.38, no.2, p.713-18, 1992), by considering a larger dictionary of bases. This results in more compact representations, lower costs, and approximate shift-invariance. We also provide a version of our algorithm which is strictly shift-invariant.