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ABSTRACT: Probabilistic models of image statistics underlie many approaches in image analysis and processing. An important class of such models have variables whose dependency graph is a tree. If the hidden variables take values on a finite set, most computations with the model can be performed exactly, including the likelihood calculation, training with the EM algorithm, etc. Crouse et al. developed one such model, the hidden Markov tree (HMT). They took particular care to limit the complexity of their model. We argue that it is beneficial to allow more complex tree-structured models, describe the use of information theoretic penalties to choose the model complexity, and present experimental results to support these proposals. For these experiments, we use what we call the hierarchical image probability (HIP) model. The differences between the HIP and the HMT models include the use of multivariate Gaussians to model the distributions of local vectors of wavelet coefficients and the use of different numbers of hidden states at each resolution. We demonstrate the broad utility of image distributions by applying the HIP model to classification, synthesis, and compression, across a variety of image types, namely, electrooptical, synthetic aperture radar, and mammograms (digitized X-rays). In all cases, we compare with the HMT.
IEEE Transactions on Image Processing 03/2006; 15(2):319-30. · 3.04 Impact Factor
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ABSTRACT: We develop a probabilistic network model over image spaces and demonstrate its broad utility in mammographic image analysis, particularly with respect to computer-aided diagnosis. The model employs a multi-scale pyramid decomposition to factor images across scale and a network of tree-structured hidden variables to capture long-range spatial dependencies. This factoring makes the computation of the density functions local and tractable. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters are found with maximum likelihood estimation using the expectation-maximization algorithm. The utility of the model is demonstrated for three applications: (1) detection of mammographic masses for computer-aided diagnosis; (2) qualitative assessment of model structure through mammographic synthesis; and (3) compression of mammographic regions of interest. 2003 Elsevier Science B.V. All rights reserved.
12/2003;
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ABSTRACT: We develop a probabilistic network model over image spaces and demonstrate its broad utility in mammographic image analysis, particularly with respect to computer-aided diagnosis. The model employs a multi-scale pyramid decomposition to factor images across scale and a network of tree-structured hidden variables to capture long-range spatial dependencies. This factoring makes the computation of the density functions local and tractable. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters are found with maximum likelihood estimation using the expectation-maximization algorithm. The utility of the model is demonstrated for three applications: (1) detection of mammographic masses for computer-aided diagnosis; (2) qualitative assessment of model structure through mammographic synthesis; and (3) compression of mammographic regions of interest.
Medical Image Analysis 07/2003; 7(2):187-204. · 4.42 Impact Factor
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Medical Image Analysis. 01/2003; 7:187-204.
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ABSTRACT: In this paper we summarize our results for two classes of hierarchical multi-scale models that exploit contextual information for detection of structure in mammographic imagery. The first model, the hierarchical pyramid neural network (HPNN), is a discriminative model which is capable of integrating information either coarse-to-fine or fine-tocoarse for microcalcification and mass detection. The second model, the hierarchical image probability (HIP) model, captures short-range and contextual dependencies through a combination of coarse-to-fine factoring and a set of hidden variables. The HIP model, being a generative model, has broad utility, and we present results for classification, synthesis and compression of mammographic mass images. The two models demonstrate the utility of the hierarchical multi-scale framework for computer assisted detection and diagnosis.
06/2002;
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ABSTRACT: This paper describes a pattern recognition architecture, which we term hierarchical pyramid/neural network (HPNN), that learns to exploit image structure at multiple resolutions for detecting clinically significant features in digital/digitized mammograms. The HPNN architecture consists of a hierarchy of neural networks, each network receiving feature inputs at a given scale as well as features constructed by networks lower in the hierarchy. Networks are trained using a novel error function for the supervised learning of image search/detection tasks when the position of the objects to be found is uncertain or ill defined. We have evaluated the HPNN's ability to eliminate false positive (FP) regions of interest generated by the University of Chicago's (UofC) Computer-aided diagnosis (CAD) systems for microcalcification and mass detection. Results show that the HPNN architecture, trained using the uncertain object position (UOP) error function, reduces the FP rate of a mammographic CAD system by approximately 50% without significant loss in sensitivity. Investigation into the types of FPs that the HPNN eliminates suggests that the pattern recognizer is automatically learning and exploiting contextual information. Clinical utility is demonstrated through the evaluation of an integrated system in a clinical reader study. We conclude that the HPNN architecture learns contextual relationships between features at multiple scales and integrates these features for detecting microcalcifications and breast masses.
IEEE Transactions on Medical Imaging 04/2002; 21(3):239-50. · 3.64 Impact Factor
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ABSTRACT: We develop a probability model over image spaces and demonstrate its broad utility in mammographic image analysis. The model employs a pyramid representation to factor images across scale and a tree-structured set of hidden variables to capture long-range spatial dependencies. This factoring makes the computation of the density functions local and tractable. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters are found with maximum likelihood estimation using the EM algorithm. The utility of the model is demonstrated for three applications; 1) detection of mammographic masses in computer-aided diagnosis 2) qualitative assessment of model structure through mammographic synthesis and 3) lossless compression of mammographic regions of interest. 1.
10/2001;
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ABSTRACT: Mammographic Computer-Aided Diagnosis (CAD) systems are an approach for low-cost double reading. Though results to date have been promising, current systems often suffer from unacceptably high false positive rates. Improved methods are needed for optimally setting the system parameters, particularly in the case of statistical models that are common elements of most CAD systems. In this research project we developed a framework for building hierarchical pattern recognizers for CAD based on information theoretic criteria, e.g., the minimum description length (MDL). As part of this framework, we developed a hierarchical image probability (HIP) model. HIP models are well-suited to information theoretic methods since they are generative. We developed architecture search algorithms based on information theory, and applied these to mammographic CAD. The resulting mass detection algorithm, for example, reduced the false positive rate of a CAD system by 30% with no loss of sensitivity. We showed that the criteria reliably correlate with performance on new data. The framework allows many other applications not possible with most pattern recognition algorithms, including rejection of novel examples that can't be reliably classified, synthesis of artificial images to investigate the structure learned by the model, and compression, which is as good as JPEG.
07/2001;
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05/2001;
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ABSTRACT: In hyperspectral imagery one pixel typically consists of a mixture of the re#ectance spectra of several materials, where the mixture coe#cients correspond to the abundances of the constituting materials. We assume linear combinations of re#ectance spectra with some additive normal sensor noise and derive a probabilistic MAP framework for analyzing hyperspectral data. As the material re- #ectance characteristics are not know a priori, we face the problem of unsupervised linear unmixing. The incorporation of di#erent prior information #e.g. positivity and normalization of the abundances # naturally leads to a family of interesting algorithms, for example in the noise-free case yielding an algorithm that can be understood as constrained independent component analysis #ICA#. Simulations underline the usefulness of our theory. 1 Introduction Currenthyperspectral remote sensing technology can form images of ground surface re#ectance at a few hundred wavelengths simultaneously, ...
12/2000;
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ABSTRACT: We formulate a model for probability distributions on image spaces. We show that any distribution of images can be factored exactly into conditional distributions of feature vectors at one resolution (pyramid level) conditioned on the image information at lower resolutions. We would like to factor this over positions in the pyramid levels to make it tractable, but such factoring may miss long-range dependencies. To capture long-range dependencies, we introduce hidden class labels at each pixel in the pyramid. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters can be found with maximum likelihood estimation using the EM algorithm. We have obtained encouraging preliminary results on the problems of detecting various objects in SAR images and target recognition in optical aerial images. 1. INTRODUCTION Many approaches to object recognition in images estimate 99 , the probability that an object of ...
12/2000;
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ABSTRACT: We formulate a model for probability distributions on image spaces. We show that any distribution of images can be factored exactly into conditional distributions of feature vectors at one resolution (pyramid level) conditioned on the image information at lower resolutions. We would like to factor this over positions in the pyramid levels to make it tractable, but such factoring may miss long-range dependencies. To fix this, we introduce hidden class labels at each pixel in the pyramid. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters can be found with maximum likelihood estimation using the EM algorithm. We have obtained encouraging preliminary results on the problems of detecting masses in mammograms. Keywords: Mammography, CAD, Image Probability 1. INTRODUCTION Many approaches to object recognition in images estimate Pr(class j image). By contrast, a model of the probability distribution of images,...
08/2000;
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ABSTRACT: In hyperspectral imagery one pixel typically consists of a mixture of the reectance spectra of several materials, where the mixture coecients correspond to the abundances of the constituting materials. We assume linear combinations of reectance spectra with some additive normal sensor noise and derive a probabilistic MAP framework for analyzing hyperspectral data. As the material re- ectance characteristics are not know a priori, we face the problem of unsupervised linear unmixing. The incorporation of dierent prior information (e.g. positivity and normalization of the abundances) naturally leads to a family of interesting algorithms, for example in the noise-free case yielding an algorithm that can be understood as constrained independent component analysis (ICA). Simulations underline the usefulness of our theory. 1 Introduction Current hyperspectral remote sensing technology can form images of ground surface reectance at a few hundred wavelengths simultaneously, w...
07/2000;
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29th Applied Image Pattern Recognition Workshop (AIPR 2000), 16-18 October 2000, Washington, DC, USA, Proceedings; 01/2000
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VLSI Signal Processing. 01/2000; 26:39-46.
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Advances in Neural Information Processing Systems 12, [NIPS Conference, Denver, Colorado, USA, November 29 - December 4, 1999]; 01/1999
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Advances in Neural Information Processing Systems 12, [NIPS Conference, Denver, Colorado, USA, November 29 - December 4, 1999]; 01/1999
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ABSTRACT: Acoustic signals recorded simultaneously in a reverberant environment can be described as sums of differently convolved sources. The task of source separation is to identify the multiple channels and possibly to invert those in order to obtain estimates of the underling sources. We tackle the problem by explicitly exploiting the non-stationarity of the acoustic sources. Changing cross-correlations at multiple times give a sufficient set of constraints for the unknown channels. A least squares optimization allows us to estimate a forward model, identifying thus the multi-path channel. In the same manner we can find an FIR backward model, which generates well separated model sources. Under certain conditions we obtain up to 14 dB signal enhancement in a real room environment. 1 Introduction A growing number of researchers have published in recent years on the problem of blind source separation. For one, the problem seems of relevance in various application areas such as speech enhanceme...
07/1998;
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Advances in Neural Information Processing Systems 11, [NIPS Conference, Denver, Colorado, USA, November 30 - December 5, 1998]; 01/1998
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ABSTRACT: In independent component analysis (ICA) an instantaneous mix of sources can be recovered using maximum Likelihood (ML). In Convolutive blind source separation (BSS) the mixture arises as a combination of differently convolved source signals due to time delays and a reverberating acoustic environment. Instead of modeling a particular time instant now a time window of the mixed signals has to be modeled. This allows to combine ICA with traditional ML signal modeling techniques. Here we use an auto-regressive (AR) model of the sources leading to a generalization of contextual ICA [18] to the convolutive case. This may improve source separation avoiding the typical whitening of the sources, and may allow us to incorporation simultaneous enhancing of the signal based on the AR models. 1 Introduction Independent component analysis (ICA) aims to find statistical independent signals in an instantaneous linear mix. This concept was first introduced and formalized by Comon [7]. In recent years ...
10/1997;
