R-3 Repository :: Browsing by Author "Romberg, Justin"

Browsing by Author "Romberg, Justin"

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Adding Linguistic Constraints to Document Image Decoding: Comparing the Iterated Complete Path and Stack Algorithms
(2001-01-20) Popat, Kris; Greene, Dan; Romberg, Justin; Bloomberg, Dan
Beginning with an observed document image and a model of how the image has been degraded, Document Image Decoding recognizes printed text by attempting to find a most probable path through a hypothesized Markov source. The incorporation of linguistic constraints, which are expressed by a sequential predictive probabilistic language model, can improve recognition accuracy significantly in the case of moderately to severely corrupted documents. Two methods of incorporating linguistic constraints in the best-path search are described, analyzed and compared. The first, called the iterated complete path algorithm, involves iteratively rescoring complete paths using conditional language model probability distributions of increasing order, expanding state only as necessary with each iteration. A property of this approach is that it results in a solution that is exactly optimal with respect to the specified source, degradation, and language models; no approximation is necessary. The second approach considered is the Stack algorithm, which is often used in speech recognition and in the decoding of convolutional codes. Experimental results are presented in which text line images that have been corrupted in a known way are recognized using both the ICP and Stack algorithms. This controlled experimental setting preserves many of the essential features and challenges of real text line decoding, while highlighting the important algorithmic issues.
Approximation and Compression of Piecewise Smooth Images Using a Wavelet/Wedgelet Geometric Model
(2003-09-01) Romberg, Justin; Wakin, Michael; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Inherent to photograph-like images are two types of structures: large smooth regions and geometrically smooth edge contours separating those regions. Over the past years, efficient representations and algorithms have been developed that take advantage of each of these types of structure independently: quadtree models for 2D wavelets are well-suited for uniformly smooth images (CÂ² everywhere), while quadtree-organized wedgelet approximations are appropriate for purely geometrical images (containing nothing but CÂ² contours). This paper shows how to combine the wavelet and wedgelet representations in order to take advantage of both types of structure simultaneously. We show that the asymptotic approximation and rate-distortion performance of a wavelet-wedgelet representation on piecewise smooth images mirrors the performance of both wavelets (for uniformly smooth images) and wedgelets (for purely geometrical images). We also discuss an efficient algorithm for fitting the wavelet-wedgelet representation to an image; the convenient quadtree structure of the combined representation enables new algorithms such as the recent WSFQ geometric image coder.
Bayesian Tree-Structured Image Modeling
(2000-04-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint statistics of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training (using the EM algorithm, for example). In this paper, we propose two reduced-parameter HMT models that capture the general structure of a broad class of grayscale images. The image HMT (iHMT) model leverages the fact that for a large class of images the structure of the HMT is self-similar across scale. This allows us to reduce the complexity of the iHMT to just nine easily trained parameters (independent of the size of the image and the number of wavelet scales). In the universal HMT (uHMT) we take a Bayesian approach and fix these nine parameters. The uHMT requires no training of any kind. While simple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of the key structures modeled by the full HMT. Based on these new models, we develop a shift-invariant wavelet denoising scheme that outperforms all algorithms in the current literature.
Bayesian Tree-Structured Image Modeling using Wavelet-domain Hidden Markov Models
(1999-07-20) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training to fit an HMT model to a given data set (using the Expectation-Maximization algorithm, for example). In this paper, we greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images. This simplified model specifies the HMT parameters with just nine meta-parameters (independent of the size of the image and the number of wavelet scales). We also introduce a Bayesian universal HMT (uHMT) that mixes these nine parameters. The uHMT requires no training of any kind. While extremely simple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of the key structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms other wavelet-based estimators in the current literature, both in mean-square error and visual metrics.
Bayesian Tree-Structured Image Modeling using Wavelet-domain Hidden Markov Models
(2001-07-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training to fit an HMT model to a given data set (using the Expectation-Maximization algorithm, for example). In this paper, we greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images. This simplified model specifies the HMT parameters with just nine meta-parameters (independent of the size of the image and the number of wavelet scales). We also introduce a Bayesian universal HMT (uHMT) that fixes these nine parameters. The uHMT requires no training of any kind. While extremely simple, we show using a series of image estimation/denoising experiments that these new models retain nearly all of the key image structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms other wavelet-based estimators in the current literature, both visually and in mean-square error.
Bayesian Wavelet Domain Image Modeling using Hidden Markov Trees
(1999-10-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Wavelet-domain hidden Markov models have proven to be useful tools for statiscal signal and image processing. The hidden Markov tree (HMT) model captures the key features o teh join statistics of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training (using the EM algorithm, for example). In this paper, we propose two reduced-parameter HMT models that capture the general structure of a broad class of grayscale images. The image HMT (iHMT) model leverages the fact that for a large class of images the structure of the HMT is self-similar across scale. This allows us to reduce the complexity of teh iHMT to just nine easily trained parameters (independent of the size of teh image and the number of wavelet scales). In the universal HMT (uHMT) we take a Bayesian approach and fix these nine parameters. The uHMT requires no training of any kind. While simple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of the key structures modeled by the full HMT. Based on these new models, we develop a shift-invariant wavelet denoising scheme that outperforms all algorithms in the current literature.
A Geometric Hidden Markov Tree Wavelet Model
(2003-08-01) Romberg, Justin; Wakin, Michael; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
In the last few years, it has become apparent that traditional wavelet-based image processing algorithms and models have significant shortcomings in their treatment of edge contours. The standard modeling paradigm exploits the fact that wavelet coefficients representing smooth regions in images tend to have small magnitude, and that the multiscale nature of the wavelet transform implies that these small coefficients will persist across scale (the canonical example is the venerable zero-tree coder). The edge contours in the image, however, cause more and more large magnitude wavelet coefficients as we move down through scale to finer resolutions. But if the contours are smooth, they become simple as we zoom in on them, and are well approximated by straight lines at fine scales. Standard wavelet models exploit the grayscale regularity of the smooth regions of the image, but not the geometric regularity of the contours. In this paper, we build a model that accounts for this geometric regularity by capturing the dependencies between complex wavelet coefficients along a contour. The Geometric Hidden Markov Tree (GHMT) assigns each wavelet coefficient (or spatial cluster of wavelet coefficients) a hidden state corresponding to a linear approximation of the local contour structure. The shift and rotational-invariance properties of the complex wavelet transform allow the GHMT to model the behavior of each coefficient given the presence of a linear edge at a specified orientation --- the behavior of the wavelet coefficient given the state. By connecting the states together in a quadtree, the GHMT ties together wavelet coefficients along a contour, and also models how the contour itself behaves across scale. We demonstrate the effectiveness of the model by applying it to feature extraction.
Geometric Methods for Wavelet-Based Image Compression
(SPIE, 2003-08-01) Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Natural images can be viewed as combinations of smooth regions, textures, and geometry. Wavelet-based image coders, such as the space-frequency quantization (SFQ) algorithm, provide reasonably efficient representations for smooth regions (using zerotrees, for example) and textures (using scalar quantization) but do not properly exploit the geometric regularity imposed on wavelet coefficients by features such as edges. In this paper, we develop a representation for wavelet coefficients in geometric regions based on the wedgelet dictionary, a collection of geometric atoms that construct piecewise-linear approximations to contours. Our wedgeprint representation implicitly models the coherency among geometric wavelet coefficients. We demonstrate that a simple compression algorithm combining wedgeprints with zerotrees and scalar quantization can achieve near-optimal rate-distortion performance D(R) ~ (log R)Â²/RÂ² for the class of piecewise-smooth images containing smooth CÂ² regions separated by smooth CÂ² discontinuities. Finally, we extend this simple algorithm and propose a complete compression framework for natural images using a rate-distortion criterion to balance the three representations. Our Wedgelet-SFQ (WSFQ) coder outperforms SFQ in terms of visual quality and mean-square error.
Geometric Tools for Image Compression
(2002-11-01) Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Images typically contain strong geometric features, such as edges, that impose a structure on pixel values and wavelet coefficients. Modeling the joint coherent behavior of wavelet coefficients is difficult, and standard image coders fail to fully exploit this geometric regularity. We introduce wedgelets as a geometric tool for image compression. Wedgelets offer piecewise-linear approximations of edge contours and can be efficiently encoded. We describe the fundamental challenges that arise when applying such a tool to image compression. To meet these challenges, we also propose an efficient rate-distortion framework for natural image compression using wedgelets.
Hidden Markov Tree Modeling of Complex Wavelet Transforms
(2000-06-01) Choi, Hyeokho; Romberg, Justin; Baraniuk, Richard G.; Kingsbury, Nicholas G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
Multiresolution signal and image models such as the hidden Markov tree aim to capture the statistical structure of smooth and singular (edgy) regions. Unfortunately, models based on the orthogonal wavelet transform suffer from shift-variance, making them less accurate and realistic. In this paper, we extend the HMT modeling framework to the complex wavelet transform, which features near shift-invariance and improved angular resolution compared to the standard wavelet transform. The model is computationally efficient (with linear-time computation and processing algorithms) and applicable to general Bayesian inference problems as a prior density for the data. In a simple estimation experiment, the complex wavelet HMT model outperforms a number of high-performance denoising algorithms, including redundant wavelet thresholding (cycle spinning) and the redundant HMT.
Hidden Markov Tree Models for Complex Wavelet Transforms
(2002-05-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Kingsbury, Nicholas G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
Multiresolution models such as the hidden Markov tree (HMT) aim to capture the statistical structure of signals and images by leveraging two key wavelet transform properties: wavelet coefficients representing smooth/singular regions in a signal have small/large magnitude, and small/large magnitudes persist through scale. Unfortunately, the HMT based on the conventional (fully decimated) wavelet transform suffers from shift-variance, making it less accurate and realistic. In this paper, we extend the HMT modeling framework to the complex wavelet transform, which features near shift-invariance and improved directionality compared to the standard wavelet transform. The complex HMT model is computationally efficient (with linear-time computation and processing algorithms) and applicable to general Bayesian inference problems as a prior density for images. We demonstrate the effectiveness of the model with two applications. In a simple estimation experiment, the complex wavelet HMT model outperforms a number of high-performance denoising algorithms, including redundant wavelet thresholding (cycle spinning) and the redundant HMT. A multiscale maximum likelihood texture classification algorithm produces fewer errors with the new model than with a standard HMT.
Image Compression using an Efficient Edge Cartoon + Texture Model
(IEEE Computer Society, 2002-04-01) Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Wavelet-based image coders optimally represent smooth regions and isolated point singularities. However, wavelet coders are less adept at representing perceptually important edge singularities, and coding performance suffers significantly as a result. In this paper, we propose a novel two-stage image coder framework based on modeling images as edge cartoons + textures. In stage 1, we infer and efficiently code the edge information from the image using a multiscale wedgelet decomposition. In stage 2, we code the residual, "edgeless" texture image using a standard wavelet coder. Our preliminary coder improves significantly over standard wavelet coding techniques in terms of visual quality.
Multiplicative Multiscale Image Decompositions: Analysis and Modeling
(2000-07-01) Romberg, Justin; Riedi, Rudolf H.; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Multiscale processing, in particular using the wavelet transform, has emerged as an incredibly effective paradigm for signal processing and analysis. In this paper, we discuss a close relative of the Haar wavelet transform, the multiscale multiplicative decomposition. While the Haar transform captures the differences between signal approximations at different scales, the multiplicative decomposition captures their ratio. The multiplicative decomposition has many of the properties that have made wavelets so successful. Most notably, the multipliers are a sparse representation for smooth signals, they have a dependency structure similar to wavelet coefficients, and they can be calculated efficiently. The multiplicative decomposition is also a more natural signal representation than the wavelet transform for some problems. For example, it is extremely easy to incorporate positivity constraints into multiplier domain processing. In addition, there is a close relationship between the multiplicative decomposition and the Poisson process; a fact that has been exploited in the field of photon-limited imaging. In this paper, we will show that the multiplicative decomposition is also closely tied with the Kullback-Leibler distance between two signals. This allows us to derive an n-term KL approximation scheme using the multiplicative decomposition.
Multiscale Classification using Complex Wavelets and Hidden Markov Tree Models
(2000-09-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Kingsbury, Nicholas G.; Digital Signal Processing (http://dsp.rice.edu/)
Multiresolution signal and image models such as the hidden Markov tree (HMT) aim to capture the statistical structure of smooth and singular (textured and edgy) regions. Unfortunately, models based on the orthogonalwavelet transform suffer from shift-variance, making them less accurate and realistic. In this paper, we extend the HMT modeling framework to the complex wavelet transform, which features near shift-invariance and improved angular resolution compared to the standard wavelet transform. The model is computationally efficient (featuring linear-time computation and processing algorithms) and applicable to general Bayesian inference problems as a prior density for the data. In this paper, we develop a simple multiscale maximum likelihood classification scheme based on the complex wavelet HMT that outperforms those based on traditional real-valued wavelet transforms. The resulting classification can be used as a front end in a more sophisticated multiscale segmentation algorithm.
Multiscale Edge Grammars for Complex Wavelet Transforms
(2001-10-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
Wavelet domain algorithms have risen to the forefront of image processing. The power of these algorithms is derived from the fact that the wavelet transform restructures the image in a way that makes statistical modeling easier. Since the edge singularities in an image account for the most important information, understanding how edges behave in the wavelet domain is the key to modeling. In the past, wavelet-domain statistical models have codified the tendency for wavelet coefficients representing and edge to be large across scale. In this paper, we use the complex wavelet transform to uncover the phase behavior of wavelet coefficients representing an edge. This allows us to design a hidden Markov tree model that can discriminate between large magnitude wavelet coefficients caused by texture regions in the signal, and ones caused by edges.
Multiscale Geometric Image Processing
(2003-07-01) Romberg, Justin; Wakin, Michael; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Since their introduction a little more than 10 years ago, wavelets have revolutionized image processing. Wavelet based algorithms define the state-of-the-art for applications including image coding (JPEG2000), restoration, and segmentation. Despite their success, wavelets have significant shortcomings in their treatment of edges. Wavelets do not parsimoniously capture even the simplest geometrical structure in images, and wavelet based processing algorithms often produce images with ringing around the edges. As a first step towards accounting for this structure, we will show how to explicitly capture the geometric regularity of contours in cartoon images using the wedgelet representation and a multiscale geometry model. The wedgelet representation builds up an image out of simple piecewise constant functions with linear discontinuities. We will show how the geometry model, by putting a joint distribution on the orientations of the linear discontinuities, allows us to weigh several factors when choosing the wedgelet representation: the error between the representation and the original image, the parsimony of the representation, and whether the wedgelets in the representation form "natural" geometrical structures. Finally, we will analyze a simple wedgelet coder based on these principles, and show that it has optimal asymptotic performance for simple cartoon images.
Multiscale Image Segmentation Using Joint Texture and Shape Analysis
(2000-07-01) Neelamani, Ramesh; Romberg, Justin; Riedi, Rudolf H.; Choi, Hyeokho; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
We develop a general framework to simultaneously exploit texture and shape characterization in multiscale image segmentation. By posing multiscale segmentation as a model selection problem, we invoke the powerful framework offered by minimum description length (MDL). This framework dictates that multiscale segmentation comprises multiscale texture characterization and multiscale shape coding. Analysis of current multiscale maximum a posteriori (MAP) segmentation algorithms reveals that these algorithms implicitly use a shape coder with the aim to estimate the optimal MDL solution, but find only an approximate solution. Towards achieving better segmentation estimates, we first propose a shape coding algorithm based on zero-trees which is well-suited to represent images with large homogeneous regions. For this coder, we design an efficient tree-based algorithm using dynamic programming that attains the optimal MDL segmentation estimate. To incorporate arbitrary shape coding techniques into segmentation, we design an iterative algorithm that uses dynamic programming for each iteration. Though the iterative algorithm is not guaranteed to attain exactly optimal estimates, it more effectively captures the prior set by the shape coder. Experiments demonstrate that the proposed algorithms yield excellent segmentation results on both synthetic and real world data examples.
Multiscale Wedgelet Image Analysis: Fast Decompositions and Modeling
(2002-06-01) Romberg, Justin; Wakin, Michael; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
The most perceptually important features in images are geometrical, the most prevalent being the smooth contours ("edges") that separate different homogeneous regions and delineate distinct objects. Although wavelet based algorithms have enjoyed success in many areas of image processing, they have significant short-comings in their treatment of edges. Wavelets do not parsimoniously capture even the simplest geometrical structure in images, and as a result wavelet based processing algorithms often produce images with ringing around the edges. The multiscale wedgelet framework is a first step towards explicitly capturing geometrical structure in images. The framework has two components: decomposition and representation. The multiscale wavelet decomposition divides the image into dyadic blocks at different scales and projects these image blocks onto wedgelets - simple piecewise constant functions with linear discontinuities. The multiscale wedgelet representation is an approximation of the image built out of wedgelets from the decomposition. In choosing the wedgelets to form the representation, we can weigh several factors: the error between the representation and the original image, the parsimony of the representation, and whether the wedgelets in the representation form "natural" geometrical structure. In this paper, we show that an efficient multiscale wedgelet decomposition is possible if we carefully choose the set of possible wedgelet orientations. We also present a modeling framework that makes it possible to incorporate simple geometrical constraints into the choice of wedgelet representation, resulting in parsimonious image approximations with smooth contours.
Rate-Distortion Optimized Image Compression using Wedgelets
(2002-06-01) Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Most wavelet-based image coders fail to model the joint coherent behavior of wavelet coefficients near edges. Wedgelets offer a convenient parameterization for the edges in an image, but they have yet to yield a viable compression algorithm. In this paper, we propose an extension of the zerotree-based Space-Frequency Quantization (SFQ) algorithm by adding a wedgelet symbol to its tree-pruning optimization. This incorporates wedgelets into a rate-distortion compression framework and allows simple, coherent descriptions of the wavelet coefficients near edges. The resulting method yields improved visual quality and increased compression efficiency over the standard SFQ technique.
Shift-Invariant Denoising using Wavelet-Domain Hidden Markov Trees
(1999-10-20) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint statistics of the wavelet coefficients of realworld data. One potential drawback to the HMT framework is the need for computationally expensive iterative training (using the EM algorithm, for example). In this paper, we use image structure not yet recognized by the HMT to show that the HMT parameters of real-world, grayscale images have a certain form. This leads to a description of the HMT model with just nine meta-parameters (independent of the size of the image and the number of wavelet scales). We also observe that these nine meta-parameters are similar for many images. This leads to a universal HMT (uHMT) model for grayscale images. Algorithms using the uHMT require no training of any kind. While simple, a series of image estimation/denoising experiments show that the uHMT retains nearly all of the key structures modeled by the full HMT. Based on the uHMT model, we develop a shift-invariant wavelet denoising scheme that outperforms all algorithms in the current literature.

Browsing by Author "Romberg, Justin"

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