Karl, William C.
Overview
Works:  8 works in 12 publications in 1 language and 14 library holdings 

Classifications:  TJ217.5, 
Publication Timeline
.
Most widely held works by
William C Karl
A distributed and iterative method for square root filtering in spacetime estimation by Toshio M Chin(
Book
)
4 editions published in 1994 in English and held by 4 WorldCat member libraries worldwide
We describe a distribute, and iterative approach to perform the unitary transformations in the square root information filter imple nentation of the Kalman filter, providing an alternative to the common QR factorizationbased approaches. The new approach is useful in approximate computation of filtered estimates for temporallyevolving random fields defined by local interactions and observations. Using several examples motivated by computer vision applications, we demonstrate that nearoptimal estimates can be computed for problems of practical importance using only a small number of iterations, which can be performed in a finely parallel manner over the spatial domain of the random field
4 editions published in 1994 in English and held by 4 WorldCat member libraries worldwide
We describe a distribute, and iterative approach to perform the unitary transformations in the square root information filter imple nentation of the Kalman filter, providing an alternative to the common QR factorizationbased approaches. The new approach is useful in approximate computation of filtered estimates for temporallyevolving random fields defined by local interactions and observations. Using several examples motivated by computer vision applications, we demonstrate that nearoptimal estimates can be computed for problems of practical importance using only a small number of iterations, which can be performed in a finely parallel manner over the spatial domain of the random field
Sequential optical flow estimation using temporal coherence by Toshio M Chin(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
A theory for multiscale stochastic realization by William W Irving(
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Multiscale Representations of Markov Random Fields(
)
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
Recently, a framework for multiscale stochastic modeling was introduced based on coarsetofine scalerecursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. In this paper, we show that this model class is also quite rich. In particular, we describe how 1D Markov processes and 2D Markov random fields (MRF's) can be represented within this framework. The recursive structure of 1D Markov processes makes them simple to analyze, and generally leads to computationally efficient algorithms for statistical inference. On the other hand, 2D MRF's are well known to be very difficult to analyze due to their noncausal structure, and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification. In contrast, our multiscale representations are based on scalerecursive models and thus lead naturally to scalerecursive algorithms, which can be substantially more efficient computationally than those associated with MRF models. In 1D, the multiscale representation is a generalization of the midpoint deflection construction of Brownian motion. The representation of 2D MRF's is based on a further generalization to a "midline" deflection construction. The exact representations of 2D MRF's are used to motivate a class of multiscale approximate MRF models based on onedimensional wavelet transforms. We demonstrate the use of these latter models in the context of texture representation and, in particular, we show how they can be used as approximations for or alternatives to wellknown MRF texture models
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
Recently, a framework for multiscale stochastic modeling was introduced based on coarsetofine scalerecursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. In this paper, we show that this model class is also quite rich. In particular, we describe how 1D Markov processes and 2D Markov random fields (MRF's) can be represented within this framework. The recursive structure of 1D Markov processes makes them simple to analyze, and generally leads to computationally efficient algorithms for statistical inference. On the other hand, 2D MRF's are well known to be very difficult to analyze due to their noncausal structure, and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification. In contrast, our multiscale representations are based on scalerecursive models and thus lead naturally to scalerecursive algorithms, which can be substantially more efficient computationally than those associated with MRF models. In 1D, the multiscale representation is a generalization of the midpoint deflection construction of Brownian motion. The representation of 2D MRF's is based on a further generalization to a "midline" deflection construction. The exact representations of 2D MRF's are used to motivate a class of multiscale approximate MRF models based on onedimensional wavelet transforms. We demonstrate the use of these latter models in the context of texture representation and, in particular, we show how they can be used as approximations for or alternatives to wellknown MRF texture models
Wavelet Packet Based Transient Signal Classification(
)
1 edition published in 2006 in English and held by 0 WorldCat member libraries worldwide
Nonstationary signals are not well suited for detection and classification by traditional Fourier methods. An alternate means of analysis needs to be employed so that valuable timefrequency information is not lost. The wavelet packet transform is one such timefrequency analysis tool. This paper summarizes which examine the feasibility of applying the wavelet packet transform to automatic transient signal classification through the development of a classification algorithm for biologically generated underwater acoustic signals in ocean noise. The formulation of a wavelet packet based feature set specific to the classification of snapping shrimp and whale clicks is given
1 edition published in 2006 in English and held by 0 WorldCat member libraries worldwide
Nonstationary signals are not well suited for detection and classification by traditional Fourier methods. An alternate means of analysis needs to be employed so that valuable timefrequency information is not lost. The wavelet packet transform is one such timefrequency analysis tool. This paper summarizes which examine the feasibility of applying the wavelet packet transform to automatic transient signal classification through the development of a classification algorithm for biologically generated underwater acoustic signals in ocean noise. The formulation of a wavelet packet based feature set specific to the classification of snapping shrimp and whale clicks is given
Reconstructing Binary Polygonal Objects From Projections: A Statistical View(
)
1 edition published in 1994 in English and held by 0 WorldCat member libraries worldwide
In many applications of tomography, the fundamental quantities of interest in an image are geometric ones. In these instances, pixel based signal processing and reconstruction is at best inefficient, and at worst, nonrobust in its use of the available tomographic data. Classical reconstruction techniques such as Filtered BackProjection tend to produce spurious features when data is sparse and noisy; and these \ghosts" further complicate the process of extracting what is often a limited number of rather simple geometric features. In this paper we present a framework that, in its most general form, is a statistically optimal technique for the extraction of specific geometric features of objects directly from the noisy projection data. We focus on the tomographic reconstruction of binary polygonal objects from sparse and noisy data. In our setting, the tomographic reconstruction problem is essentially formulated as a (finite dimensional) parameter estimation problem. In particular, the vertices of binary polygons are used as their defining parameters. Under the assumption that the projection data are corrupted by Gaussian white noise, we use the Maximum Likelihood (ML) criterion, when the number of parameters is assumed known, and the Minimum Description Length (MDL) criterion for reconstruction when the number of parameters is not known. The resulting optimization problems are nonlinear and thus are plagued by numerous extraneous local extreme, making their solution far from trivial. In particular, proper initialization of any iterative technique is essential for good performance. To this end, we provide a novel method to construct a reliable yet simple initial guess for the solution. This procedure is based on the estimated moments of the object, which may be conveniently obtained directly from the noisy projection data
1 edition published in 1994 in English and held by 0 WorldCat member libraries worldwide
In many applications of tomography, the fundamental quantities of interest in an image are geometric ones. In these instances, pixel based signal processing and reconstruction is at best inefficient, and at worst, nonrobust in its use of the available tomographic data. Classical reconstruction techniques such as Filtered BackProjection tend to produce spurious features when data is sparse and noisy; and these \ghosts" further complicate the process of extracting what is often a limited number of rather simple geometric features. In this paper we present a framework that, in its most general form, is a statistically optimal technique for the extraction of specific geometric features of objects directly from the noisy projection data. We focus on the tomographic reconstruction of binary polygonal objects from sparse and noisy data. In our setting, the tomographic reconstruction problem is essentially formulated as a (finite dimensional) parameter estimation problem. In particular, the vertices of binary polygons are used as their defining parameters. Under the assumption that the projection data are corrupted by Gaussian white noise, we use the Maximum Likelihood (ML) criterion, when the number of parameters is assumed known, and the Minimum Description Length (MDL) criterion for reconstruction when the number of parameters is not known. The resulting optimization problems are nonlinear and thus are plagued by numerous extraneous local extreme, making their solution far from trivial. In particular, proper initialization of any iterative technique is essential for good performance. To this end, we provide a novel method to construct a reliable yet simple initial guess for the solution. This procedure is based on the estimated moments of the object, which may be conveniently obtained directly from the noisy projection data
Foundations of Automatic Target Recognition(
)
1 edition published in 2010 in English and held by 0 WorldCat member libraries worldwide
The research funded under this grant focused on several key challenges arising in automatic target recognition (ATR) systems. The robust estimation of geometric features is a critical aspect of ATR systems and thus methods for robust boundary extraction and feature enhancement were developed based on both statistical modeling and compressed sensing. Another set of challenges was related to novel, nonconventional sensing geometries arising in modern layeredsensing systems. Traditional sensing has focused on single sensors and single aspects, e.g. conventional monostatic, narrow aspect SAR. But as new sensing paradigms are considered, new methods for image estimation and processing are needed. In response, novel, robust methods for wideangle image formation and multistatic multisensor data fusion were developed, based on powerful sparsity constraints. In addition, recent methods from compressed sensing were applied to SAR imaging problems of interest to the Air Force to reduce sampling requirements and improve robustness. Finally, imaging of scenes with moving targets has become a problem of great interest to AFRL. In response new methods for the formation and treatment of scenes with motion were developed based on over complete dictionaries
1 edition published in 2010 in English and held by 0 WorldCat member libraries worldwide
The research funded under this grant focused on several key challenges arising in automatic target recognition (ATR) systems. The robust estimation of geometric features is a critical aspect of ATR systems and thus methods for robust boundary extraction and feature enhancement were developed based on both statistical modeling and compressed sensing. Another set of challenges was related to novel, nonconventional sensing geometries arising in modern layeredsensing systems. Traditional sensing has focused on single sensors and single aspects, e.g. conventional monostatic, narrow aspect SAR. But as new sensing paradigms are considered, new methods for image estimation and processing are needed. In response, novel, robust methods for wideangle image formation and multistatic multisensor data fusion were developed, based on powerful sparsity constraints. In addition, recent methods from compressed sensing were applied to SAR imaging problems of interest to the Air Force to reduce sampling requirements and improve robustness. Finally, imaging of scenes with moving targets has become a problem of great interest to AFRL. In response new methods for the formation and treatment of scenes with motion were developed based on over complete dictionaries
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Related Identities
 Willsky, Alan S.
 Chin, Toshio M. Author
 Center for Intelligent Control Systems (U.S.)
 MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
 SRI INTERNATIONAL MENLO PARK CA
 Bigelow, Elsie Karl
 BOSTON UNIV MA
 MASSACHUSETTS INST OF TECH CAMBRIDGE
 Karl, William Raymond 1915
 Karl, Rudolph
Associated Subjects