Karl, William Clement
Overview
Works:  25 works in 59 publications in 1 language and 79 library holdings 

Roles:  Author 
Classifications:  TJ217.5, 
Publication Timeline
.
Most widely held works by
William Clement Karl
Optical flow computation via multiscale regularizations by M. R Luettgen(
Book
)
4 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
The apparent motion of brightness patterns in an image is referred to as the optical flow. In computational vision, optical flow is an important input into higher level vision algorithms performing tasks such as segmentation, tracking, object detection, robot guidance and recovery of shape information. In addition, methods for computing optical flow are an essential part of motion compensated coding schemes. In this paper, we present a new approach to the problem of computing optical flow. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation which arises from the often used "smoothness constraint" regularization term. We utilize the interpretation of the smoothness constraint as a "fractal prior" to motivate regularization based on a recently introduced class of multiscale stochastic models. These models are associated with efficient multiscale smoothing algorithms, and experiments on several image sequences demonstrate the substantial computational savings that can be achieved through their use
4 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
The apparent motion of brightness patterns in an image is referred to as the optical flow. In computational vision, optical flow is an important input into higher level vision algorithms performing tasks such as segmentation, tracking, object detection, robot guidance and recovery of shape information. In addition, methods for computing optical flow are an essential part of motion compensated coding schemes. In this paper, we present a new approach to the problem of computing optical flow. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation which arises from the often used "smoothness constraint" regularization term. We utilize the interpretation of the smoothness constraint as a "fractal prior" to motivate regularization based on a recently introduced class of multiscale stochastic models. These models are associated with efficient multiscale smoothing algorithms, and experiments on several image sequences demonstrate the substantial computational savings that can be achieved through their use
Reconstructing objects from projections by
William Clement Karl(
Book
)
4 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
The classical theory of surfaces and support functions is extended to the discrete, general dimensional case, enabling the development of a linear, local consistency test for a set of support measurements. The close tie between consistency and curvature is exploited to develop various discrete definitions of surface curvature for use as measures of smoothness. Global definitions of smoothness based on the isoperimetric inequality are also provided. This thesis contributes to the field of reconstruction from projections by extending and clarifying previous work on the planar case, by providing computationally attractive solutions to certain problems, and by suggesting new approaches to existing issues."
4 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
The classical theory of surfaces and support functions is extended to the discrete, general dimensional case, enabling the development of a linear, local consistency test for a set of support measurements. The close tie between consistency and curvature is exploited to develop various discrete definitions of surface curvature for use as measures of smoothness. Global definitions of smoothness based on the isoperimetric inequality are also provided. This thesis contributes to the field of reconstruction from projections by extending and clarifying previous work on the planar case, by providing computationally attractive solutions to certain problems, and by suggesting new approaches to existing issues."
Reconstructing ellipsoids from projections by
William Clement Karl(
Book
)
3 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Local tests for consistency of support hyperplane data(
Book
)
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
Efficient multiscale regularization with applications to the computation of optical flow by M. R Luettgen(
Book
)
4 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
A new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation which arises from the often used "smoothness constraint" type regularization. We utilize the interpretation of the smoothness constraint as a "fractal prior" to motivate regularization based on a recently introduced class of multiscale stochastic models. The solution of the new problem formulation is computed with an efficient multiscale algorithm
4 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
A new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation which arises from the often used "smoothness constraint" type regularization. We utilize the interpretation of the smoothness constraint as a "fractal prior" to motivate regularization based on a recently introduced class of multiscale stochastic models. The solution of the new problem formulation is computed with an efficient multiscale algorithm
Curvatures of surfaces and their shadows by
William Clement Karl(
Book
)
3 editions published in 1989 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1989 in English and held by 4 WorldCat member libraries worldwide
A fast multiscale tomographic reconstruction method from complete but possibly noisy projection data by M Bhatia(
Book
)
3 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
Reconstructing parametrized objects from projections : a statistical view by
Peyman Milanfar(
Book
)
3 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
Statistical approaches to the tomographic reconstruction of finitely parameterized geometric objects by
Peyman Milanfar(
Book
)
3 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Recovering the moments of a function from its radontransform projections : necessary and sufficient conditions by
Peyman Milanfar(
Book
)
3 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Momentbased variational approach to tomographic reconstruction by
Peyman Milanfar(
Book
)
3 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
Sequential filtering multiframe visual reconstruction by T. M Chin(
Book
)
3 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide
Using natural wavelet bases and multiscale stochastic models for tomographic reconstruction by M Bhatia(
Book
)
4 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
We use a multiscale natural pixel type representation of an object, originally developed for incomplete data problems, to construct nearly orthonormal basis functions. The coefficients of expansion of an object in these basis functions are obtained as the 1D wavelet transform of the (strip integral) projections of the object. This enables us to formulate a multiscale tomographic reconstruction technique wherein the object is reconstructed at multiple scales or resolutions. A complete reconstruction is obtained by combining the reconstructions at different scales. The nearly orthonormal behavior of the basis functions results in a system matrix, relating the input (the object coefficients) and the output (the projection data), which is extremely sparse. The system matrix, in addition to being sparse, is wellconditioned and has a symmetric blockToeplitz structure if the angular projections are uniformly spaced between 0 degrees and 180 degrees. Fast inversion algorithms exist for these matrices. The multiscale reconstruction technique can find applications in object feature recognition directly from projection data, tackling illposed imaging problems where the projection data are incomplete and/or noisy, and construction of multiscale stochastic models for which fast estimation algorithms exist. In this paper, we include examples illustrating the above applications of our multiscale reconstruction technique
4 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
We use a multiscale natural pixel type representation of an object, originally developed for incomplete data problems, to construct nearly orthonormal basis functions. The coefficients of expansion of an object in these basis functions are obtained as the 1D wavelet transform of the (strip integral) projections of the object. This enables us to formulate a multiscale tomographic reconstruction technique wherein the object is reconstructed at multiple scales or resolutions. A complete reconstruction is obtained by combining the reconstructions at different scales. The nearly orthonormal behavior of the basis functions results in a system matrix, relating the input (the object coefficients) and the output (the projection data), which is extremely sparse. The system matrix, in addition to being sparse, is wellconditioned and has a symmetric blockToeplitz structure if the angular projections are uniformly spaced between 0 degrees and 180 degrees. Fast inversion algorithms exist for these matrices. The multiscale reconstruction technique can find applications in object feature recognition directly from projection data, tackling illposed imaging problems where the projection data are incomplete and/or noisy, and construction of multiscale stochastic models for which fast estimation algorithms exist. In this paper, we include examples illustrating the above applications of our multiscale reconstruction technique
Estimation of dynamically evolving ellipsoids with applications to medical imaging by
S Jaggi(
Book
)
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Multiresolution statistical analysis and assimilation of large ocean data sets by Paul Werner Fieguth(
Book
)
2 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
A sufficient condition for the stability of interval matrix polynomials by
William Clement Karl(
Book
)
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
Control of vibrational systems by
William Clement Karl(
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
Probabilistc and sequential computation of optical flow using temporal coherence by Toshio M Chin(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Processing of MR images of the human brain(
Book
)
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
Multiscale object recognition and feature extraction using wavelet networks (U)(
)
1 edition published in 1995 in English and held by 0 WorldCat member libraries worldwide
In this work we present a novel method of object recognition and feature generation based on multiscale object descriptions obtained using wavelet networks in combination with morphological filtering. First morphological filtering techniques are used to obtain structural information about the object. Then, wavelet networks are used to extract or capture geometric information about an object at a series of scales. A wavelet network is of the form of a 11/2 layer neural network with the sigmoid functions replaced by wavelet functions. Like neural networks, wavelet networks are universal approximators. In contrast to neural networks, the initialization of a wavelet network follows directly from a commonly known transformation namely, the discrete dyadic wavelet decomposition. In contrast to a dyadic wavelet decomposition, the wavelet parameters are then allowed to vary to fit the data. Although developed in the context of function approximation, wavelet networks naturally fit in this object recognition framework because of the geometric nature of the network parameters (i.e. translations, rotations, and dilations). Wavelet networks are the basis for a hierarchical object recognition scheme where the wavelet network representation of the object at each scale is a feature vector which may be used to classify the object. At coarse scales, the feature vector is used to narrow the field of possible objects and to yield pose information. This information may also be used to generate candidate matches between the data and more detailed object models. The wavelet network representation at finer scales is then used to identify the object from this reduced space of possible objects. In keeping with our proposed integrated approach to ATD/R we demonstrate how wavelet networks may be applied to anomaly suppression in laser range images by fitting a multiresolution wavelet basis to the data in conjunction with the expectationmaximization (EM) algorithm
1 edition published in 1995 in English and held by 0 WorldCat member libraries worldwide
In this work we present a novel method of object recognition and feature generation based on multiscale object descriptions obtained using wavelet networks in combination with morphological filtering. First morphological filtering techniques are used to obtain structural information about the object. Then, wavelet networks are used to extract or capture geometric information about an object at a series of scales. A wavelet network is of the form of a 11/2 layer neural network with the sigmoid functions replaced by wavelet functions. Like neural networks, wavelet networks are universal approximators. In contrast to neural networks, the initialization of a wavelet network follows directly from a commonly known transformation namely, the discrete dyadic wavelet decomposition. In contrast to a dyadic wavelet decomposition, the wavelet parameters are then allowed to vary to fit the data. Although developed in the context of function approximation, wavelet networks naturally fit in this object recognition framework because of the geometric nature of the network parameters (i.e. translations, rotations, and dilations). Wavelet networks are the basis for a hierarchical object recognition scheme where the wavelet network representation of the object at each scale is a feature vector which may be used to classify the object. At coarse scales, the feature vector is used to narrow the field of possible objects and to yield pose information. This information may also be used to generate candidate matches between the data and more detailed object models. The wavelet network representation at finer scales is then used to identify the object from this reduced space of possible objects. In keeping with our proposed integrated approach to ATD/R we demonstrate how wavelet networks may be applied to anomaly suppression in laser range images by fitting a multiresolution wavelet basis to the data in conjunction with the expectationmaximization (EM) algorithm
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Related Identities
 Willsky, Alan S.
 Center for Intelligent Control Systems (U.S.)
 Massachusetts Institute of Technology Laboratory for Information and Decision Systems
 Verghese, George C.
 Milanfar, Peyman Author
 Bhatia, M. Author
 Luettgen, Mark R. (Mark Robert) Author
 Chin, Toshio M. Author
 MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
 Fieguth, Paul Werner 1968 Author
Alternative Names
Karl, W. C.
Karl, W. C. (William Clement)
Karl, W. Clem
Karl, W. Clem (William Clem)
Languages