Graphical models, such as Bayesian networks and Markov RandomFields represent statistical depende... more Graphical models, such as Bayesian networks and Markov RandomFields represent statistical dependencies of variables by agraph. Local "belief propagation" rules of the sort proposed byPearl [18] are guaranteed to converge to the correct posterior probabilitiesin singly connected graphical models. Recently, a numberof researchers have empirically demonstrated good performance of"loopy belief propagation"--using these same rules on graphs withloops. Perhaps the most
Page 1. A Probabilistic Approach to the Design of Structural Selectivity of Proteins Thesis submi... more Page 1. A Probabilistic Approach to the Design of Structural Selectivity of Proteins Thesis submitted for the degree of Doctor of Philosophy By Menachem Fromer SUBMITTED TO THE SENATE OF THE HEBREW UNIVERSITY OF JERUSALEM June 2010 Page 2. ...
Side-chainpredictionisanimportantsubtaskintheprotein-folding problem. We show that flnding a mini... more Side-chainpredictionisanimportantsubtaskintheprotein-folding problem. We show that flnding a minimal energy side-chain con- flguration is equivalent to performing inference in an undirected graphical model. The graphical model is relatively sparse yet has manycycles. Weusedthisequivalencetoassesstheperformanceof approximate inference algorithms in a real-world setting. Specifl- callywecomparedbeliefpropagation(BP),generalizedBP(GBP) and naive mean fleld (MF). In cases where exact inference was possible, max-product BP al- ways found the global
The problem of finding the most probable (MAP) configuration i n graphical models comes up in a w... more The problem of finding the most probable (MAP) configuration i n graphical models comes up in a wide range of applications. In a general graphical model this problem is NP hard, but various approximate algorithms have been developed. Linear programming (LP) relaxations are a standard method in computer science for approximating combinatorial problems and have been used for finding the
Matrix factorization is a fundamental building block in many com- puter vision and machine learni... more Matrix factorization is a fundamental building block in many com- puter vision and machine learning algorithms. In this work we focus on the prob- lem of "structure from motion" in which one wishes to recover the camera motion and the 3D coordinates of certain points given their 2D locations. This problem may be reduced to a low rank factorization problem. When all the 2D locations are known, singular value decomposition yields a least squares factorization of the measurements matrix. In realistic scenarios this assumption does not hold: some of the data is missing, the measurements have correlated noise, and the scene may contain multiple objects. Under these conditions, most existing fac- torization algorithms fail while human perception is relat ively unchanged. In this work we present an EM algorithm for matrix factorization that takes advantage of prior information and imposes strict constraints on the r esulting matrix factors. We present results on challenging sequences.
2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007
Many low-level vision algorithms assume a prior probability over images, and there has been great... more Many low-level vision algorithms assume a prior probability over images, and there has been great interest in trying to learn this prior from examples. Since images are very non Gaussian, high dimensional, continuous signals, learning their distribution presents a tremendous computational challenge. Perhaps the most successful recent algorithm is the Fields of Experts (FOE) [20] model which has shown impressive performance by modeling image statistics with a product of potentials defined on filter outputs. However, as in previous models of images based on filter outputs [30], calculating the probability of an image given the model requires evaluating an intractable partition function. This makes learning very slow (requires Monte-Carlo sampling at every step) and makes it virtually impossible to compare the likelihood of two different models. Given this computational difficulty, it is hard to say whether nonintuitive features learned by such models represent a true property of natural images or an artifact of the approximations used during learning.
Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, 2005
A wide range of low level vision problems have been formulated in terms of finding the most proba... more A wide range of low level vision problems have been formulated in terms of finding the most probable assignment of a Markov Random Field (or equivalently the lowest energy configuration). Perhaps the most successful example is stereo vision. For the stereo problem, it has been shown that finding the global optimum is NP hard but good results have been obtained using a number of approximate optimization algorithms.
This discussion document records an email conversation in preparation for the Triestemeeting.Back... more This discussion document records an email conversation in preparation for the Triestemeeting.BackgroundThe result that `belief propagation xed-points are zero gradient points of the Bethe free energy"(Yedidia, 2000; Yedidia et al., 2000c) is an interesting one, since the sum-product algorithm (orbelief propagation) has proved so useful for decoding sparse graph codes. The sort of interestingideas motivated by this idea include: One
International Joint Conference on Artificial Intelligence, 2003
"Inference" problems arise in statistical physics, computer vision, error - correcting ... more "Inference" problems arise in statistical physics, computer vision, error - correcting coding theory, and AI We explain the principles behind the belief propagation (BP) algorithm, which is an efficient way to solve inference problems based on passing lo - cal messages We develop a unified approach, with examples, notation, and graphical models borrowed from the relevant disciplines We explain
Belief propagation (BP) was only supposed to work for tree-like networks but works surprisingly w... more Belief propagation (BP) was only supposed to work for tree-like networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it finds for general graphs. We show that BP can only converge to a stationary point of an approximate free
We propose a generalized belief propagation (GBP) receiver for two-dimensional (2-D) channels wit... more We propose a generalized belief propagation (GBP) receiver for two-dimensional (2-D) channels with memory, which is applicative to 2-D intersymbol interference (ISI) equalization and multi-user detection (MUD). Our experimental study demonstrates that under non-trivial interference conditions, the performance of this fully tractable GBP receiver is almost identical to the performance of the optimal maximum a-posteriori (MAP) receiver.
Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., 2004
... Kobi Levi and Yair Weiss School of Computer Science and Engineering The Hebrew University of ... more ... Kobi Levi and Yair Weiss School of Computer Science and Engineering The Hebrew University of Jerusalem 91904 Jerusalem, Israel {kobilevi,yweiss ... W.Freeman and M.Roth [2] developed a method for hand gesture recognition based on the global orientation histogram of the ...
2004 Conference on Computer Vision and Pattern Recognition Workshop, 2004
In the last few years, object detection techniques have progressed immensely. Impressive detectio... more In the last few years, object detection techniques have progressed immensely. Impressive detection results have been achieved for many objects such as faces and cars . The robustness of these systems emerges from a training stage utilizing thousands of positive examples. One approach to enable learning from a small set of training examples is to find an efficient set of features that accurately represent the target object. Unfortunately, automatically selecting such a feature set is a difficult task in itself.
2007 Information Theory and Applications Workshop, 2007
Generalized belief propagation (GBP) algorithm has been shown recently to infer the a-posteriori ... more Generalized belief propagation (GBP) algorithm has been shown recently to infer the a-posteriori probabilities of finite-state input two-dimensional (2-D) Gaussian channels with memory in a practically accurate manner, thus enabling nearoptimal estimation of the transmitted symbols and the Shannontheoretic information rates. In this note, a rationalization of this excellent performance of GBP is addressed.
The quality of image stitching is measured by the similarity of the stitched image to each of the... more The quality of image stitching is measured by the similarity of the stitched image to each of the input images, and by the visibility of the seam between the stitched images. In order to define and get the best possible stitching, we introduce several formal cost functions for the evaluation of the quality of stitching. In these cost functions, the similarity to the input images and the visibility of the seam are defined in the gradient domain, minimizing the disturbing edges along the seam. A good image stitching will optimize these cost functions, overcoming both photometric inconsistencies and geometric misalignments between the stitched images. This approach is demonstrated in various applications, including generation of panoramic images, object blending, and removal of compression artifacts. Comparisons with existing methods show the benefits of optimizing the measures in the gradient domain.
Graphical models, such as Bayesian networks and Markov RandomFields represent statistical depende... more Graphical models, such as Bayesian networks and Markov RandomFields represent statistical dependencies of variables by agraph. Local "belief propagation" rules of the sort proposed byPearl [18] are guaranteed to converge to the correct posterior probabilitiesin singly connected graphical models. Recently, a numberof researchers have empirically demonstrated good performance of"loopy belief propagation"--using these same rules on graphs withloops. Perhaps the most
Page 1. A Probabilistic Approach to the Design of Structural Selectivity of Proteins Thesis submi... more Page 1. A Probabilistic Approach to the Design of Structural Selectivity of Proteins Thesis submitted for the degree of Doctor of Philosophy By Menachem Fromer SUBMITTED TO THE SENATE OF THE HEBREW UNIVERSITY OF JERUSALEM June 2010 Page 2. ...
Side-chainpredictionisanimportantsubtaskintheprotein-folding problem. We show that flnding a mini... more Side-chainpredictionisanimportantsubtaskintheprotein-folding problem. We show that flnding a minimal energy side-chain con- flguration is equivalent to performing inference in an undirected graphical model. The graphical model is relatively sparse yet has manycycles. Weusedthisequivalencetoassesstheperformanceof approximate inference algorithms in a real-world setting. Specifl- callywecomparedbeliefpropagation(BP),generalizedBP(GBP) and naive mean fleld (MF). In cases where exact inference was possible, max-product BP al- ways found the global
The problem of finding the most probable (MAP) configuration i n graphical models comes up in a w... more The problem of finding the most probable (MAP) configuration i n graphical models comes up in a wide range of applications. In a general graphical model this problem is NP hard, but various approximate algorithms have been developed. Linear programming (LP) relaxations are a standard method in computer science for approximating combinatorial problems and have been used for finding the
Matrix factorization is a fundamental building block in many com- puter vision and machine learni... more Matrix factorization is a fundamental building block in many com- puter vision and machine learning algorithms. In this work we focus on the prob- lem of "structure from motion" in which one wishes to recover the camera motion and the 3D coordinates of certain points given their 2D locations. This problem may be reduced to a low rank factorization problem. When all the 2D locations are known, singular value decomposition yields a least squares factorization of the measurements matrix. In realistic scenarios this assumption does not hold: some of the data is missing, the measurements have correlated noise, and the scene may contain multiple objects. Under these conditions, most existing fac- torization algorithms fail while human perception is relat ively unchanged. In this work we present an EM algorithm for matrix factorization that takes advantage of prior information and imposes strict constraints on the r esulting matrix factors. We present results on challenging sequences.
2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007
Many low-level vision algorithms assume a prior probability over images, and there has been great... more Many low-level vision algorithms assume a prior probability over images, and there has been great interest in trying to learn this prior from examples. Since images are very non Gaussian, high dimensional, continuous signals, learning their distribution presents a tremendous computational challenge. Perhaps the most successful recent algorithm is the Fields of Experts (FOE) [20] model which has shown impressive performance by modeling image statistics with a product of potentials defined on filter outputs. However, as in previous models of images based on filter outputs [30], calculating the probability of an image given the model requires evaluating an intractable partition function. This makes learning very slow (requires Monte-Carlo sampling at every step) and makes it virtually impossible to compare the likelihood of two different models. Given this computational difficulty, it is hard to say whether nonintuitive features learned by such models represent a true property of natural images or an artifact of the approximations used during learning.
Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, 2005
A wide range of low level vision problems have been formulated in terms of finding the most proba... more A wide range of low level vision problems have been formulated in terms of finding the most probable assignment of a Markov Random Field (or equivalently the lowest energy configuration). Perhaps the most successful example is stereo vision. For the stereo problem, it has been shown that finding the global optimum is NP hard but good results have been obtained using a number of approximate optimization algorithms.
This discussion document records an email conversation in preparation for the Triestemeeting.Back... more This discussion document records an email conversation in preparation for the Triestemeeting.BackgroundThe result that `belief propagation xed-points are zero gradient points of the Bethe free energy"(Yedidia, 2000; Yedidia et al., 2000c) is an interesting one, since the sum-product algorithm (orbelief propagation) has proved so useful for decoding sparse graph codes. The sort of interestingideas motivated by this idea include: One
International Joint Conference on Artificial Intelligence, 2003
"Inference" problems arise in statistical physics, computer vision, error - correcting ... more "Inference" problems arise in statistical physics, computer vision, error - correcting coding theory, and AI We explain the principles behind the belief propagation (BP) algorithm, which is an efficient way to solve inference problems based on passing lo - cal messages We develop a unified approach, with examples, notation, and graphical models borrowed from the relevant disciplines We explain
Belief propagation (BP) was only supposed to work for tree-like networks but works surprisingly w... more Belief propagation (BP) was only supposed to work for tree-like networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it finds for general graphs. We show that BP can only converge to a stationary point of an approximate free
We propose a generalized belief propagation (GBP) receiver for two-dimensional (2-D) channels wit... more We propose a generalized belief propagation (GBP) receiver for two-dimensional (2-D) channels with memory, which is applicative to 2-D intersymbol interference (ISI) equalization and multi-user detection (MUD). Our experimental study demonstrates that under non-trivial interference conditions, the performance of this fully tractable GBP receiver is almost identical to the performance of the optimal maximum a-posteriori (MAP) receiver.
Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., 2004
... Kobi Levi and Yair Weiss School of Computer Science and Engineering The Hebrew University of ... more ... Kobi Levi and Yair Weiss School of Computer Science and Engineering The Hebrew University of Jerusalem 91904 Jerusalem, Israel {kobilevi,yweiss ... W.Freeman and M.Roth [2] developed a method for hand gesture recognition based on the global orientation histogram of the ...
2004 Conference on Computer Vision and Pattern Recognition Workshop, 2004
In the last few years, object detection techniques have progressed immensely. Impressive detectio... more In the last few years, object detection techniques have progressed immensely. Impressive detection results have been achieved for many objects such as faces and cars . The robustness of these systems emerges from a training stage utilizing thousands of positive examples. One approach to enable learning from a small set of training examples is to find an efficient set of features that accurately represent the target object. Unfortunately, automatically selecting such a feature set is a difficult task in itself.
2007 Information Theory and Applications Workshop, 2007
Generalized belief propagation (GBP) algorithm has been shown recently to infer the a-posteriori ... more Generalized belief propagation (GBP) algorithm has been shown recently to infer the a-posteriori probabilities of finite-state input two-dimensional (2-D) Gaussian channels with memory in a practically accurate manner, thus enabling nearoptimal estimation of the transmitted symbols and the Shannontheoretic information rates. In this note, a rationalization of this excellent performance of GBP is addressed.
The quality of image stitching is measured by the similarity of the stitched image to each of the... more The quality of image stitching is measured by the similarity of the stitched image to each of the input images, and by the visibility of the seam between the stitched images. In order to define and get the best possible stitching, we introduce several formal cost functions for the evaluation of the quality of stitching. In these cost functions, the similarity to the input images and the visibility of the seam are defined in the gradient domain, minimizing the disturbing edges along the seam. A good image stitching will optimize these cost functions, overcoming both photometric inconsistencies and geometric misalignments between the stitched images. This approach is demonstrated in various applications, including generation of panoramic images, object blending, and removal of compression artifacts. Comparisons with existing methods show the benefits of optimizing the measures in the gradient domain.
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