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## Learning low-level vision (2000)

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Venue: | International Journal of Computer Vision |

Citations: | 578 - 30 self |

### Citations

8903 |
Probabilistic reasoning in intelligent systems: networks of plausible inference.
- Pearl
- 1988
(Show Context)
Citation Context ...ring local scene regions. The former allows initial scene estimates; the later allows the estimates to propagate. We train from image/scene pairs and apply the Bayesian machinery of graphical models (=-=Pearl, 1988-=-; Binford et al., 1988; Jordan, 1998). We were in uenced by the work of Weiss (Weiss, 1997), who pointed out the speed advantage of Bayesian methods over conventional relaxation methods for propagatin... |

6603 |
Neural Networks for Pattern Recognition
- Bishop
- 1995
(Show Context)
Citation Context ..., d. We undo this normalization after scene inference. We extracted center-aligned 7x7 and 3x3 pixel patches, Fig. 3, from the training images and scenes. Applying Principal Components Analysis (PCA) =-=[6]-=- to the training set, we summarized each 3-color patch of image or scene by a 9-d vector. From 40,000 image/scene pair samples, we t 15 cluster Gaussian mixtures to the marginalized probabilities, ass... |

5116 | Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images
- Geman, Geman
- 1984
(Show Context)
Citation Context ...x can be di cult to compute without approximations (Knill and Richards, 1996). We make the Markov assumption: we divide both the image and scene into patches, and assign one node of a Markov network (=-=Geman and Geman, 1984-=-; Pearl, 1988; Jordan, 1998) to each patch. We draw the network as nodes connected by lines, which indicate statistical dependencies. Given the variables at intervening nodes, two nodes of a Markov ne... |

1882 |
Statistical Decision Theory And Bayesian Analysis (2nd ed
- Berger
- 1993
(Show Context)
Citation Context ... to be estimated might be projected object velocities, surface shapes and re ectance patterns, or missing high frequency details. Low-level vision problems are typically underconstrained, so Bayesian =-=[3, 23, 38]-=- and regularization techniques [31] are fundamental. There has been much work and progress (for example, [23, 25, 15]), but di culties remain in working with complex, real images. Typically, prior pro... |

1717 |
Robot Vision
- Horn
- 1986
(Show Context)
Citation Context ...ards, 1996; Szeliski, 1989) and regularization techniques (Poggio et al., 1985) are fundamental. There has been muchwork and progress (for example, (Knill and Richards, 1996; Landy and Movshon, 1991; =-=Horn, 1986-=-)), but di culties remain in working with complex, real images. Typically, prior probabilities or constraints are hypothesized, rather than learned. z x current address: MIT Media Laboratory current a... |

1632 |
Spatial interaction and the statistical analysis of lattice systems (with discussions
- Besag
- 1974
(Show Context)
Citation Context ... = Z xj xjdxj ^xj MAP = argmax [xj] Z P (x; y)dx (1) all xi, i 6= j max [ all xi, i 6= j ] P (x; y):(2) For a Markov random eld, the joint probability over the scenes x and images y can be written as =-=[4, 13,12]-=-: Y P (x; y) = (xi;xj) Y (xk;yk); (3) neighboring i;j where we haveintroduced pairwise compatibility functions, and , described below. The factorized structure of Eq. (3) allows the marginalization an... |

1388 | The laplacian pyramid as a compact image code
- Burt, Adelson
- 1983
(Show Context)
Citation Context ..., then interpolated back up to the original resolution to form (a). The missing high frequency detail, (b) minus (a), is the \scene" to be estimated, (d) (this is the rst level of a Laplacian pyramid =-=[7]-=-). The low frequencies of (a) are removed to form the input bandpassed \image". We contrast normalize the image and scene by the local contrast of the input bandpassed image, yielding (c) and (d). Fig... |

803 | editor. Learning in graphical models
- Jordan
- 1999
(Show Context)
Citation Context ...r allows initial scene estimates; the later allows the estimates to propagate. We train from image/scene pairs and apply the Bayesian machinery of graphical models (Pearl, 1988; Binford et al., 1988; =-=Jordan, 1998-=-). We were in uenced by the work of Weiss (Weiss, 1997), who pointed out the speed advantage of Bayesian methods over conventional relaxation methods for propagating local measurement information. For... |

661 | Contour tracking by stochastic propagation of conditional density
- Isard, Blake
- 1996
(Show Context)
Citation Context ...nsional space is not feasible. To address that, we evaluate (xj;yj) and (xj;xk) only at a restricted set of discrete points, a subset of our training set. (For other sample-based representations see (=-=Isard and Blake, 1996-=-; DeBonet and Viola, 1998)). Our nal MAP (or MMSE) estimates will be maxima over (or weights on) a subset of training samples. In all our examples, we used the MAP estimate. The estimated scene at eac... |

490 |
What is the goal of sensory coding
- Field
- 1994
(Show Context)
Citation Context ... and cubic spline interpolation are shown as well. The algorithm \makesup" detail which, while almost certainly not correct, is plausible and visually pleasing. As emphasized by other authors (e.g., (=-=Field, 1994-=-)), the visual world has much more structure than would images of random collections of pixel values. The results of this section show that we can exploit this structure to estimate missing resolution... |

480 | Pyramid-based texture analysis/synthesis.
- Heeger, Bergen
- 1995
(Show Context)
Citation Context ... of the human visual system (Olshausen and Field, 1996; Bell and Sejnowski, 1997; Simoncelli, 1997), or have used statistical characterizations of images to analyse and synthesize realistic textures (=-=Heeger and Bergen, 1995-=-; DeBonet and Viola, 1998; Zhu and Mumford, 1997; Simoncelli, 1997). These methods may help us understand the early stages of representation and processing, but unfortunately, they don't address how a... |

474 | Generalized belief propagation
- Yedidia, Freeman, et al.
- 2000
(Show Context)
Citation Context ..." (Kschischang and Frey, 1998; McEliece et al., 1998) and recent theoretical work (Weiss, 1998; Weiss and Freeman, ijcv99rev2.tex; 16/07/2000; 23:01; p.7Belief propagation 8 William T. Freeman 1999; =-=Yedidia et al., 2000-=-) provide support for a very simple approximation: applying the propagation rules of Eqs. (8) and (7) even in the network with loops. Table 1 summarizes results from (Weiss and Freeman, 1999): (1) for... |

407 |
Scene Labeling by Relaxation Operations
- Rosenfeld, Hummel, et al.
- 1976
(Show Context)
Citation Context ...sion problems, but restricted themselves to linear models (Kersten et al., 1987; Hurlbert and Poggio, 1988), too weak for many applications. Our approach is similar in spirit to relaxation labelling (=-=Rosenfeld et al., 1976-=-; Kittler and Illingworth, 1985), but our Bayesian propagation algorithm is more e cient and we use training data to derive propagation parameters. We interpret images by modeling the relationship bet... |

404 | Turbo decoding as an instance of Pearl’s ‘belief propagation’ algorithm
- McEliece, MacKay, et al.
- 1998
(Show Context)
Citation Context ...ohibitive. Researchers have proposed a variety of approximations (Geman and Geman, 1984; Geiger and Girosi, 1991; Jordan, 1998). Strong empirical results in \Turbo codes" (Kschischang and Frey, 1998; =-=McEliece et al., 1998-=-) and recent theoretical work (Weiss, 1998; Weiss and Freeman, ijcv99rev2.tex; 16/07/2000; 23:01; p.7Belief propagation 8 William T. Freeman 1999; Yedidia et al., 2000) provide support for a very sim... |

396 | Shape from shading. - Brooks, Horn - 1989 |

320 |
Graphical Models for Machine Learning and Digital Communications.
- Frey
- 1998
(Show Context)
Citation Context ...gmaxxj . For linear xj topologies, these propagation rules are equivalent to well-known Bayesian inference methods, such as the Kalman lter and the forward-backward algorithm for Hidden Markov Models =-=[29, 26, 39, 20,11]-=-. Finding the posterior probability distribution for a grid-structured Markov network with loops is computationally expensive and avariety ofapproximations have been proposed [13, 12,20]. Strong empir... |

291 |
Computational vision and regularization theory
- Poggio, Torre, et al.
- 1985
(Show Context)
Citation Context ...analysis, database search, and robotics. Low-level vision problems are typically under-constrained, so Bayesian (Berger, 1985; Knill and Richards, 1996; Szeliski, 1989) and regularization techniques (=-=Poggio et al., 1985-=-) are fundamental. There has been muchwork and progress (for example, (Knill and Richards, 1996; Landy and Movshon, 1991; Horn, 1986)), but di culties remain in working with complex, real images. Typi... |

241 | On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs - Weiss, Freeman |

204 | Bayesian Modeling of Uncertainty in Low Level Vision.
- Szeliski
- 1989
(Show Context)
Citation Context ...mates are important for various tasks in image analysis, database search, and robotics. Low-level vision problems are typically under-constrained, so Bayesian (Berger, 1985; Knill and Richards, 1996; =-=Szeliski, 1989-=-) and regularization techniques (Poggio et al., 1985) are fundamental. There has been muchwork and progress (for example, (Knill and Richards, 1996; Landy and Movshon, 1991; Horn, 1986)), but di culti... |

193 | Probabilistic independence networks for hidden Markov probability models.
- Smyth, Heckerman, et al.
- 1996
(Show Context)
Citation Context ...tion rules are equivalent to standard Bayesian inference methods, such as the Kalman lter and the forward-backward algorithm for Hidden Markov Models (Pearl, 1988; Luettgen et al., 1994; Weiss, 1997; =-=Smyth et al., 1997-=-; Frey, 1998; Jordan, 1998). A second factorization of the joint probability can also be used instead of Eq. (1), although it is only valid for chains or trees, while Eq. (1) is valid for general Mark... |

164 |
Parallel and deterministic algorithms from MRFs: Surface reconstruction
- Geiger, Girosi
- 1991
(Show Context)
Citation Context ...scribed in text. The compatibility functions and are de ned below. For a Markov random eld, the joint probability over the scenes x and images y can be written as (Besag, 1974; Geman and Geman, 1984; =-=Geiger and Girosi, 1991-=-): P (x1;x2;:::;xN;y1;y2;:::;yN)= Y (xi;xj) Y (xk;yk); (1) where we have introduced pairwise compatibility functions, and , which are learned from the training data. (i; j) indicates neighboring nodes... |

161 | Statistical models for images: Compression, restoration and synthesis. In
- Simoncelli
- 1997
(Show Context)
Citation Context ...arch theme has been to study the statistics of natural images. Researchers have related those statistics to properties of the human visual system (Olshausen and Field, 1996; Bell and Sejnowski, 1997; =-=Simoncelli, 1997-=-), or have used statistical characterizations of images to analyse and synthesize realistic textures (Heeger and Bergen, 1995; DeBonet and Viola, 1998; Zhu and Mumford, 1997; Simoncelli, 1997). These ... |

143 |
A Bayesian approach to image expansion for improved definition,”
- Schultz, Stevenson
- 1994
(Show Context)
Citation Context ...he successes of recent texture synthesis methods (Heeger and Bergen, 1995; DeBonet and Viola, 1998; Zhu and Mumford, 1997; Simoncelli, 1997), gives us hope to handle textured areas well, too. Others (=-=Schultz and Stevenson, 1994-=-) have used a Bayesian method for super-resolution, hypothesizing the prior probability. In contrast, the VISTA approach learns the relationship between sharp and blurred images from training examples... |

139 | Iterative decoding of compound codes by probability propagation in graphical models.
- Kschischang, Frey
- 1998
(Show Context)
Citation Context ...ps can be computationally prohibitive. Researchers have proposed a variety of approximations (Geman and Geman, 1984; Geiger and Girosi, 1991; Jordan, 1998). Strong empirical results in \Turbo codes" (=-=Kschischang and Frey, 1998-=-; McEliece et al., 1998) and recent theoretical work (Weiss, 1998; Weiss and Freeman, ijcv99rev2.tex; 16/07/2000; 23:01; p.7Belief propagation 8 William T. Freeman 1999; Yedidia et al., 2000) provide... |

88 |
Accommodation in Computer Vision
- Tenenbaum
- 1970
(Show Context)
Citation Context ...work, an approach supported by experimental and theoretical studies. The intuitions of this paper{propagate local estimates to nd a best, global solution{have a long tradition in computational vision =-=[1, 33, 15, 31]-=-. The power of the VISTA approach lies in the large training database, allowing rich prior probabilities and rendering models, and the belief propagation, allowing e - cient scene inference. Applied t... |

77 |
The generic viewpoint assumption in a framework for visual perception.
- Freeman
- 1994
(Show Context)
Citation Context ...tions, shown in the middle and right of Fig. 17. The shape explanation for the crescents image requires nongeneric alignment of the assumed lighting direction (from the left) with the inferred shape (=-=Freeman, 1994-=-). While disambiguating shading from re ectance is fundamental to interpreting images by computer, it has received relatively little research attention. Shape-from-shading algorithms typically assume ... |

77 | Belief propagation and revision in networks with loops.
- Weiss
- 1997
(Show Context)
Citation Context .... Inference in networks without loops For networks without loops, the Markov assumption leads to simple \message-passing" rules for computing the MAP and MMSE estimates during inference (Pearl, 1988; =-=Weiss, 1998-=-; Jordan, 1998). The factorized structure of Eq. (1) allows the marginalization and maximization operators of Eqs. (2) and (3) to pass through and factors with unrelated arguments. For example, for th... |

63 |
Emergence of simple-cell receptive eld properties by learning a sparse code for natural images
- Olshausen, Field
- 1996
(Show Context)
Citation Context ...7/2000; 23:01; p.12 William T. Freeman A recent research theme has been to study the statistics of natural images. Researchers have related those statistics to properties of the human visual system (=-=Olshausen and Field, 1996-=-; Bell and Sejnowski, 1997; Simoncelli, 1997), or have used statistical characterizations of images to analyse and synthesize realistic textures (Heeger and Bergen, 1995; DeBonet and Viola, 1998; Zhu ... |

57 | Texture recognition using a nonparametric multi-scale statistical model. In:
- Debonet, Viola
- 1998
(Show Context)
Citation Context ...e statistics to properties of the human visual system [28, 2,36], or have used statistical methods with biologically plausible image representations to analyse and synthesize realistic image textures =-=[14, 8,42,36]-=-. These methods may help us understand the early stages of representation and processing, but unfortunately, they don't address how a visual system might interpret images, i.e., estimate the underlyin... |

54 |
Synthesizing a color algorithm from examples.
- Hurlbert, Poggio
- 1983
(Show Context)
Citation Context ... rich ones, learned from the training data. Several researchers have applied related learning approaches to lowlevel vision problems, but restricted themselves to linear models (Kersten et al., 1987; =-=Hurlbert and Poggio, 1988-=-), too weak for many applications. Our approach is similar in spirit to relaxation labelling (Rosenfeld et al., 1976; Kittler and Illingworth, 1985), but our Bayesian propagation algorithm is more e c... |

48 |
The &independent components' of natural scenes are edge "lters, Vision Res.
- Bell, Sejnowski
- 1997
(Show Context)
Citation Context ...n problems would have many applications. A recent research theme has been to learn the statistics of natural images. Researchers have related those statistics to properties of the human visual system =-=[28, 2,36]-=-, or have used statistical methods with biologically plausible image representations to analyse and synthesize realistic image textures [14, 8,42,36]. These methods may help us understand the early st... |

48 | Interpreting images by propagating Bayesian beliefs
- Weiss
- 1996
(Show Context)
Citation Context ...estimates to propagate. We train from image/scene pairs and apply the Bayesian machinery of graphical models (Pearl, 1988; Binford et al., 1988; Jordan, 1998). We were in uenced by the work of Weiss (=-=Weiss, 1997-=-), who pointed out the speed advantage of Bayesian methods over conventional relaxation methods for propagating local measurement information. For a related approach, but with heuristically derived pr... |

38 | Learning to estimate scenes from images
- Freeman, Pasztor
- 1999
(Show Context)
Citation Context ...blems presented here, we found good results by using the marginal statistics measured from the training data, without modications by iterated proportional tting. Based on a factorization described in =-=[10, 9]-=-, for a message from scene nodes j to k, we used (xj;xk)= P(xj;xk) P(xk) and (xj;yj) = P(yjjxj). We t the probabilities with mixtures of Gaussians. An alternate method, which we nd gives comparable re... |

36 |
Bayesian inference in model-based machine vision
- Binford, Levitt, et al.
- 1989
(Show Context)
Citation Context ...ene regions. The former allows initial scene estimates; the later allows the estimates to propagate. We train from image/scene pairs and apply the Bayesian machinery of graphical models (Pearl, 1988; =-=Binford et al., 1988-=-; Jordan, 1998). We were in uenced by the work of Weiss (Weiss, 1997), who pointed out the speed advantage of Bayesian methods over conventional relaxation methods for propagating local measurement in... |

27 |
A practical approach to fractal-based image compression
- Pentland, Horowitz
- 1991
(Show Context)
Citation Context ...ge representation used in compression (Polvere, 1998) (Fig. 13c) allows zooming, although its image generation model will not hold for all images. 1 Selecting the nearest neighbor from training data (=-=Pentland and Horowitz, 1993-=-) (Fig. 9a) ignores important spatial consistency constraints. Figure 6. Example images from a training set of 80 images from two Corel database categories: African grazing animals, and urban skylines... |

23 |
EÆcient multiscale regularization with applications to the computation of optical
- Luettgen, Karl, et al.
- 1994
(Show Context)
Citation Context ...tant, we add layers of image and scene patches at other spatial scales, connecting scene patches to image patches at the same scale, and to scene patches at neighboring scales and positions. (Unlike (=-=Luettgen et al., 1994-=-), this is not a tree because of the connections between spatial neighbors). The Markov network topology of Fig. 2 implies that knowing the scene at position j: (1) provides all the information about ... |

21 |
Relaxation labelling algorithms-A review
- Kittler, Illingworth
- 1986
(Show Context)
Citation Context ...icted themselves to linear models (Kersten et al., 1987; Hurlbert and Poggio, 1988), too weak for many applications. Our approach is similar in spirit to relaxation labelling (Rosenfeld et al., 1976; =-=Kittler and Illingworth, 1985-=-), but our Bayesian propagation algorithm is more e cient and we use training data to derive propagation parameters. We interpret images by modeling the relationship between local regions of images an... |

16 | Bayesian model of surface perception,”
- Freeman, Viola
- 1998
(Show Context)
Citation Context ...ntensities will not allow us to distinguish the causes of the crescent image or the bump image. Furthermore, while people report consistentinterpretations for the crescent and bump images (data from (=-=Freeman and Viola, 1998-=-)), each image has multiple feasible scene explanations, shown in the middle and right of Fig. 17. The shape explanation for the crescents image requires nongeneric alignment of the assumed lighting d... |

15 | Associative learning of scene parameters from images
- Kersten, OToole, et al.
- 1987
(Show Context)
Citation Context ...ing models can then be rich ones, learned from the training data. Several researchers have applied related learning approaches to lowlevel vision problems, but restricted themselves to linear models (=-=Kersten et al., 1987-=-; Hurlbert and Poggio, 1988), too weak for many applications. Our approach is similar in spirit to relaxation labelling (Rosenfeld et al., 1976; Kittler and Illingworth, 1985), but our Bayesian propag... |

8 |
Perceptual organization of occluding contours generated by opaque surfaces,” in
- Saund
- 1999
(Show Context)
Citation Context ... speed advantage of Bayesian methods over conventional relaxation methods for propagating local measurement information. For a related approach, but with heuristically derived propagation rules, see (=-=Saund, 1999-=-). We call our approach VISTA, Vision by Image/Scene TrAining. It is a general machinery that may apply to various vision problems. We illustrate it for estimating missing image details, disambiguatin... |

6 | 2000, `Learning motion analysis - Freeman, Haddon |

6 |
Prior learning and Gibbs reaction-di usion
- Zhu, Mumford
- 1997
(Show Context)
Citation Context ...1996; Bell and Sejnowski, 1997; Simoncelli, 1997), or have used statistical characterizations of images to analyse and synthesize realistic textures (Heeger and Bergen, 1995; DeBonet and Viola, 1998; =-=Zhu and Mumford, 1997-=-; Simoncelli, 1997). These methods may help us understand the early stages of representation and processing, but unfortunately, they don't address how a visual system might interpret images, i.e., est... |

5 | Markov Networks for Low-Level Vision
- Freeman, Pasztor
- 1999
(Show Context)
Citation Context ...blems presented here, we found good results by using the marginal statistics measured from the training data, without modications by iterated proportional tting. Based on a factorization described in =-=[10, 9]-=-, for a message from scene nodes j to k, we used (xj;xk)= P(xj;xk) P(xk) and (xj;yj) = P(yjjxj). We t the probabilities with mixtures of Gaussians. An alternate method, which we nd gives comparable re... |

3 |
Recovering re ectance and illumination in a world of painted polyhedra
- Sinha, Adelson
- 1993
(Show Context)
Citation Context ...terpreting images by computer, it has received relatively little research attention. Shape-from-shading algorithms typically assume constant or known surface albedo markings (Horn and Brooks, 1989). (=-=Sinha and Adelson, 1993-=-) have addressed this problem, but in a blocks world with pre-segmented junctions and regions. Generalization to the world of real images has proved di cult. A Bayesian approach using pixelbased image... |

2 | Pasztor: 1999, `Learning to estimate scenes from images - Freeman, C |

2 | Movshon (eds - Landy, A |

2 |
Mars v. 1.0, A quadtree based fractal image coder/decoder'. http://inls.ucsd.edu/y/Fractals
- Polvere
- 1998
(Show Context)
Citation Context ...elationship between sharp and blurred images from training examples, and achieves better results. Among nonBayesian methods for super-resolution, the fractal image representation used in compression (=-=Polvere, 1998-=-) (Fig. 13c) allows zooming, although its image generation model will not hold for all images. 1 Selecting the nearest neighbor from training data (Pentland and Horowitz, 1993) (Fig. 9a) ignores impor... |

1 |
Bayesian inferernce inmodel-based machine vision
- Binford, Levitt, et al.
- 1988
(Show Context)
Citation Context ...oring local scene regions. The former allows initial scene estimates; the later allows the estimates to propagate. We train from image/scene pairs and apply the Bayesian machinery of graphical models =-=[29, 5, 20]-=-. We were inspired by the work of Weiss [39], who pointed out the speed advantage of Bayesian methods over conventional relaxation methods for propagating local measurement information. For a related ... |

1 |
ijcv99rev2.tex; 16/07/2000; 23:01; p.40 by Image/Scene Training 41
- Barrow, Tenenbaum
- 1981
(Show Context)
Citation Context ...iate to the problem at hand. The intuitions of this paper{propagate local estimates to nd a best, global solution{have a long tradition in computational vision and have been implemented in many ways (=-=Barrow and Tenenbaum, 1981-=-; Rosenfeld et al., 1976; Horn, 1986; Poggio et al., 1985). The power of the VISTA approach lies in the large training database, allowing rich prior probabilities, the selection of scene candidates, w... |

1 | Heeger: 1994, `Summation and division by neurons in primate visual cortex - Carandini, J |

1 |
ijcv99rev2.tex; 16/07/2000; 23:01; p.42 by Image/Scene Training 43
- Weiss, Freeman
- 1999
(Show Context)
Citation Context ...reeman 1999; Yedidia et al., 2000) provide support for a very simple approximation: applying the propagation rules of Eqs. (8) and (7) even in the network with loops. Table 1 summarizes results from (=-=Weiss and Freeman, 1999-=-): (1) for Gaussian processes, the MMSE propagation scheme can converge only to the true posterior means. (2) Even for nonGaussian processes, if the MAP propagation scheme converges, it nds at least a... |

1 | personal communication. ijcv99rev2.tex; 16/07/2000; 23:01; p.40 Vision by Image/Scene Training 41 - Adelson - 1995 |