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347
A Survey of Shape Analysis Techniques
 Pattern Recognition
, 1998
"... This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems. ..."
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Cited by 200 (2 self)
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This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.
Flat Zones Filtering, Connected Operators, and Filters by Reconstruction
 IEEE Transactions on Image Processing
, 1995
"... This paper deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created b ..."
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Cited by 112 (9 self)
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This paper deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the fiat zones of the functions. It is shown that, from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the fiat zones of the functions increase with the level of the pyramid. In other words, the fiat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of fiat zones are described.
Deformotion  Deforming Motion, Shape Average and the Joint Registration and Segmentation of Images
 International Journal of Computer Vision
, 2002
"... What does it mean for a deforming object to be "moving" (see Fig. 1)? How can we separate the overall motion (a finitedimensional group action) from the more general deformation (a di#eomorphism)? In this paper we propose a definition of motion for a deforming object and introduce a notion of "shap ..."
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Cited by 105 (16 self)
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What does it mean for a deforming object to be "moving" (see Fig. 1)? How can we separate the overall motion (a finitedimensional group action) from the more general deformation (a di#eomorphism)? In this paper we propose a definition of motion for a deforming object and introduce a notion of "shape average" as the entity that separates the motion from the deformation. Our definition allows us to derive novel and e#cient algorithms to register nonequivalent shapes using regionbased methods, and to simultaneously approximate and register structures in greyscale images. We also extend the notion of shape average to that of a "moving average" in order to track moving and deforming objects through time.
On Advances in Statistical Modeling of Natural Images
 Journal of Mathematical Imaging and Vision
, 2003
"... Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modelin ..."
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Cited by 98 (5 self)
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Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modeling of natural images that attempt to explain these patterns. Two categories of results are considered: (i) studies of probability models of images or image decompositions (such as Fourier or wavelet decompositions), and (ii) discoveries of underlying image manifolds while restricting to natural images. Applications of these models in areas such as texture analysis, image classification, compression, and denoising are also considered.
Perspectives on the Theory and Practice of Belief Functions
 International Journal of Approximate Reasoning
, 1990
"... The theory of belief functions provides one way to use mathematical probability in subjective judgment. It is a generalization of the Bayesian theory of subjective probability. When we use the Bayesian theory to quantify judgments about a question, we must assign probabilities to the possible answer ..."
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Cited by 86 (7 self)
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The theory of belief functions provides one way to use mathematical probability in subjective judgment. It is a generalization of the Bayesian theory of subjective probability. When we use the Bayesian theory to quantify judgments about a question, we must assign probabilities to the possible answers to that question. The theory of belief functions is more flexible; it allows us to derive degrees of belief for a question from probabilities for a related question. These degrees of belief may or may not have the mathematical properties of probabilities; how much they differ from probabilities will depend on how closely the two questions are related. Examples of what we would now call belieffunction reasoning can be found in the late seventeenth and early eighteenth centuries, well before Bayesian ideas were developed. In 1689, George Hooper gave rules for combining testimony that can be recognized as special cases of Dempster's rule for combining belief functions (Shafer 1986a). Similar rules were formulated by Jakob Bernoulli in his Ars Conjectandi, published posthumously in 1713, and by JohannHeinrich Lambert in his Neues Organon, published in 1764 (Shafer 1978). Examples of belieffunction reasoning can also be found in more recent work, by authors
Approximations of shape metrics and application to shape warping and empirical shape statistics
 Foundations of Computational Mathematics
, 2004
"... Abstract. This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [11], we conside ..."
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Cited by 85 (19 self)
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Abstract. This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [11], we consider the characteristic functions of the subsets of R 2 and their distance functions. The L 2 norm of the difference of characteristic functions, the L ∞ and the W 1,2 norms of the difference of distance functions define interesting topologies, in particular the wellknown Hausdorff distance. Because of practical considerations arising from the fact that we deal with
Kernel Density Estimation and Intrinsic Alignment for Knowledgedriven Segmentation: Teaching Level Sets to Walk
 International Journal of Computer Vision
, 2004
"... We address the problem of image segmentation with statistical shape priors in the context of the level set framework. Our paper makes two contributions: Firstly, we propose to generate invariance of the shape prior to certain transformations by intrinsic registration of the evolving level set fun ..."
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Cited by 84 (16 self)
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We address the problem of image segmentation with statistical shape priors in the context of the level set framework. Our paper makes two contributions: Firstly, we propose to generate invariance of the shape prior to certain transformations by intrinsic registration of the evolving level set function. In contrast to existing approaches to invariance in the level set framework, this closedform solution removes the need to iteratively optimize explicit pose parameters. Moreover, we will argue that the resulting shape gradient is more accurate in that it takes into account the e#ect of boundary variation on the object's pose.
Occlusion models for natural images: a statistical study of a scale invariant dead leaves model
 International Journal of Computer Vision
"... Abstract. We develop a scaleinvariant version of Matheron’s “dead leaves model ” for the statistics of natural images. The model takes occlusions into account and resembles the image formation process by randomly adding independent elementary shapes, such as disks, in layers. We compare the empiric ..."
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Cited by 70 (1 self)
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Abstract. We develop a scaleinvariant version of Matheron’s “dead leaves model ” for the statistics of natural images. The model takes occlusions into account and resembles the image formation process by randomly adding independent elementary shapes, such as disks, in layers. We compare the empirical statistics of two large databases of natural images with the statistics of the occlusion model, and find an excellent qualitative, and good quantitative agreement. At this point, this is the only image model which comes close to duplicating the simplest, elementary statistics of natural images—such as, the scale invariance property of marginal distributions of filter responses, the full cooccurrence statistics of two pixels, and the joint statistics of pairs of Haar wavelet responses. natural images, stochastic image model, nonGaussian statistics, scaling, dead leaves model, occluKeywords: sions, clutter 1.
Extraction of Visual Features for Lipreading
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2002
"... The multimodal nature of speech is often ignored in humancomputer interaction but lip deformation, and other body such as head and arm motion all convey additional information. We integrate speech cues from many sources and this improves intelligibility, especially when the acoustic signal is de ..."
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Cited by 66 (2 self)
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The multimodal nature of speech is often ignored in humancomputer interaction but lip deformation, and other body such as head and arm motion all convey additional information. We integrate speech cues from many sources and this improves intelligibility, especially when the acoustic signal is degraded. This paper shows how this additional, often complementary, visual speech information can be used for speech recognition. Three methods for parameterising lip image sequences for recognition using hidden Markov models are compared. Two of these are topdown approaches that fit a model of the inner and outer lip contours and derive lipreading features from a principal component analysis of shape, or shape and appearance respectively. The third, bottomup, method uses a nonlinear scalespace analysis to form features directly from the pixel intensity. All methods are compared on a multitalker visual speech recognition task of isolated letters.