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770
Active Appearance Models Revisited
 International Journal of Computer Vision
, 2003
"... Active Appearance Models (AAMs) and the closely related concepts of Morphable Models and Active Blobs are generative models of a certain visual phenomenon. Although linear in both shape and appearance, overall, AAMs are nonlinear parametric models in terms of the pixel intensities. Fitting an AAM to ..."
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Cited by 456 (39 self)
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Active Appearance Models (AAMs) and the closely related concepts of Morphable Models and Active Blobs are generative models of a certain visual phenomenon. Although linear in both shape and appearance, overall, AAMs are nonlinear parametric models in terms of the pixel intensities. Fitting an AAM to an image consists of minimizing the error between the input image and the closest model instance; i.e. solving a nonlinear optimization problem. We propose an efficient fitting algorithm for AAMs based on the inverse compositional image alignment algorithm. We show how the appearance variation can be "projected out" using this algorithm and how the algorithm can be extended to include a "shape normalizing" warp, typically a 2D similarity transformation. We evaluate our algorithm to determine which of its novel aspects improve AAM fitting performance.
Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
, 1999
"... Measurements of geometric primitives, such as rotations or rigid transformations, are often noisy and we need to use statistics either to reduce the uncertainty or to compare measurements. Unfortunately, geometric primitives often belong to manifolds and not vector spaces. We have already shown [9] ..."
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Cited by 198 (24 self)
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Measurements of geometric primitives, such as rotations or rigid transformations, are often noisy and we need to use statistics either to reduce the uncertainty or to compare measurements. Unfortunately, geometric primitives often belong to manifolds and not vector spaces. We have already shown [9] that generalizing too quickly even simple statistical notions could lead to paradoxes. In this article, we develop some basic probabilistic tools to work on Riemannian manifolds: the notion of mean value, covariance matrix, normal law, Mahalanobis distance and χ² test. We also present an efficient algorithm to compute the mean value and tractable approximations of the normal and χ² laws for small variances.
Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape
 TO APPEAR IEEE TRANSACTIONS ON MEDICAL IMAGING
, 2004
"... A primary goal of statistical shape analysis is to describe the variability of a population of geometric objects. A standard technique for computing such descriptions is principal component analysis. However, principal component analysis is limited in that it only works for data lying in a Euclidean ..."
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Cited by 180 (34 self)
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A primary goal of statistical shape analysis is to describe the variability of a population of geometric objects. A standard technique for computing such descriptions is principal component analysis. However, principal component analysis is limited in that it only works for data lying in a Euclidean vector space. While this is certainly sufficient for geometric models that are parameterized by a set of landmarks or a dense collection of boundary points, it does not handle more complex representations of shape. We have been developing representations of geometry based on the medial axis description or mrep. While the medial representation provides a rich language for variability in terms of bending, twisting, and widening, the medial parameters are not elements of a Euclidean vector space. They are in fact elements of a nonlinear Riemannian symmetric space. In this paper we develop the method of principal geodesic analysis, a generalization of principal component analysis to the manifold setting. We demonstrate its use in describing the variability of mediallydefined anatomical objects. Results of applying this framework on a population of hippocampi in a schizophrenia study are presented.
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinitedimensional spaces and their pairwise di#erences are quantified using the lengths of ge ..."
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Cited by 172 (39 self)
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For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinitedimensional spaces and their pairwise di#erences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradientbased shooting method to solve for the tangent that connects any two shapes via a geodesic.
Salient geometric features for partial shape matching and similarity
 jTOG
"... This article introduces a method for partial matching of surfaces represented by triangular meshes. Our method matches surface regions that are numerically and topologically dissimilar, but approximately similar regions. We introduce novel local surface descriptors which efficiently represent the ge ..."
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Cited by 153 (7 self)
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This article introduces a method for partial matching of surfaces represented by triangular meshes. Our method matches surface regions that are numerically and topologically dissimilar, but approximately similar regions. We introduce novel local surface descriptors which efficiently represent the geometry of local regions of the surface. The descriptors are defined independently of the underlying triangulation, and form a compatible representation that allows matching of surfaces with different triangulations. To cope with the combinatorial complexity of partial matching of large meshes, we introduce the abstraction of salient geometric features and present a method to construct them. A salient geometric feature is a compound highlevel feature of nontrivial local shapes. We show that a relatively small number of such salient geometric features characterizes the surface well for various similarity applications. Matching salient geometric features is based on indexing rotationinvariant features and a voting scheme accelerated by geometric hashing. We demonstrate the effectiveness of our method with a number of applications, such as computing selfsimilarity, alignments, and subparts similarity.
Generic vs. person specific active appearance models
 Image and Vision Computing
"... Active Appearance Models (AAMs) are generative parametric models that have been successfully used in the past to model faces. Anecdotal evidence, however, suggests that the performance of an AAM built to model the variation in appearance of a single person across pose, illumination, and expression ( ..."
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Cited by 133 (4 self)
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Active Appearance Models (AAMs) are generative parametric models that have been successfully used in the past to model faces. Anecdotal evidence, however, suggests that the performance of an AAM built to model the variation in appearance of a single person across pose, illumination, and expression (Person Specific AAM) is substantially better than the performance of an AAM built to model the variation in appearance of many faces, including unseen subjects not in the training set (Generic AAM). In this paper we present an empirical evaluation that shows that Person Specific AAMs are, as expected, both easier to build and more robust to fit than Generic AAMs. Moreover, we show that: (1) building a generic shape model is far easier than building a generic appearance model, and (2) the shape component is the main cause of the reduced fitting robustness of Generic AAMs. We then proceed to describe two refinements to Generic AAMs to improve their performance: (1) a refitting procedure to improve the quality of the groundtruth data used to build the AAM and (2) a new fitting algorithm. For both refinements we demonstrate vastly improved fitting performance. 1
Diffusion snakes: introducing statistical shape knowledge into the MumfordShah functional
 J. OF COMPUTER VISION
, 2002
"... We present a modification of the MumfordShah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneit ..."
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Cited by 130 (15 self)
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We present a modification of the MumfordShah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes. We propose a closedform, parameterfree solution for incorporating invariance with respect to similarity transformations in the variational framework. We show segmentation results on artificial and realworld images with and without prior shape information. In the cases of noise, occlusion or strongly cluttered background the shape prior significantly improves segmentation. Finally we compare our results to those obtained by a level set implementation of geodesic active contours.
Feature detection and tracking with constrained local models
, 2006
"... We present an efficient and robust model matching method which uses a joint shape and texture appearance model to generate a set of region template detectors. The model is fitted to an unseen image in an iterative manner by generating templates using the joint model and the current parameter estimat ..."
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Cited by 122 (3 self)
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We present an efficient and robust model matching method which uses a joint shape and texture appearance model to generate a set of region template detectors. The model is fitted to an unseen image in an iterative manner by generating templates using the joint model and the current parameter estimates, correlating the templates with the target image to generate response images and optimising the shape parameters so as to maximise the sum of responses. The appearance model is similar to that used in the AAM [1]. However in our approach the appearance model is used to generate likely feature templates, instead of trying to approximate the image pixels directly. We show that when applied to human faces, our Constrained Local Model (CLM) algorithm is more robust and more accurate than the original AAM search method, which relies on the image reconstruction error to update the model parameters. We demonstrate improved localisation accuracy on two publicly available face data sets and improved tracking on a challenging set of incar face sequences. 1
Interactive Graph Cut Based Segmentation With Shape Priors
 IN CVPR, PAGES I: 755–762
, 2005
"... ... alternative to pure automatic segmentation in many applications. While automatic segmentation can be very challenging, a small amount of user input can often resolve ambiguous decisions on the part of the algorithm. In this work, we devise a graph cut algorithm for interactive segmentation which ..."
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Cited by 116 (0 self)
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... alternative to pure automatic segmentation in many applications. While automatic segmentation can be very challenging, a small amount of user input can often resolve ambiguous decisions on the part of the algorithm. In this work, we devise a graph cut algorithm for interactive segmentation which incorporates shape priors. While traditional graph cut approaches to interactive segmentation are often quite successful, they may fail in cases where there are diffuse edges, or multiple similar objects in close proximity to one another. Incorporation of shape priors within this framework mitigates these problems. Positive results on both medical and natural images are demonstrated.
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 114 (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.