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57
Shape priors using Manifold Learning Techniques
 in &quot;11th IEEE International Conference on Computer Vision, Rio de Janeiro
, 2007
"... We introduce a nonlinear shape prior for the deformable model framework that we learn from a set of shape samples using recent manifold learning techniques. We model a category of shapes as a finite dimensional manifold which we approximate using Diffusion maps, that we call the shape prior manifol ..."
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Cited by 39 (2 self)
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We introduce a nonlinear shape prior for the deformable model framework that we learn from a set of shape samples using recent manifold learning techniques. We model a category of shapes as a finite dimensional manifold which we approximate using Diffusion maps, that we call the shape prior manifold. Our method computes a Delaunay triangulation of the reduced space, considered as Euclidean, and uses the resulting space partition to identify the closest neighbors of any given shape based on its Nyström extension. Our contribution lies in three aspects. First, we propose a solution to the preimage problem and define the projection of a shape onto the manifold. Based on closest neighbors for the Diffusion distance, we then describe a variational framework for manifold denoising. Finally, we introduce a shape prior term for the deformable framework through a nonlinear energy term designed to attract a shape towards the manifold at given constant embedding. Results on shapes of cars and ventricule nuclei are presented and demonstrate the potentials of our method.
Translated Poisson mixture model for stratification learning
 Int. J. Comput. Vision
, 2000
"... A framework for the regularized and robust estimation of nonuniform dimensionality and density in high dimensional noisy data is introduced in this work. This leads to learning stratifications, that is, mixture of manifolds representing different characteristics and complexities in the data set. Th ..."
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Cited by 24 (2 self)
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A framework for the regularized and robust estimation of nonuniform dimensionality and density in high dimensional noisy data is introduced in this work. This leads to learning stratifications, that is, mixture of manifolds representing different characteristics and complexities in the data set. The basic idea relies on modeling the high dimensional sample points as a process of Translated Poisson mixtures, with regularizing restrictions, leading to a model which includes the presence of noise. The Translated Poisson distribution is useful to model a noisy counting process, and it is derived from the noiseinduced translation of a regular Poisson distribution. By maximizing the loglikelihood of the process counting the points falling into a local ball, we estimate the local dimension and density. We show that
A General Framework for Manifold Alignment
"... Manifold alignment has been found to be useful in many fields of machine learning and data mining. In this paper we summarize our work in this area and introduce a general framework for manifold alignment. This framework generates a family of approaches to align manifolds by simultaneously matching ..."
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Cited by 12 (2 self)
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Manifold alignment has been found to be useful in many fields of machine learning and data mining. In this paper we summarize our work in this area and introduce a general framework for manifold alignment. This framework generates a family of approaches to align manifolds by simultaneously matching the corresponding instances and preserving the local geometry of each given manifold. Some approaches like semisupervised alignment and manifold projections can be obtained as special cases. Our framework can also solve multiple manifold alignment problems and be adapted to handle the situation when no correspondence information is available. The approaches are described and evaluated both theoretically and experimentally, providing results showing useful knowledge transfer from one domain to another. Novel applications of our methods including identification of topics shared by multiple document collections, and biological structure alignment are discussed in the paper.
Joint Manifolds for Data Fusion
, 2009
"... The emergence of lowcost sensing architectures for diverse modalities has made it possible to deploy sensor networks that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these networks acquire large amounts of very highdimensional data ..."
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Cited by 8 (2 self)
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The emergence of lowcost sensing architectures for diverse modalities has made it possible to deploy sensor networks that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these networks acquire large amounts of very highdimensional data. For example, even a relatively small network of cameras can generate massive amounts of highdimensional image and video data. One way to cope with such a data deluge is to develop lowdimensional data models. Manifold models provide a particularly powerful theoretical and algorithmic framework for capturing the structure of data governed by a lowdimensional set of parameters, as is often the case in a sensor network. However, these models do not typically take into account dependencies among multiple sensors. We thus propose a new joint manifold framework for data ensembles that exploits such dependencies. We show that joint manifold structure can lead to improved performance for a variety of signal processing algorithms for applications including classification and manifold learning. Additionally, recent results concerning random projections of manifolds enable us to formulate a networkscalable dimensionality reduction scheme that efficiently fuses the data from all sensors.
Lipreading by locality discriminant graph
 in Proc. ICIP
, 2007
"... The major problem in building a good lipreading system is to extract effective visual features from enormous quantity of video sequences data. For appearancebased feature analysis in lipreading, classical methods, e.g. DCT, PCA and LDA, are usually applied to dimensionality reduction. We present a ..."
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Cited by 7 (0 self)
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The major problem in building a good lipreading system is to extract effective visual features from enormous quantity of video sequences data. For appearancebased feature analysis in lipreading, classical methods, e.g. DCT, PCA and LDA, are usually applied to dimensionality reduction. We present a new pattern classification algorithm, called Locality Discriminant Graph (LDG), and develop a novel lipreading framework to successfully apply LDG to the problem. LDG takes both advantage of manifold learning and Fisher criteria to seek the linear embedding which preserves the local neighborhood affinity within same class while discriminating the neighborhood among different classes. The LDG embedding is computed in closedform and tuned by the only open parameter of kNN number. Experiments on AVICAR corpus database provide evidence that the graphbased pattern classification methods can outperform classical ones for lipreading. Index Terms — Lipreading, graph embedding, discriminant analysis, audiovisual speech, discrete cosine transform.
ActiveContourBased Image Segmentation using Machine Learning Techniques
 in &quot;10th IEEE International Conference on Medical Image Computing and Computer Assisted Intervention
, 2007
"... Abstract. We introduce a nonlinear shape prior for the deformable model framework that we learn from a set of shape samples using recent manifold learning techniques. We model a category of shapes as a finite dimensional manifold which we approximate using Diffusion maps. Our method computes a Dela ..."
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Cited by 7 (0 self)
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Abstract. We introduce a nonlinear shape prior for the deformable model framework that we learn from a set of shape samples using recent manifold learning techniques. We model a category of shapes as a finite dimensional manifold which we approximate using Diffusion maps. Our method computes a Delaunay triangulation of the reduced space, considered as Euclidean, and uses the resulting space partition to identify the closest neighbors of any given shape based on its Nyström extension. We derive a nonlinear shape prior term designed to attract a shape towards the shape prior manifold at given constant embedding. Results on shapes of ventricle nuclei demonstrate the potential of our method for segmentation tasks. Fig. 1. Aligned shape samples of the right ventricle nucleus from different subjects corresponding, from left to right, to 2 young, 2 midage, and 2 old subjects; the last shape sample originates from a subject with Alzheimer’s Disease. While shapes appear quite similar, they usually cannot be considered as small deformations around a mean shape.
Classification of Potential Nuclei in Prostate Histology Images using Shape Manifold Learning
"... Abstract – The demanding step in the development of ancillary systems for the diagnosis of cancer and other diseases based on nuclear morphometry is the delineation of nuclei in the images of stained tissue sections. Various constituents of the tissue section such as cellular and extracellular elem ..."
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Cited by 7 (0 self)
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Abstract – The demanding step in the development of ancillary systems for the diagnosis of cancer and other diseases based on nuclear morphometry is the delineation of nuclei in the images of stained tissue sections. Various constituents of the tissue section such as cellular and extracellular elements, staining artefacts, debris of nuclei, and clusters of overlapping nuclei apart from the image acquisition noise to name a few contribute to in the complexity of the task. In this paper, we pose the problem of selection of nuclei in tissue section as classification of shapes using manifold learning on training images followed by outofsample extension for unknown test images. Experimental results demonstrate the effectiveness of the proposed algorithm Index Terms – Manifold learning, diffusion maps, nuclear morphometry, outofsample extension.
Dominant texture and diffusion distance manifolds
 Computer Graphics Forum
"... Texture synthesis techniques require nearly uniform texture samples, however identifying suitable texture samples in an image requires significant data preprocessing. To eliminate this work, we introduce a fully automatic pipeline to detect dominant texture samples based on a manifold generated usin ..."
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Cited by 6 (2 self)
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Texture synthesis techniques require nearly uniform texture samples, however identifying suitable texture samples in an image requires significant data preprocessing. To eliminate this work, we introduce a fully automatic pipeline to detect dominant texture samples based on a manifold generated using the diffusion distance. We define the characteristics of dominant texture and three different types of outliers that allow us to efficiently identify dominant texture in feature space. We demonstrate how this method enables the analysis/synthesis of a wide range of natural textures. We compare textures synthesized from a sample image, with and without dominant texture detection. We also compare our approach to that of using a texture segmentation technique alone, and to using Euclidean, rather than diffusion, distances between texture features.
Parametrization of Linear Systems Using Diffusion Kernels
, 2011
"... Modeling natural and artificial systems has a key role in various applications, and has long been a task that drew enormous efforts. In this work, instead of exploring predefined models, we aim at implicitly identifying the system degrees of freedom. This approach circumvents the dependency of a spe ..."
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Cited by 6 (3 self)
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Modeling natural and artificial systems has a key role in various applications, and has long been a task that drew enormous efforts. In this work, instead of exploring predefined models, we aim at implicitly identifying the system degrees of freedom. This approach circumvents the dependency of a specific predefined model for a specific task or system, and enables a generic datadriven method to characterize a system based solely on its output observations. We claim that each system can be viewed as a black box controlled by several independent parameters. Moreover, we assume that the perceptual characterization of the system output is determined by these independent parameters. Consequently, by recovering the independent controlling parameters, we find in fact a generic modeling for the system. In this work, we propose a supervised algorithm to recover the controlling parameters of natural and artificial linear systems. The proposed algorithm relies on nonlinear independent component analysis using diffusion kernels and spectral analysis. Employment of the proposed algorithm on both synthetic and real examples has shown accurate recovery of parameters.