A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Well-known linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1

Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon's information-theoretic approach and the projection pursuit approach. Using maximum entropy approximations of differential entropy, we introduce a family of new contrast (objective) functions for ICA. These contrast functions enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model, and it is shown how to choose contrast functions that are robust and/or of minimum variance. Finally, we introduce simple fixed-point algorithms for practical optimizatio...

In this paper, we present a novel approach to synthetically generating bidirectional texture functions (BTFs) of real-world surfaces. Unlike a conventional two-dimensional texture, a BTF is a sixdimensional function that describes the appearance of texture as a function of illumination and viewing directions. The BTF captures the appearance change caused by visible small-scale geometric details on surfaces. From a sparse set of images under different viewing /lighting settings, our approach generates BTFs in three steps. First, it recovers approximate 3D geometry of surface details using a shape-from-shading method. Then, it generates a novel version of the geometric details that has the same statistical properties as the sample surface with a non-parametric sampling method. Finally, it employs an appearance preserving procedure to synthesize novel images for the recovered or generated geometric details under various viewing/lighting settings, which then define a BTF. Our experimental results demonstrate the effectiveness of our approach. CR Categories: I.2.10 [Artificial Intelligence]: Vision and Scene Understanding---modeling and recovery of physical attributes I.3.7 [Computer Graphics]: Three-dimensional Graphics and Realism---color, shading, shadowing, and texture I.4.8 [Image Processing]: Scene Analysis---color, photometry, shading Keywords: Bidirectional Texture Functions, Reflectance and Shading Models, Texture Synthesis, Shape-from-Shading, Photometric Stereo, Image-Based Rendering.

Principal Component Analysis (PCA) has been of great interest in computer vision and pattern recognition. In particular, incrementally learning a PCA model, which is computationally e#cient for large scale problems as well as adaptable to reflect the variable state of a dynamic system, is an attractive research topic with numerous applications such as adaptive background modelling and active object recognition. In addition, the conventional PCA, in the sense of least mean squared error minimisation, is susceptible to outlying measurements.

Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, the linear version of the ICA problem is approached from an information-theoretic viewpoint, using Comon's framework of minimizing mutual information of the components. Using maximum entropy approximations of dioeerential entropy, we introduce a family of new contrast (objective) functions for ICA, which can also be considered 1-D projection pursuit indexes. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model. It is shown how to choose optimal contrast functions according to dioeerent criteria. Novel algorithms for maximizing the contrast functions are then introduced. Hebbian-like learning rules are shown to result from gradient descent methods. Finally, in order to speed up the conv...

In this correspondence, we propose a novel class of Learning Vector Quantizers (LVQs) based on multivariate data ordering principles. A special case of the novel LVQ class is the Median LVQ, which uses either the marginal median or the vector median as a multivariate estimator of location. The performance of the proposed marginal median LVQ in color image quantization is demonstrated by experiments. 1 Introduction Neural networks (NN) [1, 2] is a rapidly expanding research field which attracted the attention of scientists and engineers in the last decade. A large variety of artificial neural networks has been developed based on a multitude of learning techniques and having different topologies [2]. One prominent example of neural networks is the Learning Vector Quantizer (LVQ). It is an autoassociative nearest-neighbor classifier which classifies arbitrary patterns into classes using an error correction encoding procedure related to competitive learning [1]. In order to make a distinct...

∗ Signatures are on file in the Graduate School. This dissertation presents two topics from opposite disciplines: one is from a parametric realm and the other is based on nonparametric methods. The first topic is a jackknife maximum likelihood approach to statistical model selection and the second one is a convex hull peeling depth approach to nonparametric massive multivariate data analysis. The second topic includes simulations and applications on massive astronomical data. First, we present a model selection criterion, minimizing the Kullback-Leibler distance by using the jackknife method. Various model selection methods have been developed to choose a model of minimum Kullback-Liebler distance to the true model, such as Akaike information criterion (AIC), Bayesian information criterion (BIC), Minimum description length (MDL), and Bootstrap information criterion. Likewise, the jackknife method chooses a model of minimum Kullback-Leibler distance through bias reduction. This bias, which is inevitable in model

First we explain the interplay between robust loss functions, nonlinear lters and Bayes smoothers for edge-preserving image reconstruction. Then we prove the surprising fact that maximum posterior smoothers are nonlinear lters. A (generalized) Potts prior for segmentation and piecewise smoothing of noisy signals and images is adopted. For one-dimensional signals, an exact solution for the maximum posterior mode- based on dynamic programming- is derived. After, some results on the performance of nonlinear lters on jumps and ramps we nally introduce a cascade of nonlinear lters with varying scale parameters and discuss the choice of parameters for segmentation and piecewise smoothing.

We introduce some recent and very recent smoothing methods which focus on the preservation of boundaries, spikes and canyons in presence of noise. We try to point out basic principles they have in common; the most important one is the robustness aspect. It is reflected by the use of `cup functions' in the statistical loss functions instead of squares; such cup functions were introduced early in robust statistics to downweight outliers. Basically, they are variants of truncated squares. We discuss all the methods in the common framework of `energy functions', i.e we associate to (most of ) the algorithms a `loss function' in such a fashion that the output of the algorithm or the `estimate' is a global or local minimum of this loss function. The third aspect we pursue is the correspondence between loss functions and their local minima and nonlinear filters. We shall argue that the nonlinear filters can be interpreted as variants of gradient descent on the loss functions. This way we can ...

In this paper we study occluding contour artifacts in the area-based stereo matching. These artifacts are false, although highly correlated responses of the matching operator to the occlusion boundary and cause the objects extend beyond their true boundaries in disparity maps. The effect is so strong that it cannot be ignored. Current matching methods do not attempt to avoid the problem. We show what is the physical phenomenon that gives rise to the artifacts and design a matching criterion that accommodates the presence of the occlusions as opposite to methods that identify and remove the artifacts. This approach leads to the problem of measurement contamination studied in statistics. We show that such problem is hard given finite computational resources, unless more independent measurements directly related to occluding contours is available. What can be achieved is the substantial reduction of the artifacts, especially for large matching templates. Reduced artifacts allow for easier...