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

This paper presents a secure (tamper-resistant) algorithm for watermarking images, and a methodology for digital watermarking that may be generalized to audio, video, and multimedia data. We advocate that a watermark should be constructed as an independent and identically distributed (i.i.d.) Gaussian random vector that is imperceptibly inserted in a spread-spectrum-like fashion into the perceptually most significant spectral components of the data. We argue that insertion of a watermark under this regime makes the watermark robust to signal processing operations (such as lossy compression, filtering, digital-analog and analog-digital conversion, requantization, etc.), and common geometric transformations (such as cropping, scaling, translation, and rotation) provided that the original image is available and that it can be succesfully registered against the transformed watermarked image. In these cases, the watermark detector unambiguously identifies the owner. Further, the use of Gaussian noise, ensures strong resilience to multiple-document, or collusional, attacks. Experimental results are provided to support these claims, along with an exposition of pending open problems.

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Abstract—As an object moves through the field of view of a camera, the images of the object may change dramatically. This is not simply due to the translation of the object across the image plane. Rather, complications arise due to the fact that the object undergoes changes in pose relative to the viewing camera, changes in illumination relative to light sources, and may even become partially or fully occluded. In this paper, we develop an efficient, general framework for object tracking—one which addresses each of these complications. We first develop a computationally efficient method for handling the geometric distortions produced by changes in pose. We then combine geometry and illumination into an algorithm that tracks large image regions using no more computation than would be required to track with no accommodation for illumination changes. Finally, we augment these methods with techniques from robust statistics and treat occluded regions on the object as statistical outliers. Throughout, we present experimental results performed on live video sequences demonstrating the effectiveness and efficiency of our methods. Index Terms—Visual tracking, real-time vision, illumination, motion estimation, robust statistics.

Since the Lucas-Kanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision. Applications range from optical flow, tracking, and layered motion, to mosaic construction, medical image registration, and face coding. Numerous algorithms have been proposed and a variety of extensions have been made to the original formulation. We present an overview of image alignment, describing most of the algorithms in a consistent framework. We concentrate on the inverse compositional algorithm, an efficient algorithm that we recently proposed. We examine which of the extensions to the Lucas-Kanade algorithm can be used with the inverse compositional algorithm without any significant loss of efficiency, and which cannot. In this paper, Part 3 in a series of papers, we cover the extension of image alignment to allow linear appearance variation. We first consider linear appearance variation when the error function is the Euclidean L2 norm. We describe three different algorithms, the simultaneous, project out, and normalization inverse compositional algorithms, and empirically compare them. Afterwards we consider the combination of linear appearance variation with the robust error functions described in Part 2 of this series. We first derive robust versions of the simultaneous and normalization algorithms. Since both of these algorithms are very inefficient, as in Part 2 we derive efficient approximations based on spatial coherence. We end with an empirical evaluation of the robust algorithms.

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.

In this paper we study both market risks and non-market risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent". We examine the measures of risk provided and the related actions required by SPAN, by the SEC/NASD rules and by quantile based methods. We demonstrate the universality of scenario-based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile-based methods.

Two images of a single scene/object are related by the epipolar geometry, which can be described by a 3×3 singular matrix called the essential matrix if images' internal parameters are known, or the fundamental matrix otherwise. It captures all geometric information contained in two images, and its determination is very important in many applications such as scene modeling and vehicle navigation. This paper gives an introduction to the epipolar geometry, and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty. A well-founded measure is proposed to compare these techniques. Projective reconstruction is also reviewed. The software which we have developed for this review is available on the Internet.

We present a new technique for the display of high-dynamic-range images, which reduces the contrast while preserving detail. It is based on a two-scale decomposition of the image into a base layer, encoding large-scale variations, and a detail layer. Only the base layer has its contrast reduced, thereby preserving detail. The base layer is obtained using an edge-preserving filter called the bilateral filter. This is a non-linear filter, where the weight of each pixel is computed using a Gaussian in the spatial domain multiplied by an influence function in the intensity domain that decreases the weight of pixels with large intensity differences. We express bilateral filtering in the framework of robust statistics and show how it relates to anisotropic diffusion. We then accelerate bilateral filtering by using a piecewise-linear approximation in the intensity domain and appropriate subsampling. This results in a speed-up of two orders of magnitude. The method is fast and requires no parameter setting.

this article with the regression case. To explain this, we will introduce a suitable definition of a margin that is maximized in both cases