Abstract. This paper has two goals. The first is to develop a variety of robust methods for the computation of the Fundamental Matrix, the calibration-free representation of camera motion. The methods are drawn from the principal categories of robust estimators, viz. case deletion diagnostics, M-estimators and random sampling, and the paper develops the theory required to apply them to non-linear orthogonal regression problems. Although a considerable amount of interest has focussed on the application of robust estimation in computer vision, the relative merits of the many individual methods are unknown, leaving the potential practitioner to guess at their value. The second goal is therefore to compare and judge the methods. Comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery. In contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth. A variety of error measures are examined. The experiments allow a statistically satisfying and quasi-optimal method to be synthesized, which is shown to be stable with up to 50 percent outlier contamination, and may still be used if there are more than 50 percent outliers. Performance bounds are established for the method, and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined. The results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers.

A traditional approach to extracting geometric information from a large scene is to compute multiple 3-D depth maps from stereo pairs or direct range finders, and then to merge the 3-D data This is not only computationally intensive, but the resulting merged depth maps may be subject to merging errors, especially if the relative poses between depth maps are not known exactly. The 3-D data may also have to be resampled before merging, which adds additional complexity and potential sources of errors. This paper provides a means of directly extracting 3-D data covering a very wide field of view, thus by-passing the need for numerous depth map merging. In our work, cylindrical images are first composited from sequences of images taken while the camera is rotated 360 ffi about a vertical axis. By taking such image panoramas at different camera locations, we can recover 3-D data of the scene using a set of simple techniques: feature tracking, an 8-point structure from motion algorithm, and...

This article develops a dynamic generalization of the nonuniform rational B-spline (NURBS) model. NURBS have become a de facto standard in commercial modeling systems because of their power to represent free-form shapes as well as common analytic shapes. To date, however, they have been viewed as purely geometric primitives that require the user to manually adjust multiple control points and associated weights in order to design shapes. Dynamic NURBS, or D-NURBS, are physics-based models that incorporate mass distributions, inertial deformation energies, and other physical quantities into the popular NURBS geometric substrate. Using D-NURBS, a modeler can interactively sculpt curves and surfaces and design complex shapes to required specifications not only in the traditional indirect fashion, by adjusting control points and weights, but also through direct physical manipulation, by applying simulated forces and local and global shape constraints. D-NURBS move and deform in a physically intuitive manner in response to the user's direct manipulations. Their dynamic behavior results from the numerical integration of a set of nonlinear differential equations that automatically evolve the control points and weights in response to the applied forces and constraints. To derive these equations, we employ Lagrangian mechanics and finite-element-like discretization. Our approach supports the trimming of D-NURBS surfaces using D-NURBS curves. We demonstrate D-NURBS models and constraints in applications including the rounding of solids, optimal surface fitting to unstructured data, surface design from cross-sections, and free-form deformation. We also introduce a new technique for 2D shape metamorphosis using constrained D-NURBS surfaces.

We present a new multiple-instance (MI) learning technique (EMDD) that combines EM with the diverse density (DD) algorithm.

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Kernel methods like Support Vector Machines have successfully been used for text categorization. A standard choice of kernel function has been the inner product between the vector-space representationoftwo documents, in analogy with classical information retrieval (IR) approaches. Latent Semantic Indexing (LSI) has been successfully used for IR purposes as a technique for capturing semantic relations between terms and inserting them into the similarity measure between two documents. One of its main drawbacks, in IR, is its computational cost. In this paper we describe how the LSI approach can be implementedinakernel-de ned feature space. We provide experimental results demonstrating that the approach can significantly improve performance, and that it does not impair it.

In this paper, we propose two generic text summarization methods that create text summaries by ranking and extracting sentences from the original documents. The rst method uses standard IR methods to rank sentence relevances, while the second method uses the latent semantic analysis technique to identify semantically important sentences, for summary creations. Both methods strive to select sentences that are highly ranked and di erent from each other. This is an attempt to create a summary with a wider coverage of the document's main content and less redundancy. Performance evaluations on the two summarization methods are conducted by comparing their summarization outputs with the manual summaries generated by three independent human evaluators. The evaluations also study the in uence of di erent VSM weighting schemes on the text summarization performances. Finally, the causes of the large disparities in the evaluators ' manual summarization results are investigated, and discussions on human text summarization patterns are presented.

We envision a future in which the global economy and the Internet will merge and evolve together into an information economy bustling with billions of economically motivated software agents that exchange information goods and services with humans and other agents. Economic software agents will differ in important ways from their human counterparts, and these differences may have significant beneficial or harmful effects upon the global economy. It is therefore important to consider the economic incentives and behaviors of economic software agents, and to use every available means to anticipate their collective interactions. We survey research conducted by the Information Economies group at IBM Research aimed at understanding collective interactions among agents that dynamically price information goods or services. In particular, we study the potential impact of widespread shopbot usage on prices, the price dynamics that may ensue from various mixtures of automated pricing ...

Indexing systems for the World Wide Web, such as Lycos and Alta Vista, play an essential role in making the Web useful and usable. These systems are based on Information Retrieval methods for indexing plain text documents, but also include heuristics for adjusting their document rankings based on the special HTML structure of Web documents. In this paper, we describe a wide range of such heuristics---including a novel one inspired by reinforcement learning techniques for propagating rewards through a graph---which can be used to affect a search engine's rankings. We then demonstrate a system which learns to combine these heuristics automatically, based on feedback collected unintrusively from users, resulting in much improved rankings. 1 Introduction Lycos (Mauldin & Leavitt 1994), Alta Vista, and similar Web search engines have become essential as tools for locating information on the ever-growing World Wide Web. Underlying these systems are statistical methods for indexing plain te...

This paper presents dynamic NURBS, or D-NURBS, a physics-based generalization of Non-Uniform Rational B-Splines. NURBS have become a de facto standard in commercial modeling systems because of their power to represent both free-form shapes and common analytic shapes. Traditionally, however, NURBS have been viewed as purely geometric primitives, which require the designer to interactively adjust many degrees of freedom (DOFs) -- control points and associated weights -- to achieve desired shapes. The conventional shape modi cation process can often be clumsy and laborious. D-NURBS are physics-based models that incorporate mass distributions, internal deformation energies, forces, and other physical quantities into the NURBS geometric substrate. Their dynamic behavior, resulting from the numerical integration of a set of nonlinear differential equations, produces physically meaningful, hence intuitive shape variation. Consequently, a modeler can interactively sculpt complex shapes to required specifications not only in the traditional indirect fashion, by adjusting control points and setting weights, but also through direct physical manipulation, by applying simulated forces and local and global shape constraints. We use Lagrangian mechanics to formulate the equations of motion for D-NURBS curves, tensor-product D-NURBS surfaces, swung D-NURBS surfaces, and triangular D-NURBS surfaces. We apply finite element analysis to reduce these equations to eficient numerical algorithms computable at interactive rates on common graphics workstations. We implement a prototype modeling environment based on D-NURBS, and demonstrate that D-NURBS can be effective tools in a wide range of CAGD applications such as shape blending, scattered data fitting, and interactive sculpting.