Abstract. This paper considers, the determination of internal camera parameters from two views of a point set in three dimensions. A non-iterative algorithm is given for determining the focal lengths of the two cameras, as well as their relative placement, assuming all other internal camera parameters to be known. It is shown that this is all the information that may be deduced from a set of image correspondences. 1

Abstract. A method based on graph theory is investigated for creating global parametrizations for surface triangulations for the purpose of smooth surface fitting. The parametrizations, which are planar triangulations, are the solutions of linear systems based on convex combinations. A particular parametrization, called shape-preserving, is found to lead to visually smooth surface approximations. A standard approach to fitting a smooth parametric curve c(t) through a given sequence of points xi = (xi,yi,zi) ∈ IR 3, i = 1,...,N is to first make a parametrization, a corresponding increasing sequence of parameter values ti. By finding smooth functions x,y,z: [t1,tN] → IR for which x(ti) = xi, y(ti) = yi, z(ti) = zi, an interpolatory curve

This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.

We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to an unchanging number of "neurons". If allowed exponential time for computation, they turn out to have unbounded power. However, under polynomial-time constraints there are limits on their capabilities, though being more powerful than Turing Machines. (A similar but more restricted model was shown to be polynomial-time equivalent to classical digital computation in the previous work [20].) Moreover, there is a precise correspondence between nets and standard non-uniform circuits with equivalent resources, and as a consequence one has lower bound constraints on what they can compute. This relationship is perhaps surprising since our analog devices do not change in any manner with input size. We note that these networks are not likely to solve polynomially NP-hard problems, as the equality ...

The author has developed a new version of his Fortran multiprecision computation system that is based on the Fortran-90 language. With this new approach, a translator program is not required — translation of Fortran code for multiprecision is accomplished by merely utilizing advanced features of Fortran-90, such as derived data types and operator extensions. This approach results in more reliable translation and also permits programmers of multiprecision applications to utilize the full power of the Fortran-90 language. Three multiprecision datatypes are supported in this system: multiprecision integer, real and complex. All the usual Fortran conventions for mixed mode operations are supported, and many of the Fortran intrinsics, such as SIN, EXP and MOD, are supported with multiprecision arguments. This paper also briefly describes an interesting application of this software, wherein new number-theoretic identities have been discovered by means of multiprecision computations.

This paper describes a technique for using magnetic motion capture data to determine the joint parameters of an articulated hierarchy. This technique makes it possible to determine limb lengths, joint locations, and sensor placement for a human subject without external measurements. Instead, the joint parameters are inferred with high accuracy from the motion data acquired during the capture session. The parameters are computed by performing a linear least squares fit of a rotary joint model to the input data. A hierarchical structure for the articulated model can also be determined in situations where the topology of the model is not known. Once the system topology and joint parameters have been recovered, the resulting model can be used to perform forward and inverse kinematic procedures. We present the results of using the algorithm on human motion capture data, as well as validation results obtained with data from a simulation and a wooden linkage of known dimensions.

Many real-world systems are naturally modeled as hybrid stochastic processes, i.e., stochastic processes that contain both discrete and continuous variables. Examples include speech recognition, target tracking, and monitoring of physical systems. The task is usually to perform probabilistic inference, i.e., infer the hidden state of the system given some noisy observations. For example, we can ask what is the probability that a certain word was pronounced given the readings of our microphone, what is the probability that a submarine is trying to surface given our sonar data, and what is the probability of a valve being open given our pressure and flow readings. Bayesian networks are

In response to a letter from Goldbach, Euler considered sums of the form 1 X k=1 ` 1 + 1 2 m + \Delta \Delta \Delta + 1 k m ' (k + 1) \Gamman for positive integers m and n. Euler was able to give explicit values for certain of these sums in terms of the Riemann zeta function. In a recent companion paper, Euler's results were extended to a significantly larger class of sums of this type, including sums with alternating signs. This research was facilitated by numerical computations using an algorithm that can determine, with high confidence, whether or not a particular numerical value can be expressed as a rational linear combination of several given constants. The present paper presents the numerical techniques used in these computations and lists many of the experimental results that have been obtained.

We present a method for applying complex textures to hand-drawn characters in cel animation. The method correlates features in a simple, textured, 3-D model with features on a hand-drawn figure, and then distorts the model to conform to the hand-drawn artwork. The process uses two new algorithms: a silhouette detection scheme and a depth-preserving warp. The silhouette detection algorithm is simple and efficient, and it produces continuous, smooth, visible contours on a 3-D model. The warp distorts the model in only two dimensions to match the artwork from a given camera perspective, yet preserves 3-D effects such as self-occlusion and foreshortening. The entire process allows animators to combine complex textures with hand-drawn artwork, leveraging the strengths of 3-D computer graphics while retaining the expressiveness of traditional handdrawn cel animation.

Many pattern recognition tasks, including estimation, classification, and the finding of similar objects, make use of linear models. The fundamental operation in such tasks is the computation of the dot product between a query vector and a large database of instance vectors. Often we are interested primarily in those instance vectors which have high dot products with the query. We present a random sampling based algorithm that enables us to identify, for any given query vector, those instance vectors which have large dot products, while avoiding explicit computation of all dot products. We provide experimental results that demonstrate considerable speedups for text retrieval tasks. 1 Introduction In pattern recognition tasks, a database of instances to be processed (images, signals, documents,...) is commonly represented as a set of a vectors x 1 ; : : : ; xn of numeric feature values. Examples of feature values include the number of times a word occurs in a document, the coordinates...