In this paper we introduce through-the-lens camera control, a body of techniques that permit a user to manipulate a virtual camera by controlling and constraining features in the image seen through its lens. Rather than solving for camera parameters directly, constrained optimization is used to compute their time derivatives based on desired changes in user-defined controls. This effectively permits new controls to be defined independent of the underlying parameterization. The controls can also serve as constraints, maintaining their values as others are changed. We describe the techniques in general and work through a detailed example of a specific camera model. Our implementation demonstrates a gallery of useful controls and constraints and provides some examples of how these may be used in composing images and animations.

Abstract—The purpose of this contribution is to generalize some recent results on sparse representations of signals in redundant bases. The question that is considered is the following: given a matrix of dimension ( ) with and a vector = , find a sufficient condition for to have a unique sparsest representation as a linear combination of columns of. Answers to this question are known when is the concatenation of two unitary matrices and either an extensive combinatorial search is performed or a linear program is solved. We consider arbitrary matrices and give a sufficient condition for the unique sparsest solution to be the unique solution to both a linear program or a parametrized quadratic program. The proof is elementary and the possibility of using a quadratic program opens perspectives to the case where = + with a vector of noise or modeling errors. Index Terms—Basis pursuit, global matched filter, linear program, quadratic program, redundant dictionaries, sparse representations. I.

Accurate registration between real and virtual objects is crucial for augmented reality applications. Existing tracking methods are individually inadequate: magnetic trackers are inaccurate, mechanical trackers are cumbersome, and vision-based trackers are computationally problematic. We present a hybrid tracking method that combines the accuracy of vision-based tracking with the robustness of magnetic tracking without compromising real-time performance or usability. We demonstrate excellent registration in three sample applications.

We present a method for recovering 3D human body motion from monocular video sequences using robust image matching, joint limits and non-self-intersection constraints, and a new sample-andrefine search strategy guided by rescaled cost-function covariances. Monocular 3D body tracking is challenging: for reliable tracking at least 30 joint parameters need to be estimated, subject to highly nonlinear physical constraints; the problem is chronically illconditioned as about 1/3 of the d.o.f. (the depth-related ones) are almost unobservable in any given monocular image; and matching an imperfect, highly flexible, self-occluding model to cluttered image features is intrinsically hard. To reduce correspondence ambiguities we use a carefully designed robust matching-cost metric that combines robust optical flow, edge energy, and motion boundaries. Even so, the ambiguity, nonlinearity and non-observability make the parameter-space cost surface multi-modal, unpredictable and illconditioned, so minimizing it is difficult. We discuss the limitations of CONDENSATION-like samplers, and introduce a novel hybrid search algorithm that combines inflated-covariance-scaled sampling and continuous optimization subject to physical constraints. Experiments on some challenging monocular sequences show that robust cost modelling, joint and self-intersection constraints, and informed sampling are all essential for reliable monocular 3D body tracking.

HINE Parameters X0, X1, ....Xp Output E0, E1,....Ep Error Desired Output D0, D1,...Dp Y0, Y1,...Yp Input w w0 w1 AT&T Laboratories (c) COST FUNCTION Output E0, E1,....Ep Error Desired Output D0, D1,...Dp Y0, Y1,...Yp X0, X1, ....Xp Input Parameters w B R A COMPUTING THE GRADIENT WITH BACKPROPAGATION O = A(I1, I2) dI1 = dO ¶ A ¶ I1 dI2 = dO ¶ A ¶ I2 - The learning machine is composed of modules (e.g. layers) - Each module can do two things: 1- compute its outputs from its inputs (FPROP) 2- compute gradient vectors at its inputs from gradient vectors at its outputs (BPROP) A O, dO I1, dI1 I2, dI2 AT&T Laboratories (c) AN INTERESTING SPECIAL CASE: MULTILAYER NETWORKS X0, X1, ....Xp Output Desired Output D0, D1,...Dp Y0, Y1,...Yp Input || D - Y || 2 2 1 WX F() WX F() Mean Square Error Parameters (weights + biases) w Weight matrix E0, E1,....Ep Sigmoids + Biase

This paper proposes and analyzes an approach to estimating the generalization performance of a support vector machine (SVM) for text classification. Without any computation intensive resampling, the new estimators are computationally much more ecient than cross-validation or bootstrap, since they can be computed immediately from the form of the hypothesis returned by the SVM. Moreover, the estimators delevoped here address the special performance measures needed for text classification. While they can be used to estimate error rate, one can also estimate the recall, the precision, and the F 1 . A theoretical analysis and experiments on three text classification collections show that the new method can effectively estimate the performance of SVM text classifiers in a very efficient way.

Abstract. The decomposition method is currently one of the major methods for solving support vector machines. An important issue of this method is the selection of working sets. In this paper through the design of decomposition methods for bound-constrained SVM formulations we demonstrate that the working set selection is not a trivial task. Then from the experimental analysis we propose a simple selection of the working set which leads to faster convergences for difficult cases. Numerical experiments on different types of problems are conducted to demonstrate the viability of the proposed method.

Animation through the numerical simulation of physics-based graphics models offers unsurpassed realism, but it can be computationally demanding. Likewise, finding controllers that enable physics-based models to produce desired animations usually entails formidable computational cost. This paper demonstrates the possibility of replacing the numerical simulation and control of model dynamics with a dramatically more efficient alternative. In particular, we propose the NeuroAnimator, a novel approach to creating physically realistic animation that exploits neural networks. NeuroAnimators are automatically trained off-line to emulate physical dynamics through the observation of physics-based models in action. Depending on the model, its neural network emulator can yield physically realistic animation one or two orders of magnitude faster than conventional numerical simulation. Furthermore, by exploiting the network structure of the NeuroAnimator, we introduce a fast algorithm for learning controllers that enables either physics-based models or their neural network emulators to synthesize motions satisfying prescribed animation goals. We demonstrate NeuroAnimators for passive and active (actuated) rigid body, articulated, and deformable physics-based models.

A major difficulty for 3D human body tracking from monocular image sequences is the near non-observability of kinematic degrees of freedom that generate motion in depth. For known link (body segment) lengths, the strict non-observabilities reduce to twofold ‘forwards/backwards flipping ’ ambiguities for each link. These imply 2 # links formal inverse kinematics solutions for the full model, and hence linked groups of O(2 # links) local minima in the model-image matching cost function. Choosing the wrong minimum leads to rapid mistracking, so for reliable tracking, rapid methods of investigating alternative minima within a group are needed. Previous approaches to this have used generic search methods that do not exploit the specific problem structure. Here, we complement these by using simple kinematic reasoning to enumerate the tree of possible forwards/backwards flips, thus greatly speeding the search within each linked group of minima. Our methods can be used either deterministically, or within stochastic ‘jump-diffusion ’ style search processes. We give experimental results on some challenging monocular human tracking sequences, showing how the new kinematic-flipping based sampling method improves and complements existing ones.

Optimization problems involving eigenvalues arise in many applications. Let x be a vector of real parameters and let A(x) be a continuously differentiable symmetric matrix function of x. We consider a particular problem which occurs frequently: the minimization of the maximum eigenvalue of A(x), subject to linear constraints and bounds on x. The eigenvalues of A(x) are not differentiable at points x where they coalesce, so the optimization problem is said to be nonsmooth. Furthermore, it is typically the case that the optimization objective tends to make eigenvalues coalesce at a solution point. There are three main purposes of the paper. The first is to present a clear and self-contained derivation of the Clarke generalized gradient of the max eigenvalue function in terms of a "dual matrix". The second purpose is to describe a new algorithm, based on the ideas of a previous paper by the author (SIAM J. Matrix Anal. Appl. 9 (1988) 256-268), which is suitable for solving l...