Optimal sequential classification theory generalizes naturally from that of single-hypothesis classification. However, longer sequences require characterization with higher-order probability distributions; consequently, the design of optimal classifiers can become computationally prohibitive for real-time applications. A Markov assumption for the class random process provides structure to the distribution, enabling efficient evaluation with a limited number of arithmetic operations; the Viterbi algorithm exploits this property to provide a computationally inexpensive maximum a posteriori classifier when the Markov process is first-order. This letter extends this classical result for general order Markov processes and assesses the additional computational cost in terms of multiplication operations. Additionally, a second efficient algorithm is provided which determines the optimal hypothesis if a sample-level loss function is used. In contrast to the Viterbi classifier which implicitly penalizes all erroneous sequences equally, this classifier judges misclassifications more gradually, providing higher flexibility for challenging classification tasks.

When constructing 3D geometry for use in cel animation, the reference drawings of the object or character often contain various view-specific distortions, which cannot be captured with conventional 3D models.In this work we present a technique called View-Dependent Geometry, wherein a 3D model changes shape based on the direction it is viewed from.A view-dependent model consists of a base model, a set of key deformations (deformed versions of the base model), and a set of corresponding key viewpoints (which relate each 2D reference drawing to the 3D base model).Given an arbitrary viewpoint, our method interpolates the key deformations to generate a 3D model that is specific to the new viewpoint, thereby capturing the viewdependent distortions of the reference drawings.

In image-based rendering, images acquired from a scene are used to represent the scene itself.A number of reference images are required to fully represent even the simplest scene.This leads to a number of problems during image acquisition and subsequent reconstruction.We present the multiple-center-of-projection image, a single image acquired from multiple locations, which solves many of the problems of working with multiple range images.This work develops and discusses multiple-center-ofprojection images, and explains their advantages over conventional range images for image-based rendering.The contributions include greater flexibility during image acquisition and improved image reconstruction due to greater connectivity information.We discuss the acquisition and rendering of multiple-center-of-projection datasets, and the associated sampling issues.We also discuss the unique epipolar and correspondence properties of this class of image.