Simultaneous inference for misaligned multivariate functional data

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and reference

An Automated Algorithm for Approximation of Temporal Video Data Using Linear B'EZIER Fitting

This paper presents an efficient method for approximation of temporal video data using linear Bezier fitting. For a given sequence of frames, the proposed method estimates the intensity variations of each pixel in temporal dimension using linear Bezier fitting in Euclidean space. Fitting of each segment ensures upper bound of specified mean squared error. Break and fit criteria is employed to minimize the number of segments required to fit the data. The proposed method is well suitable for lossy compression of temporal video data and automates the fitting process of each pixel. Experimental results show that the proposed method yields good results both in terms of objective and subjective quality measurement parameters without causing any blocking artifacts.Comment: 14 Pages, IJMA 201

Multi-Scale 3D Scene Flow from Binocular Stereo Sequences

Scene flow methods estimate the three-dimensional motion field for points in the world, using multi-camera video data. Such methods combine multi-view reconstruction with motion estimation. This paper describes an alternative formulation for dense scene flow estimation that provides reliable results using only two cameras by fusing stereo and optical flow estimation into a single coherent framework. Internally, the proposed algorithm generates probability distributions for optical flow and disparity. Taking into account the uncertainty in the intermediate stages allows for more reliable estimation of the 3D scene flow than previous methods allow. To handle the aperture problems inherent in the estimation of optical flow and disparity, a multi-scale method along with a novel region-based technique is used within a regularized solution. This combined approach both preserves discontinuities and prevents over-regularization – two problems commonly associated with the basic multi-scale approaches. Experiments with synthetic and real test data demonstrate the strength of the proposed approach.National Science Foundation (CNS-0202067, IIS-0208876); Office of Naval Research (N00014-03-1-0108