Duality based optical flow algorithms with applications

We consider the popular TV-L1 optical flow formulation, and the so-called dual-ity based algorithm for minimizing the TV-L1 energy. The original formulation is extended to allow for vector valued images, and minimization results are given. In addition we consider di↵erent definitions of total variation regulariza-tion, and related formulations of the optical flow problem that may be used with a duality based algorithm. We present a highly optimized algorithmic setup to estimate optical flows, and give five novel applications. The first application is registration of medical images, where X-ray images of di↵erent hands, taken using di↵erent imaging devices are registered using a TV-L1 optical flow algo-rithm. We propose to regularize the input images, using sparsity enhancing regularization of the image gradient to improve registration results. The second application is registration of 2D chromatograms, where registration only have to be done in one of the two dimensions, resulting in a vector valued registration problem with values having several hundred dimensions. We propose a nove

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

A splitting algorithm for directional regularization and sparsification

We present a new split-type algorithm for the min-imization of a p-harmonic energy with added data fi-delity term. The half-quadratic splitting reduces the original problem to two straightforward problems, that can be minimized efficiently. The minimizers to the two sub-problems can typically be computed pointwise and are easily implemented on massively parallel proces-sors. Furthermore the splitting method allows for the computation of solutions to a large number of more ad-vanced directional regularization problems. In particu-lar we are able to handle robust, non-convex data terms, and to define a 0-harmonic regularization energy where we sparsify directions by means of an L0 norm.