Differential methods belong to the most widely used techniques for optic flow computation in image sequences. They can be classified into local methods such as the Lucas-Kanade technique or Bigün's structure tensor method, and into global methods such as the Horn/Schunck approach and its extensions. Often local methods are more robust under noise, while global techniques yield dense flow fields. The goal of this paper is to contribute to a better understanding and the design of differential methods in four ways: (i) We juxtapose the role of smoothing/regularisation processes that are required in local and global differential methods for optic flow computation. (ii) This discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches: It yields dense flow fields that are robust against noise. (iii) Spatiotemproal and nonlinear extensions to this hybrid method are presented. (iv) We propose a simple confidence measure for optic flow methods that minimise energy functionals. It allows to sparsify a dense flow field gradually, depending on the reliability required for the resulting flow. Comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure.

In this paper, we suggest a variational model for optic flow computation based on non-linearised and higher order constancy assumptions. Besides the common grey value constancy assumption, also gradient constancy, as well as the constancy of the Hessian and the Laplacian are proposed. Since the model strictly refrains from a linearisation of these assumptions, it is also capable to deal with large displacements. For the minimisation of the rather complex energy functional, we present an efficient numerical scheme employing two nested fixed point iterations. Following a coarse-to-fine strategy it turns out that there is a theoretical foundation of so-called warping techniques hitherto justified only on an experimental basis. Since our algorithm consists of the integration of various concepts, ranging from different constancy assumptions to numerical implementation issues, a detailed account of the effect of each of these concepts is included in the experimental section. The superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques. Further experiments also confirm excellent robustness under noise and insensitivity to parameter variations.

Most variational optic flow approaches just consist of three constituents: a data term, a smoothness term and a smoothness weight. In this paper, we present an approach that harmonises these three components. We start by developing an advanced data term that is robust under outliers and varying illumination conditions. This is achieved by using constraint normalisation, and an HSV colour representation with higher order constancy assumptions and a separate robust penalisation. Our novel anisotropic smoothness is designed to work complementary to the data term. To this end, it incorporates directional information from the data constraints to enable a filling-in of information solely in the direction where the data term gives no information, yielding an optimal complementary smoothing behaviour. This strategy is applied in the spatial as well as in the spatiotemporal domain. Finally, we propose a simple method for automatically determining the optimal smoothness weight. This method bases on a novel concept that we call "optimal prediction principle" (OPP). It states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence. The benefits of our "optic flow in harmony" (OFH) approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used Middlebury optic flow benchmark.

Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for remov- ing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widelyused JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec.

Recent progress in passive facial performance capture has shown impressively detailed results on highly articulated motion. However, most methods rely on complex multi-camera set-ups, controlled lighting or fiducial markers. This prevents them from being used in general environments, outdoor scenes, during live action on a film set, or by freelance animators and everyday users who want to capture their digital selves. In this paper, we therefore propose a lightweight passive facial performance capture approach that is able to reconstruct high-quality dynamic facial geometry from only a single pair of stereo cameras. Our method succeeds under uncontrolled and time-varying lighting, and also in outdoor scenes. Our approach builds upon and extends recent image-based scene flow computation, lighting estimation and shading-based refinement algorithms. It integrates them into a pipeline that is specifically tailored towards facial performance reconstruction from challenging binocular footage under uncontrolled lighting. In an experimental evaluation, the strong capabilities of our method become explicit: We achieve detailed and spatio-temporally coherent results for expressive facial motion in both indoor and outdoor scenes -even from low quality input images recorded with a hand-held consumer stereo camera. We believe that our approach is the first to capture facial performances of such high quality from a single stereo rig and we demonstrate that it brings facial performance capture out of the studio, into the wild, and within the reach of everybody.