Andrés Bruhn

High Accuracy Optical Flow Estimation Based on a Theory for Warping

We study an energy functional for computing optical flow that combines three assumptions: a brightness constancy assumption, a gradient constancy assumption, and a discontinuity-preserving spatio-temporal smoothness constraint. In order to allow for large displacements, linearisations in the two data terms are strictly avoided. We present a consistent numerical scheme based on two nested fixed point iterations. By proving that this scheme implements a coarse-to-fine warping strategy, we give a theoretical foundation for warping which has been used on a mainly experimental basis so far. Our evaluation demonstrates that the novel method gives significantly smaller angular errors than previous techniques for optical flow estimation. We show that it is fairly insensitive to parameter variations, and we demonstrate its excellent robustness under noise.

Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods

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 Bigüns 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 novel 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) Spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method. (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.

Highly Accurate Optic Flow Computation with Theoretically Justified Warping

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.

Optic Flow in Harmony

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 spatio-temporal 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.

A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods

Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude.

Variational optical flow computation in real time

This paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations. Although these numerical schemes are among the fastest methods for solving equation systems, they are rarely applied in the field of computer vision. We demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real-time performance on standard PCs. As a representative for variational optic flow methods, we consider the recently introduced combined local-global method. It can be considered as a noise-robust generalization of the Horn and Schunck technique. We present a decoupled, as well as a coupled, version of the classical Gau/spl szlig/-Seidel solver, and we develop several multigrid implementations based on a discretization coarse grid approximation. In contrast, with standard bidirectional multigrid algorithms, we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies. As a consequence, no restrictions concerning the image size or the number of traversed levels have to be imposed. In the experimental section, we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multigrid methods and nonhierachical solvers. For the well-known 316/spl times/252 Yosemite sequence, we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3.06-GHz Pentium4 PC. This corresponds to a frame rate of 18 flow fields per second which outperforms the widely-used Gau/spl szlig/-Seidel method by almost three orders of magnitude.

Towards ultimate motion estimation: combining highest accuracy with real-time performance

Although variational methods are among the most accurate techniques for estimating the optical flow, they have not yet entered the field of real-time vision. Main reason is the great popularity of standard numerical schemes that are easy to implement, however, at the expense of being too slow for real-time performance. In our paper we address this problem in two ways: (i) we present an improved version of the highly accurate technique of Brox et al. (2004). Thereby we show that a separate robustification of the constancy assumptions is very useful, in particular if the I-norm is used as penalizer. As a result, a method is obtained that yields the lowest angular errors in the literature, (ii) We develop an efficient numerical scheme for the proposed approach that allows real-time performance for sequences of size 160 /spl times/ 720. To this end, we combine two hierarchical strategies: a coarse-to-fine warping strategy as implementation of a fixed point iteration for a non-convex optimisation problem and a nonlinear full multigrid method - a so called full approximation scheme (FAS) - for solving the highly nonlinear equation systems at each warping level. In the experimental section the advantage of the proposed approach becomes obvious: Outperforming standard numerical schemes by two orders of magnitude frame rates of six high quality flow fields per second are obtained on a 3.06 GHz Pentium4 PC.

Variational motion segmentation with level sets

We suggest a variational method for the joint estimation of optic flow and the segmentation of the image into regions of similar motion. It makes use of the level set framework following the idea of motion competition, which is extended to non-parametric motion. Moreover, we automatically determine an appropriate initialization and the number of regions by means of recursive two-phase splits with higher order region models. The method is further extended to the spatiotemporal setting and the use of additional cues like the gray value or color for the segmentation. It need not fear a quantitative comparison to pure optic flow estimation techniques: For the popular Yosemite sequence with clouds we obtain the currently most accurate result. We further uncover a mistake in the ground truth. Coarsely correcting this, we get an average angular error below 1 degree.

Lightweight binocular facial performance capture under uncontrolled lighting

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.

Complementary Optic Flow

We introduce the concept of complementarity between data and smoothness term in modern variational optic flow methods. First we design a sophisticated data term that incorporates HSV colour representation with higher order constancy assumptions, completely separate robust penalisation, and constraint normalisation. Our anisotropic smoothness term reduces smoothing in the data constraint direction instead of the image edge direction, while enforcing a strong filling-in effect orthogonal to it. This allows optimal complementarity between both terms and avoids undesirable interference. The high quality of our complementary optic flow (COF) approach is demonstrated by the current top ranking result at the Middlebury benchmark.