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, allow to deal with large displacements and perform well under noise or 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 systems of equations 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. In particular, discontinuity-preserving regularisation strategies are thereby in the focus of our work. (ii) We show by the examples of classical as well as more advanced variational techniques that real-time performance is possible - even for very complex optic flow models with high accuracy. Experiments show frame rates up to 63 dense flow fields per second for real-world image sequences of size 160 x 120 on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude

EpicFlow: Edge-Preserving Interpolation of Correspondences for Optical Flow

We propose a novel approach for optical flow estimation , targeted at large displacements with significant oc-clusions. It consists of two steps: i) dense matching by edge-preserving interpolation from a sparse set of matches; ii) variational energy minimization initialized with the dense matches. The sparse-to-dense interpolation relies on an appropriate choice of the distance, namely an edge-aware geodesic distance. This distance is tailored to handle occlusions and motion boundaries -- two common and difficult issues for optical flow computation. We also propose an approximation scheme for the geodesic distance to allow fast computation without loss of performance. Subsequent to the dense interpolation step, standard one-level variational energy minimization is carried out on the dense matches to obtain the final flow estimation. The proposed approach, called Edge-Preserving Interpolation of Correspondences (EpicFlow) is fast and robust to large displacements. It significantly outperforms the state of the art on MPI-Sintel and performs on par on Kitti and Middlebury

Most Likely Separation of Intensity and Warping Effects in Image Registration

This paper introduces a class of mixed-effects models for joint modeling of spatially correlated intensity variation and warping variation in 2D images. Spatially correlated intensity variation and warp variation are modeled as random effects, resulting in a nonlinear mixed-effects model that enables simultaneous estimation of template and model parameters by optimization of the likelihood function. We propose an algorithm for fitting the model which alternates estimation of variance parameters and image registration. This approach avoids the potential estimation bias in the template estimate that arises when treating registration as a preprocessing step. We apply the model to datasets of facial images and 2D brain magnetic resonance images to illustrate the simultaneous estimation and prediction of intensity and warp effects

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

Variational optic flow computation in real-time

Variational methods for optic flow computation have the reputation of producing good results at the expense of being too slow for realtime applications. We show that real-time variational computation of optic flow fields is possible when appropriate methods are combined with modern numerical techniques. We consider the CLG method, a recent variational technique that combines the quality of the dense flow fields of the Horn and Schunck approach with the noise robustness of the Lucas-Kanade method. For the linear system of equations resulting from the discretised Euler-Lagrange equations, we present different multigrid schemes in detail. We show that under realistic accuracy requirements they are up to 247 times more efficient than the widely used Gauß-Seidel algorithm. On a 3.06 GHz PC, we have computed 40 dense flow fields of size 200 x 200 pixels within a single second

DeepMatching: Hierarchical Deformable Dense Matching

We introduce a novel matching algorithm, called DeepMatching, to compute dense correspondences between images. DeepMatching relies on a hierarchical, multi-layer, correlational architecture designed for matching images and was inspired by deep convolutional approaches. The proposed matching algorithm can handle non-rigid deformations and repetitive textures and efficiently determines dense correspondences in the presence of significant changes between images. We evaluate the performance of DeepMatching, in comparison with state-of-the-art matching algorithms, on the Mikolajczyk (Mikolajczyk et al 2005), the MPI-Sintel (Butler et al 2012) and the Kitti (Geiger et al 2013) datasets. DeepMatching outperforms the state-of-the-art algorithms and shows excellent results in particular for repetitive textures.We also propose a method for estimating optical flow, called DeepFlow, by integrating DeepMatching in the large displacement optical flow (LDOF) approach of Brox and Malik (2011). Compared to existing matching algorithms, additional robustness to large displacements and complex motion is obtained thanks to our matching approach. DeepFlow obtains competitive performance on public benchmarks for optical flow estimation