Abstract. 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.

We present a method for the automatic estimation of two-parameter radial distortion models, considering polynomial as well as division models. The method first detects the longest distorted lines within the image by applying the Hough transform enriched with a radial distortion parameter. From these lines, the first distortion parameter is estimated, then we initialize the second distortion parameter to zero and the two-parameter model is embedded into an iterative nonlinear optimization process to improve the estimation. This optimization aims at reducing the distance from the edge points to the lines, adjusting two distortion parameters as well as the coordinates of the center of distortion. Furthermore, this allows detecting more points belonging to the distorted lines, so that the Hough transform is iteratively repeated to extract a better set of lines until no improvement is achieved. We present some experiments on real images with significant distortion to show the ability of the proposed approach to automatically correct this type of distortion as well as a comparison between the polynomial and division models. Source CodeThe source code, the code documentation, and the online demo are accessible at the IPOL web page of this article 1 In this page, an implementation is available for download. Compilation and usage instructions are included in the README.txt file of the archive.

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Abstract-The aim of this work is to study several strategies for the preservation of flow discontinuities in variational optical flow methods. We analyze the combination of robust functionals and diffusion tensors in the smoothness assumption. Our study includes the use of tensors based on decreasing functions, which has shown to provide good results. However, it presents several limitations and usually does not perform better than other basic approaches. It typically introduces instabilities in the computed motion fields in the form of independent blobs of vectors with large magnitude.We propose two alternatives to overcome these drawbacks: first, a simple approach that combines the decreasing function with a minimum isotropic smoothing; second, a method that looks for the best parameter configuration that preserves the important motion contours and avoid instabilities. It relies on the input images and the regularization parameter. It is fully automatic, providing a near-optimal value for many sequences, as shown in the experiments. Both proposals allow to detect the contours of the motion field and produce more stable solutions for a large range of parameters. In the experimental results, we present a detailed study and comparison of the different strategies.

In this work, we describe an implementation of the variational method proposed by Brox et al. in 2004, which yields accurate optical flows with low running times. It has several benefits with respect to the method of Horn and Schunck: it is more robust to the presence of outliers, produces piecewise-smooth flow fields and can cope with constant brightness changes. This method relies on the brightness and gradient constancy assumptions, using the information of the image intensities and the image gradients to find correspondences. It also generalizes the use of continuous L 1 functionals, which help mitigate the effect of outliers and create a Total Variation (TV) regularization. Additionally, it introduces a simple temporal regularization scheme that enforces a continuous temporal coherence of the flow fields. Source CodeThe source code, the code documentation, and the online demo are accessible at the IPOL web page of this article 1 . In this page an implementation is available for download. This file contains two directories: one for the spatial method and another for the temporal method. The spatial method is suitable for general image sequences, while the temporal method should be used when the flow fields are known to be very continuous.