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

Optical flow estimation using steered-L1 norm

Motion is a very important part of understanding the visual picture of the surrounding environment. In image processing it involves the estimation of displacements for image points in an image sequence. In this context dense optical flow estimation is concerned with the computation of pixel displacements in a sequence of images, therefore it has been used widely in the field of image processing and computer vision. A lot of research was dedicated to enable an accurate and fast motion computation in image sequences. Despite the recent advances in the computation of optical flow, there is still room for improvements and optical flow algorithms still suffer from several issues, such as motion discontinuities, occlusion handling, and robustness to illumination changes. This thesis includes an investigation for the topic of optical flow and its applications. It addresses several issues in the computation of dense optical flow and proposes solutions. Specifically, this thesis is divided into two main parts dedicated to address two main areas of interest in optical flow. In the first part, image registration using optical flow is investigated. Both local and global image registration has been used for image registration. An image registration based on an improved version of the combined Local-global method of optical flow computation is proposed. A bi-lateral filter was used in this optical flow method to improve the edge preserving performance. It is shown that image registration via this method gives more robust results compared to the local and the global optical flow methods previously investigated. The second part of this thesis encompasses the main contribution of this research which is an improved total variation L1 norm. A smoothness term is used in the optical flow energy function to regularise this function. The L1 is a plausible choice for such a term because of its performance in preserving edges, however this term is known to be isotropic and hence decreases the penalisation near motion boundaries in all directions. The proposed improved L1 (termed here as the steered-L1 norm) smoothness term demonstrates similar performance across motion boundaries but improves the penalisation performance along such boundaries

3D Motion Analysis via Energy Minimization

This work deals with 3D motion analysis from stereo image sequences for driver assistance systems. It consists of two parts: the estimation of motion from the image data and the segmentation of moving objects in the input images. The content can be summarized with the technical term machine visual kinesthesia, the sensation or perception and cognition of motion. In the first three chapters, the importance of motion information is discussed for driver assistance systems, for machine vision in general, and for the estimation of ego motion. The next two chapters delineate on motion perception, analyzing the apparent movement of pixels in image sequences for both a monocular and binocular camera setup. Then, the obtained motion information is used to segment moving objects in the input video. Thus, one can clearly identify the thread from analyzing the input images to describing the input images by means of stationary and moving objects. Finally, I present possibilities for future applications based on the contents of this thesis. Previous work in each case is presented in the respective chapters. Although the overarching issue of motion estimation from image sequences is related to practice, there is nothing as practical as a good theory (Kurt Lewin). Several problems in computer vision are formulated as intricate energy minimization problems. In this thesis, motion analysis in image sequences is thoroughly investigated, showing that splitting an original complex problem into simplified sub-problems yields improved accuracy, increased robustness, and a clear and accessible approach to state-of-the-art motion estimation techniques. In Chapter 4, optical flow is considered. Optical flow is commonly estimated by minimizing the combined energy, consisting of a data term and a smoothness term. These two parts are decoupled, yielding a novel and iterative approach to optical flow. The derived Refinement Optical Flow framework is a clear and straight-forward approach to computing the apparent image motion vector field. Furthermore this results currently in the most accurate motion estimation techniques in literature. Much as this is an engineering approach of fine-tuning precision to the last detail, it helps to get a better insight into the problem of motion estimation. This profoundly contributes to state-of-the-art research in motion analysis, in particular facilitating the use of motion estimation in a wide range of applications. In Chapter 5, scene flow is rethought. Scene flow stands for the three-dimensional motion vector field for every image pixel, computed from a stereo image sequence. Again, decoupling of the commonly coupled approach of estimating three-dimensional position and three dimensional motion yields an approach to scene ow estimation with more accurate results and a considerably lower computational load. It results in a dense scene flow field and enables additional applications based on the dense three-dimensional motion vector field, which are to be investigated in the future. One such application is the segmentation of moving objects in an image sequence. Detecting moving objects within the scene is one of the most important features to extract in image sequences from a dynamic environment. This is presented in Chapter 6. Scene flow and the segmentation of independently moving objects are only first steps towards machine visual kinesthesia. Throughout this work, I present possible future work to improve the estimation of optical flow and scene flow. Chapter 7 additionally presents an outlook on future research for driver assistance applications. But there is much more to the full understanding of the three-dimensional dynamic scene. This work is meant to inspire the reader to think outside the box and contribute to the vision of building perceiving machines.</em

Dense Optical Flow Estimation Using Sparse Regularizers from Reduced Measurements

Optical flow is the pattern of apparent motion of objects in a scene. The computation of optical flow is a critical component in numerous computer vision tasks such as object detection, visual object tracking, and activity recognition. Despite a lot of research, efficiently managing abrupt changes in motion remains a challenge in motion estimation. This paper proposes novel variational regularization methods to address this problem since they allow combining different mathematical concepts into a joint energy minimization framework. In this work, we incorporate concepts from signal sparsity into variational regularization for motion estimation. The proposed regularization uses a robust l1 norm, which promotes sparsity and handles motion discontinuities. By using this regularization, we promote the sparsity of the optical flow gradient. This sparsity helps recover a signal even with just a few measurements. We explore recovering optical flow from a limited set of linear measurements using this regularizer. Our findings show that leveraging the sparsity of the derivatives of optical flow reduces computational complexity and memory needs.Comment: 12 pages, 9 figures, and 3 table

On the application of projection methods for computing optical flow fields

Detecting optical flow means to find the apparent displacement field in a sequence of images. As starting point for many optical flow methods serves the so called optical flow constraint (OFC), that is the assumption that the gray value of a moving point does not change over time. Variational methods are amongst the most popular tools to compute the optical flow field. They compute the flow field as minimizer of an energy functional that consists of a data term to comply with the OFC and a smoothness term to obtain uniqueness of this underdetermined problem. In this article we replace the smoothness term by projecting the solution to a finite dimensional, affine subspace in the spatial variables which leads to a smoothing and gives a unique solution as well. We explain the mathematical details for the quadratic and nonquadratic minimization framework, and show how alternative model assumptions such as constancy of the brightness gradient can be incorporated. As basis functions we consider tensor products of B-splines. Under certain smoothness assumptions for the global minimizer in Sobolev scales, we prove optimal convergence rates in terms of the energy functional. Experiments are presented that demonstrate the feasibility of our approach