Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

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Computer Vision: Algorithms and Applications

The quantitative evaluation of optical flow algorithms by Barron et al. (1994) led to significant advances in performance. The challenges for optical flow algorithms today go beyond the datasets and evaluation methods proposed in that paper. Instead, they center on problems associated with complex natural scenes, including nonrigid motion, real sensor noise, and motion discontinuities. We propose a new set of benchmarks and evaluation methods for the next generation of optical flow algorithms. To that end, we contribute four types of data to test different aspects of optical flow algorithms: (1) sequences with nonrigid motion where the ground-truth flow is determined by tracking hidden fluorescent texture, (2) realistic synthetic sequences, (3) high frame-rate video used to study interpolation error, and (4) modified stereo sequences of static scenes. In addition to the average angular error used by Barron et al., we compute the absolute flow endpoint error, measures for frame interpolation error, improved statistics, and results at motion discontinuities and in textureless regions. In October 2007, we published the performance of several well-known methods on a preliminary version of our data to establish the current state of the art. We also made the data freely available on the web at http://vision.middlebury.edu/flow/ . Subsequently a number of researchers have uploaded their results to our website and published papers using the data. A significant improvement in performance has already been achieved. In this paper we analyze the results obtained to date and draw a large number of conclusions from them.

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A Database and Evaluation Methodology for Optical Flow

Variational methods are among the most successful approaches to calculate the optical flow between two image frames. A particularly appealing formulation is based on total variation (TV) regularization and the robust L1 norm in the data fidelity term. This formulation can preserve discontinuities in the flow field and offers an increased robustness against illumination changes, occlusions and noise. In this work we present a novel approach to solve the TV-L1 formulation. Our method results in a very efficient numerical scheme, which is based on a dual formulation of the TV energy and employs an efficient point-wise thresholding step. Additionally, our approach can be accelerated by modern graphics processing units. We demonstrate the real-time performance (30 fps) of our approach for video inputs at a resolution of 320 × 240 pixels.

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A duality based approach for realtime TV-L 1 optical flow

Optical flow estimation is classically marked by the requirement of dense sampling in time. While coarse-to-fine warping schemes have somehow relaxed this constraint, there is an inherent dependency between the scale of structures and the velocity that can be estimated. This particularly renders the estimation of detailed human motion problematic, as small body parts can move very fast. In this paper, we present a way to approach this problem by integrating rich descriptors into the variational optical flow setting. This way we can estimate a dense optical flow field with almost the same high accuracy as known from variational optical flow, while reaching out to new domains of motion analysis where the requirement of dense sampling in time is no longer satisfied.

Large Displacement Optical Flow: Descriptor Matching in Variational Motion Estimation

Optical flow computation is a key component in many computer vision systems designed for tasks such as action detection or activity recognition. However, despite several major advances over the last decade, handling large displacement in optical flow remains an open problem. Inspired by the large displacement optical flow of Brox and Malik, our approach, termed Deep Flow, blends a matching algorithm with a variational approach for optical flow. We propose a descriptor matching algorithm, tailored to the optical flow problem, that allows to boost performance on fast motions. The matching algorithm builds upon a multi-stage architecture with 6 layers, interleaving convolutions and max-pooling, a construction akin to deep convolutional nets. Using dense sampling, it allows to efficiently retrieve quasi-dense correspondences, and enjoys a built-in smoothing effect on descriptors matches, a valuable asset for integration into an energy minimization framework for optical flow estimation. Deep Flow efficiently handles large displacements occurring in realistic videos, and shows competitive performance on optical flow benchmarks. Furthermore, it sets a new state-of-the-art on the MPI-Sintel dataset.

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DeepFlow: Large Displacement Optical Flow with Deep Matching

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.

Highly accurate optic flow computation with theoretically justified warping

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Highly Accurate Optic Flow Computation with Theoretically Justified Warping

An important issue in computer-assisted surgery of the liver is a fast and reliable transfer of preoperative resection plans to the intraoperative situation. One problem is to match the planning data, derived from preoperative CT or MR images, with 3D ultrasound images of the liver, acquired during surgery. As the liver deforms significantly in the intraoperative situation non-rigid registration is necessary. This is a particularly challenging task because pre- and intraoperative image data stem from different modalities and ultrasound images are generally very noisy. One way to overcome these problems is to incorporate prior knowledge into the registration process. We propose a method of combining anatomical landmark information with a fast non-parametric intensity registration approach. Mathematically, this leads to a constrained optimization problem. As distance measure we use the normalized gradient field which allows for multimodal image registration. A qualitative and quantitative validation on clinical liver data sets of three different patients has been performed. We used the distance of dense corresponding points on vessel center lines for quantitative validation. The combined landmark and intensity approach improves the mean and percentage of point distances above 3 mm compared to rigid and thin-plate spline registration based only on landmarks. The proposed algorithm offers the possibility to incorporate additional a priori knowledge—in terms of few landmarks—provided by a human expert into a non-rigid registration process.

3D ultrasound-CT registration of the liver using combined landmark-intensity information

Optic fow describes the displacement field in an image sequence. Its reliable computation constitutes one of the main challenges in computer vision, and variational methods belong to the most successful techniques for achieving this goal. Variational methods recover the optic flow field as a minimiser of a suitable energy functional that involves data and smoothness terms. In this paper we present a survey on different model assumptions for each of these terms and illustrate their impact by experiments. We restrict ourselves to rotationally invariant convex functionals with a linearised data term. Such models are appropriate for small displacements. Regarding the data term, constancy assumptions on the brightness, the gradient, the Hessian, the gradient magnitude, the Laplacian, and the Hessian determinant are investigated. Local integration and nonquadratic penalisation are considered in order to improve robustness under noise. With respect to the smoothness term, we review a recent taxonomy that links regularisers to diffusion processes. It allows to distinguish five types of regularisation strategies: homogeneous, isotropic image-driven, anisotropic image-driven, isotropic flow-driven, and anisotropic flow-driven. All these regularisations can be performed either in the spatial or the spatiotemporal domain. After discussing well-posedness results for convex optic flow functionals, we sketch some numerical ideas in order to achieve realtime performance on a standard PC by means of multigrid methods, and we survey a simple and intuitive confidence measure.

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A survey on variational optic flow methods for small displacements

We present a super fast variational algorithm for the challenging problem of multimodal image registration. It is capable of registering full-body CT and PET images in about a second on a standard CPU with virtually no memory requirements. The algorithm is founded on a Gauss-Newton optimization scheme with specifically tailored, mathematically optimized computations for objective function and derivatives. It is fully parallelized and perfectly scalable, thus directly suitable for usage in many-core environments. The accuracy of our method was tested on 21 PET-CT scan pairs from clinical routine. The method was able to correct random distortions in the range from -10 cm to 10 cm translation and from -15° to 15° degree rotation to subvoxel accuracy. In addition, it exhibits excellent robustness to noise.

Nils Papenberg

Papers

Highly accurate optic flow computation with theoretically justified warping

Highly Accurate Optic Flow Computation with Theoretically Justified Warping

3D ultrasound-CT registration of the liver using combined landmark-intensity information

A survey on variational optic flow methods for small displacements

A fully parallel algorithm for multimodal image registration using normalized gradient fields