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Multiple View Geometry in Computer Vision.

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

Computer vision applications have come to rely increasingly on superpixels in recent years, but it is not always clear what constitutes a good superpixel algorithm. In an effort to understand the benefits and drawbacks of existing methods, we empirically compare five state-of-the-art superpixel algorithms for their ability to adhere to image boundaries, speed, memory efficiency, and their impact on segmentation performance. We then introduce a new superpixel algorithm, simple linear iterative clustering (SLIC), which adapts a k-means clustering approach to efficiently generate superpixels. Despite its simplicity, SLIC adheres to boundaries as well as or better than previous methods. At the same time, it is faster and more memory efficient, improves segmentation performance, and is straightforward to extend to supervoxel generation.

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SLIC Superpixels Compared to State-of-the-Art Superpixel Methods

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

The goal of this article is to review the state-of-the-art tracking methods, classify them into different categories, and identify new trends. Object tracking, in general, is a challenging problem. Difficulties in tracking objects can arise due to abrupt object motion, changing appearance patterns of both the object and the scene, nonrigid object structures, object-to-object and object-to-scene occlusions, and camera motion. Tracking is usually performed in the context of higher-level applications that require the location and/or shape of the object in every frame. Typically, assumptions are made to constrain the tracking problem in the context of a particular application. In this survey, we categorize the tracking methods on the basis of the object and motion representations used, provide detailed descriptions of representative methods in each category, and examine their pros and cons. Moreover, we discuss the important issues related to tracking including the use of appropriate image features, selection of motion models, and detection of objects.

/pdf/object-tracking-a-survey-3706dclxb5.pdf

Object tracking: A survey

We update the SVM (support vector machine) score of an object through a video sequence with a small and variable subset of support vectors. In the first frame we use all the support vectors to compute the SVM score of the object but in subsequent frames we use only a small and variable subset of support vectors to update the SVM score. In each frame we calculate the dot-products of the support vectors in the subset with the pattern of the object being tracked. The difference in the dot-products, between past and current frames, is used to update the SVM score. This is done at a fraction of the computational cost required to re-evaluate the SVM score from scratch in every frame. The two methods we develop are "cyclic subset selection", in which we break the set of all support vectors into subsets of equal size and use them cyclically, and "maximum variance subset selection", in which we choose the support vectors whose dot-product with the test pattern varied the most in previous frames. We combine these techniques together for the problem of maintaining the SVM score of objects through a video sequence. Results on real video sequences are shown.

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Subset selection for efficient SVM tracking

We present a new method for rendering novel images of flexible 3D objects from a small number of example images in correspondence. The strength of the method is the ability to synthesize images whose viewing position is significantly far away from the viewing cone of the example images (“view extrapolation”), yet without ever modeling the 3D structure of the scene. The method relies on synthesizing a chain of “trilinear tensors” that governs the warping function from the example images to the novel image, together with a multi-dimensional interpolation function that synthesizes the non-rigid motions of the viewed object from the virtual camera position. We show that two closely spaced example images alone are sufficient in practice to synthesize a significant viewing cone, thus demonstrating the ability of representing an object by a relatively small number of model images — for the purpose of cheap and fast viewers that can run on standard hardware.

/pdf/image-based-view-synthesis-by-combining-trilinear-tensors-4qxc47z56w.pdf

Image-based view synthesis by combining trilinear tensors and learning techniques

Photo-sequencing is the problem of recovering the temporal order of a set of still images of a dynamic event, taken asynchronously by a set of uncalibrated cameras. Solving this problem is a first, crucial step for analyzing (or visualizing) the dynamic content of the scene captured by a large number of freely moving spectators. We propose a geometric based solution, followed by rank aggregation to the photo-sequencing problem. Our algorithm trades spatial certainty for temporal certainty. Whereas the previous solution proposed by [4] relies on two images taken from the same static camera to eliminate uncertainty in space, we drop the static-camera assumption and replace it with temporal information available from images taken from the same (moving) camera. Our method thus overcomes the limitation of the static-camera assumption, and scales much better with the duration of the event and the spread of cameras in space. We present successful results on challenging real data sets and large scale synthetic data (250 images).

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Space-Time Tradeoffs in Photo Sequencing

We extend the l0-norm ldquosubspectralrdquo algorithms developed for sparse-LDA (Moghaddam, 2006) and sparse-PCA (Moghaddam, 2006) to more general quadratic costs such as MSE in linear (or kernel) regression. The resulting ldquosparse least squaresrdquo (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem. Specifically, for minimizing general quadratic cost functions we use a highly-efficient method for direct eigenvalue computation based on partitioned matrix inverse techniques that leads to times103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) complexity that limited the previous algorithmspsila utility for high-dimensional problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes even more efficient than forward selection. Similarly, branch-and-bound search for exact sparse least squares (ESLS) also benefits from partitioned matrix techniques. Our greedy sparse least squares (GSLS) algorithm generalizes Natarajanpsilas algorithm (Natarajan, 1995) also known as order-recursive matching pursuit (ORMP). Specifically, the forward pass of GSLS is exactly equivalent to ORMP but is more efficient, and by including the backward pass, which only doubles the computation, we can achieve a lower MSE than ORMP. In experimental comparisons with LARS (Efron, 2004), forward-GSLS is shown to be not only more efficient and accurate but more flexible in terms of choice of regularization.

Sparse regression as a sparse eigenvalue problem

Running races, such as marathons, are broadly covered by professional as well as amateur photographers. This leads to a constantly growing number of photos covering a race, making the process of identifying a particular runner in such datasets difficult. Today, such identification is often done manually. In running races, each competitor has an identification number, called the Racing Bib Number (RBN), used to identify that competitor during the race. RBNs are usually printed on a paper or cardboard tag and pined onto the competitor’s T-shirt during the race. We introduce an automatic system that receives a set of natural images taken in running sports events and outputs the participants’ RBN.

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Shai Avidan

Papers

Subset selection for efficient SVM tracking

Image-based view synthesis by combining trilinear tensors and learning techniques

Space-Time Tradeoffs in Photo Sequencing

Sparse regression as a sparse eigenvalue problem

Racing Bib Numbers Recognition.