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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.

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Object tracking: A survey

The Lucas-Kanade (LK) method is a classic tracking algorithm exploiting target structural constraints thorough template matching. Extended Lucas Kanade or ELK casts the original LK algorithm as a maximum likelihood optimization and then extends it by considering pixel object / background likelihoods in the optimization. Template matching and pixel-based object / background segregation are tied together by a unified Bayesian framework. In this framework two log-likelihood terms related to pixel object / background affiliation are introduced in addition to the standard LK template matching term. Tracking is performed using an EM algorithm, in which the E-step corresponds to pixel object/background inference, and the M-step to parameter optimization. The final algorithm, implemented using a classifier for object / background modeling and equipped with simple template update and occlusion handling logic, is evaluated on two challenging data-sets containing 50 sequences each. The first is a recently published benchmark where ELK ranks 3rd among 30 tracking methods evaluated. On the second data-set of vehicles undergoing severe view point changes ELK ranks in 1st place outperforming state-of-the-art methods.

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Extended Lucas-Kanade Tracking

The patch transform represents an image as a bag of overlapping patches sampled on a regular grid. This representation allows users to manipulate images in the patch domain, which then seeds the inverse patch transform to synthesize modified images. Possible modifications include the spatial locations of patches, the size of the output image, or the pool of patches from which an image is reconstructed. When no modifications are made, the inverse patch transform reduces to solving a jigsaw puzzle. The inverse patch transform is posed as a patch assignment problem on a Markov random field (MRF), where each patch should be used only once and neighboring patches should fit to form a plausible image. We find an approximate solution to the MRF using loopy belief propagation, introducing an approximation that encourages the solution to use each patch only once. The image reconstruction algorithm scales well with the total number of patches through label pruning. In addition, structural misalignment artifacts are suppressed through a patch jittering scheme that spatially jitters the assigned patches. We demonstrate the patch transform and its effectiveness on natural images.

The Patch Transform

Image retargeting algorithms attempt to adapt the image content to the screen without distorting the important objects in the scene. Existing methods address retargeting of a single image. In this paper we propose a novel method for retargeting a pair of stereo images. Naively retargeting each image independently will distort the geometric structure and make it impossible to perceive the 3D structure of the scene. We show how to extend a single image seam carving to work on a pair of images. Our method minimizes the visual distortion in each of the images as well as the depth distortion. A key property of the proposed method is that it takes into account the visibility relations between pixels in the image pair (occluded and occluding pixels). As a result, our method guarantees, as we formally prove, that the retargeted pair is geometrically consistent with a feasible 3D scene, similar to the original one. Hence, the retargeted stereo pair can be viewed on a stereoscopic display or processed by any computer vision algorithm. We demonstrate our method on a number of challenging indoor and outdoor stereo images.

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Geometrically consistent stereo seam carving

SpatialBoost extends AdaBoost to incorporate spatial reasoning. We demonstrate the effectiveness of SpatialBoost on the problem of interactive image segmentation. Our application takes as input a tri-map of the original image, trains SpatialBoost on the pixels of the object and the background and use the trained classifier to classify the unlabeled pixels. The spatial reasoning is introduced in the form of weak classifiers that attempt to infer pixel label from the pixel labels of surrounding pixels, after each boosting iteration. We call this variant of AdaBoost — SpatialBoost. We then extend the application to work with “GrabCut”. In GrabCut the user casually marks a rectangle around the object, instead of tediously marking a tri-map, and we pose the segmentation as the problem of learning with outliers, where we know that only positive pixels (i.e. pixels that are assumed to belong to the object) might be outliers and in fact should belong to the background.

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SpatialBoost: adding spatial reasoning to adaboost

SpatialBoost extends AdaBoost to incorporate spatial reasoning. We demonstrate the effectiveness of SpatialBoost on the problem of interactive image segmentation. Our application takes as input a tri-map of the original image, trains SpatialBoost on the pixels of the object and the background and use the trained classifier to classify the unlabeled pixels. The spatial reasoning is introduced in the form of weak classifiers that attempt to infer pixel label from the pixel labels of surrounding pixels, after each boosting iteration. We call this variant of AdaBoost -SpatialBoost. We then extend the application to work with GrabCut. In GrabCut the user casually marks a rectangle around the object, instead of tediously marking a tri-map, and we pose the segmentation as the problem of learning with outliers, where we know that only positive pixels (i.e. pixels that are assumed to belong to the object) might be outliers and in fact should belong to the background.

Shai Avidan

Papers

Extended Lucas-Kanade Tracking

The Patch Transform

Geometrically consistent stereo seam carving

SpatialBoost: adding spatial reasoning to adaboost

SpatialBoost : Adding Spatial Reasoning to AdaBoost