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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

Sparse PCA seeks approximate sparse "eigenvectors" whose projections capture the maximal variance of data. As a cardinality-constrained and non-convex optimization problem, it is NP-hard and is encountered in a wide range of applied fields, from bio-informatics to finance. Recent progress has focused mainly on continuous approximation and convex relaxation of the hard cardinality constraint. In contrast, we consider an alternative discrete spectral formulation based on variational eigenvalue bounds and provide an effective greedy strategy as well as provably optimal solutions using branch-and-bound search. Moreover, the exact methodology used reveals a simple renormalization step that improves approximate solutions obtained by any continuous method. The resulting performance gain of discrete algorithms is demonstrated on real-world benchmark data and in extensive Monte Carlo evaluation trials.

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Spectral Bounds for Sparse PCA: Exact and Greedy Algorithms

Many natural images contain reflections and transparency, i.e., they contain mixtures of reflected and transmitted light. When viewed from a moving camera, these appear as the superposition of component layer images moving relative to each other. The problem of multiple motion recovery has been previously studied by a number of researchers. However no one has yet demonstrated how to accurately recover the component images themselves. In this paper we develop an optimal approach to recovering layer images and their associated motions from an arbitrary number of composite images. We develop two different techniques for estimating the component layer images given known motion estimates. The first approach uses constrained least squares to recover the layer images. The second approach iteratively refines lower and upper bounds on the layer images using two novel compositing operations, namely minimum- and maximum-composites of aligned images. We combine these layer extraction techniques with a dominant motion estimator and a subsequent motion refinement stage. This results in a completely automated system that recovers transparent images and motions from a collection of input images.

Layer extraction from multiple images containing reflections and transparency

Locally Orderless Tracking (LOT) is a visual tracking algorithm that automatically estimates the amount of local (dis)order in the object. This lets the tracker specialize in both rigid and deformable objects on-line and with no prior assumptions. We provide a probabilistic model of the object variations over time. The model is implemented using the Earth Mover's Distance (EMD) with two parameters that control the cost of moving pixels and changing their color. We adjust these costs on-line during tracking to account for the amount of local (dis)order in the object. We show LOT's tracking capabilities on challenging video sequences, both commonly used and new, demonstrating performance comparable to state-of-the-art methods.

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Locally Orderless Tracking

We consider the problem of reconstructing the 3D coordinates of a moving point seen from a monocular moving camera, i.e., to reconstruct moving objects from line-of-sight measurements only. The task is feasible only when some constraints are placed on the shape of the trajectory of the moving point. We coin the family of such tasks as "trajectory triangulation." We investigate the solutions for points moving along a straight-line and along conic-section trajectories, We show that if the point is moving along a straight line, then the parameters of the line (and, hence, the 3D position of the point at each time instant) can be uniquely recovered, and by linear methods, from at least five views. For the case of conic-shaped trajectory, we show that generally nine views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is of a known type (like a circle in 3D Euclidean space for which seven views are sufficient). The paradigm of trajectory triangulation, in general, pushes the envelope of processing dynamic scenes forward. Thus static scenes become a particular case of a more general task of reconstructing scenes rich with moving objects (where an object could be a single point).

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Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence

We present a new method for synthesizing novel views of a 3D scene from few model images in full correspondence. The core of this work is the derivation of a tensorial operator that describes the transformation from a given tensor of three views to a novel tensor of a new configuration of three views. By repeated application of the operator on a seed tensor with a sequence of desired virtual camera positions we obtain a chain of warping functions (tensors) from the set of model images to create the desired virtual views.

Shai Avidan

Papers

Spectral Bounds for Sparse PCA: Exact and Greedy Algorithms

Layer extraction from multiple images containing reflections and transparency

Locally Orderless Tracking

Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence

Novel view synthesis in tensor space