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Multiple View Geometry in Computer Vision.

We propose a flexible technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closed-form solution, followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique and very good results have been obtained. Compared with classical techniques which use expensive equipment such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one more step from laboratory environments to real world use.

https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/tr98-71.pdf

A flexible new technique for camera calibration

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

This paper presents the top 10 data mining algorithms identified by the IEEE International Conference on Data Mining (ICDM) in December 2006: C4.5, k-Means, SVM, Apriori, EM, PageRank, AdaBoost, kNN, Naive Bayes, and CART. These top 10 algorithms are among the most influential data mining algorithms in the research community. With each algorithm, we provide a description of the algorithm, discuss the impact of the algorithm, and review current and further research on the algorithm. These 10 algorithms cover classification, clustering, statistical learning, association analysis, and link mining, which are all among the most important topics in data mining research and development.

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Top 10 algorithms in data mining

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

Certain structure detection problems can be solved by sampling a parameter space for the different structures at a finite number of points and checking each point to see if the corresponding structure has a sufficient number of inlying measurements. The measurement space is a Riemannian manifold and the measurements relevant to a given structure are near to or on a submanifold which constitutes the structure. The probability density function for the errors in the measurements is described using a generalisation of the Gaussian density to Riemannian manifolds. The conditional probability density function for the measurements yields the Fisher information which defines a metric, known as the Fisher-Rao metric, on the parameter space. The main result is a derivation of an asymptotic approximation to the Fisher-Rao metric, under the assumption that the measurement noise is small. Using this approximation to the Fisher-Rao metric, the parameter space is sampled, such that each point of the parameter space is near to at least one sample point, to within the level of accuracy allowed by the measurement errors. The probability of a false detection of a structure is estimated. The feasibility of this approach to structure detection is tested experimentally using the example of line detection in digital images.

/pdf/application-of-the-fisher-rao-metric-to-structure-detection-16q6b7932c.pdf

Application of the Fisher-Rao Metric to Structure Detection

The Minimum Description Length (MDL) criterion is used to fit a facet model of a car to an image. The best fit is achieved when the difference image between the car and the background has the greatest compression. MDL overcomes the overfitting and parameter precision problems which hamper the more usual maximum likelihood method of model fitting. Some preliminary results are shown.

Minimum Description Length method for facet matching

In certain cases, reconstruction from point correspondences between two images is ambiguous, in that two or more surfaces are obtained, each of which can give rise to the correspondences. These ambiguous surfaces are examples of rectangular hyperboloids. Each ambiguous surface is invariant under a rotation through 180° that interchanges the two possible positions for the optical centre of the camera taking the second image. As a result, the ambiguous surfaces are subject to a cubic polynomial constraint. We use this constraint to give a new proof that there are, in general, exactly ten different reconstructions compatible with five image correspondences.

/pdf/ambiguity-in-reconstruction-from-image-correspondences-wz4xvjlhta.pdf

Ambiguity in reconstruction from image correspondences

Conditional Random Fields (CRF), a structured prediction method, combines probabilistic graphical models and discriminative classification techniques in order to predict class labels in sequence recognition problems. Its extension the Hidden Conditional Random Fields (HCRF) uses hidden state variables in order to capture intermediate structures. The number of hidden states in an HCRF must be specified a priori. This number is often not known in advance. A non-parametric extension to the HCRF, with the number of hidden states automatically inferred from data, is proposed here. This is a significant advantage over the classical HCRF since it avoids ad hoc model selection procedures. Further, the training and inference procedure is fully Bayesian eliminating the over fitting problem associated with frequentist methods. In particular, our construction is based on scale mixtures of Gaussians as priors over the HCRF parameters and makes use of Hierarchical Dirichlet Process (HDP) and Laplace distribution. The proposed inference procedure uses elliptical slice sampling, a Markov Chain Monte Carlo (MCMC) method, in order to sample optimal and sparse posterior HCRF parameters. The above technique is applied for classifying human actions that occur in depth image sequences - a challenging computer vision problem. Experiments with real world video datasets confirm the efficacy of our classification approach.

/pdf/non-parametric-hidden-conditional-random-fields-for-action-3zg85yfbz5.pdf

Stephen J. Maybank

Papers

Application of the Fisher-Rao Metric to Structure Detection

Minimum Description Length method for facet matching

Ambiguity in reconstruction from image correspondences

Non-parametric Hidden Conditional Random Fields for action classification

Iteration Functions re-visited