There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Multiple View Geometry in Computer Vision.

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

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

Feature matching is at the base of many computer vision problems, such as object recognition or structure from motion. Current methods rely on costly descriptors for detection and matching. In this paper, we propose a very fast binary descriptor based on BRIEF, called ORB, which is rotation invariant and resistant to noise. We demonstrate through experiments how ORB is at two orders of magnitude faster than SIFT, while performing as well in many situations. The efficiency is tested on several real-world applications, including object detection and patch-tracking on a smart phone.

ORB: An efficient alternative to SIFT or SURF

Where feature points are used in real-time frame-rate applications, a high-speed feature detector is necessary. Feature detectors such as SIFT (DoG), Harris and SUSAN are good methods which yield high quality features, however they are too computationally intensive for use in real-time applications of any complexity. Here we show that machine learning can be used to derive a feature detector which can fully process live PAL video using less than 7% of the available processing time. By comparison neither the Harris detector (120%) nor the detection stage of SIFT (300%) can operate at full frame rate.

Clearly a high-speed detector is of limited use if the features produced are unsuitable for downstream processing. In particular, the same scene viewed from two different positions should yield features which correspond to the same real-world 3D locations [1]. Hence the second contribution of this paper is a comparison corner detectors based on this criterion applied to 3D scenes. This comparison supports a number of claims made elsewhere concerning existing corner detectors. Further, contrary to our initial expectations, we show that despite being principally constructed for speed, our detector significantly outperforms existing feature detectors according to this criterion.

/pdf/machine-learning-for-high-speed-corner-detection-5cjrw8o3xc.pdf

Machine learning for high-speed corner detection

Where feature points are used in real-time frame-rate applications, a high-speed feature detector is necessary. Feature detectors such as SIFT (DoG), Harris and SUSAN are good methods which yield high quality features, however they are too computationally intensive for use in real-time applications of any complexity. Here we show that machine learning can be used to derive a feature detector which can fully process live PAL video using less than 7% of the available processing time. By comparison neither the Harris detector (120%) nor the detection stage of SIFT (300%) can operate at full frame rate. Clearly a high-speed detector is of limited use if the features produced are unsuitable for downstream processing. In particular, the same scene viewed from two different positions should yield features which correspond to the same real-world 3D locations[1]. Hence the second contribution of this paper is a comparison corner detectors based on this criterion applied to 3D scenes. This comparison supports a number of claims made elsewhere concerning existing corner detectors. Further, contrary to our initial expectations, we show that despite being principally constructed for speed, our detector significantly outperforms existing feature detectors according to this criterion. © Springer-Verlag Berlin Heidelberg 2006.

Machine Learning for High-Speed Corner Detection

The repeatability and efficiency of a corner detector determines how likely it is to be useful in a real-world application. The repeatability is important because the same scene viewed from different positions should yield features which correspond to the same real-world 3D locations. The efficiency is important because this determines whether the detector combined with further processing can operate at frame rate. Three advances are described in this paper. First, we present a new heuristic for feature detection and, using machine learning, we derive a feature detector from this which can fully process live PAL video using less than 5 percent of the available processing time. By comparison, most other detectors cannot even operate at frame rate (Harris detector 115 percent, SIFT 195 percent). Second, we generalize the detector, allowing it to be optimized for repeatability, with little loss of efficiency. Third, we carry out a rigorous comparison of corner detectors based on the above repeatability criterion applied to 3D scenes. We show that, despite being principally constructed for speed, on these stringent tests, our heuristic detector significantly outperforms existing feature detectors. Finally, the comparison demonstrates that using machine learning produces significant improvements in repeatability, yielding a detector that is both very fast and of very high quality.

/pdf/faster-and-better-a-machine-learning-approach-to-corner-3thqerwqfu.pdf

Faster and Better: A Machine Learning Approach to Corner Detection

This paper addresses the problem of real-time 3D model-based tracking by combining point-based and edge-based tracking systems. We present a careful analysis of the properties of these two sensor systems and show that this leads to some non -trivial design choices that collectively yield extremely high performance. In particular, we present a method for integrating the two systems and robustly combining the pose estimates they produce. Further we show how on-line learning can be used to improve the performance of feature tracking. Finally, to aid real-time performance, we introduce the FAST feature detector which can perform full-frame feature detection at 400Hz. The combination of these techniques results in a system which is capable of tracking average prediction errors of 200 pixels. This level of robustness allows us to track very rapid motions, such as 50deg camera shake at 6Hz

/pdf/fusing-points-and-lines-for-high-performance-tracking-2kgezxhhk3.pdf

Fusing points and lines for high performance tracking

Presents a framework for three-dimensional model-based tracking. Graphical rendering technology is combined with constrained active contour tracking to create a robust wire-frame tracking system. It operates in real time at video frame rate (25 Hz) on standard hardware. It is based on an internal CAD model of the object to be tracked which is rendered using a binary space partition tree to perform hidden line removal. A Lie group formalism is used to cast the motion computation problem into simple geometric terms so that tracking becomes a simple optimization problem solved by means of iterative reweighted least squares. A visual servoing system constructed using this framework is presented together with results showing the accuracy of the tracker. The paper then describes how this tracking system has been extended to provide a general framework for tracking in complex configurations. The adjoint representation of the group is used to transform measurements into common coordinate frames. The constraints are then imposed by means of Lagrange multipliers. Results from a number of experiments performed using this framework are presented and discussed.

/pdf/real-time-visual-tracking-of-complex-structures-56p3xlm7ub.pdf

Tom Drummond

Papers

Machine learning for high-speed corner detection

Machine Learning for High-Speed Corner Detection

Faster and Better: A Machine Learning Approach to Corner Detection

Fusing points and lines for high performance tracking

Real-time visual tracking of complex structures