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

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

One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.

/pdf/laplacian-eigenmaps-for-dimensionality-reduction-and-data-4k0gjfvthz.pdf

Laplacian Eigenmaps for dimensionality reduction and data representation

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

Biomedical imaging is a driver of scientific discovery and a core component of medical care and is being stimulated by the field of deep learning. While semantic segmentation algorithms enable image analysis and quantification in many applications, the design of respective specialized solutions is non-trivial and highly dependent on dataset properties and hardware conditions. We developed nnU-Net, a deep learning-based segmentation method that automatically configures itself, including preprocessing, network architecture, training and post-processing for any new task. The key design choices in this process are modeled as a set of fixed parameters, interdependent rules and empirical decisions. Without manual intervention, nnU-Net surpasses most existing approaches, including highly specialized solutions on 23 public datasets used in international biomedical segmentation competitions. We make nnU-Net publicly available as an out-of-the-box tool, rendering state-of-the-art segmentation accessible to a broad audience by requiring neither expert knowledge nor computing resources beyond standard network training.

nnU-Net: a self-configuring method for deep learning-based biomedical image segmentation

This paper presents some of the computer vision techniques that were employed in order to automatically select features, measure features' displacements, and evaluate measurements during robotic visual servoing tasks. We experimented with a lot of different techniques, but the most robust proved to be the Sum-of-Squared Differences (SSD) optical flow technique. In addition, several techniques for the evaluation of the measurements are presented. One important characteristic of these techniques is that they can also be used for the selection of features for tracking in conjunction with several numerical criteria that guarantee the robustness of the servoing. These techniques are important aspects of our work since they can be used either on-line or off-line. An extension of the SSD measure to color images is presented and the results from the application of these techniques to real images are discussed. Finally, the derivation of depth maps through the controlled motion of the handeye system is outlined and the important role of the automatic feature selection algorithm in the accurate computation of the depth-related parameters is highlighted.

Selection of features and evaluation of visual measurements during robotic visual servoing tasks

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

/pdf/tensor-sparse-coding-for-positive-definite-matrices-440aijyrxs.pdf

Tensor Sparse Coding for Positive Definite Matrices

In this paper, we address the problem of recovering the intrinsic and extrinsic parameters of a camera or a group of cameras in a setting overlooking a traffic scene. Unlike many other settings, conventional camera calibration techniques are not applicable in this case. We present a method that uses certain geometric primitives commonly found in traffic scenes in order to recover calibration parameters. These primitives provide needed redundancy and are weighted depending on the significance of there corresponding image features. We show experimentally that these primitives are capable of achieving accurate results suitable for most traffic monitoring applications.

/pdf/using-geometric-primitives-to-calibrate-traffic-scenes-364tm9t67m.pdf

Using geometric primitives to calibrate traffic scenes

A mobile robot, called a ranger, equipped with a ring of sonars and a color camera is at the center of this research effort. The ranger is part of a fleet of heterogenous robots. Its task is to quickly deploy multiple smaller robots with specialized sensing capabilities, called scouts, into different rooms. In order to achieve the goal, the ranger must be able to safely navigate through potentially unknown urban environments as well as autonomously detect areas into which the scouts should be released. This paper presents the ranger's sensing and control algorithms and reports results from several different environments.

Real-time door detection in cluttered environments

Current robotic systems lack the flexibility of dynamic interaction with the environment. The use of sensors can make the robotic systems more flexible. Among the different types of sensors, vision sensors play a critical role. In this thesis, we present the framework of "controlled active vision" which states that a controlled motion of a vision sensor can maximize the performance of any robotic algorithm that involves a moving vision sensor. The research in this thesis is a bridge between conventional vision and control theory research. One of the applications of this framework is real-time robotic (eye-in-hand configuration) visual servoing around static or moving arbitrary 3-D objects. We formulate the problem of visual tracking and servoing as a problem of combining control with computer vision. Algorithms that incorporate the use of multiple windows and numerically stable confidence measures are combined with stochastic controllers in order to provide a satisfactory solution to the tracking problem. The special relations between the characteristics of computer vision and control algorithms are highlighted through a series of experimental results.
One of the most important contributions of this work is the introduction of adaptive control techniques in order to compensate for inaccurate modeling of the environment, such as depth estimation. One example is in the case of inaccurate knowledge of the features' depth where the displacements are fed to adaptive SISO controllers that estimate the desired robot motion. Our recent work extends the algorithms to full 3-D tracking and servoing. In one of the experiments, the manipulator repositions itself with respect to the static target. In another experiment, the manipulator tracks the full 3-D motion of the target without having accurate information about the system's parameters. The human operator can be integrated with the autonomous servoing modules through a sophisticated system architecture. The performance of the proposed algorithms has been tested on two real systems, the CMU DD Arm II and the TROIKABOT.

Controlled active vision

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