Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. Developed in the early 1980s by Robert M. Gray, it was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms. In simpler terms, vector quantization chooses a set of points to represent a larger set of points.
A point cloud is a discrete set of data points in space. The points may represent a 3D shape or object. Each point position has its set of Cartesian coordinates. Points may contain data other than position such as RGB colors, normals, timestamps and others. Point clouds are generally produced by 3D scanners or by photogrammetry software, which measure many points on the external surfaces of objects around them. As the output of 3D scanning processes, point clouds are used for many purposes, including to create 3D computer-aided design (CAD) or geographic information systems (GIS) models for manufactured parts, for metrology and quality inspection, and for a multitude of visualizing, animating, rendering, and mass customization applications.
Image registration is the process of transforming different sets of data into one coordinate system. Data may be multiple photographs, data from different sensors, times, depths, or viewpoints. It is used in computer vision, medical imaging, military automatic target recognition, and compiling and analyzing images and data from satellites. Registration is necessary in order to be able to compare or integrate the data obtained from these different measurements.
In computational science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. It solves a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formulae over the particle's position and velocity. Each particle's movement is influenced by its local best known position, but is also guided toward the best known positions in the search-space, which are updated as better positions are found by other particles. This is expected to move the swarm toward the best solutions.
Simultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it. While this initially appears to be a chicken or the egg problem, there are several algorithms known to solve it in, at least approximately, tractable time for certain environments. Popular approximate solution methods include the particle filter, extended Kalman filter, covariance intersection, and GraphSLAM. SLAM algorithms are based on concepts in computational geometry and computer vision, and are used in robot navigation, robotic mapping and odometry for virtual reality or augmented reality.
In electrical engineering and computer science, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces and partitions of these subsets into well-shaped and uniformly sized convex cells. Like the closely related k-means clustering algorithm, it repeatedly finds the centroid of each set in the partition and then re-partitions the input according to which of these centroids is closest. In this setting, the mean operation is an integral over a region of space, and the nearest centroid operation results in Voronoi diagrams.
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values.
Compressed sensing is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. There are two conditions under which recovery is possible. The first one is sparsity, which requires the signal to be sparse in some domain. The second one is incoherence, which is applied through the isometric property, which is sufficient for sparse signals. Compressed sensing has applications in, for example, MRI where the incoherence condition is typically satisfied.
A rapidly exploring random tree (RRT) is an algorithm designed to efficiently search nonconvex, high-dimensional spaces by randomly building a space-filling tree. The tree is constructed incrementally from samples drawn randomly from the search space and is inherently biased to grow towards large unsearched areas of the problem. RRTs were developed by Steven M. LaValle and James J. Kuffner Jr. They easily handle problems with obstacles and differential constraints and have been widely used in autonomous robotic motion planning.
D* is any one of the following three related incremental search algorithms:
The Ramer–Douglas–Peucker algorithm, also known as the Douglas–Peucker algorithm and iterative end-point fit algorithm, is an algorithm that decimates a curve composed of line segments to a similar curve with fewer points. It was one of the earliest successful algorithms developed for cartographic generalization. It produces the most accurate generalization, but it is also more time-consuming.
In robotics and computer vision, visual odometry is the process of determining the position and orientation of a robot by analyzing the associated camera images. It has been used in a wide variety of robotic applications, such as on the Mars Exploration Rovers.
The Mobile Robot Programming Toolkit (MRPT) is a cross-platform software C++ library for helping robotics researchers design and implement algorithms related to simultaneous localization and mapping (SLAM), computer vision, and motion planning. Different research groups have employed MRPT to implement projects reported in some of the major robotics journals and conferences.
The Point Cloud Library (PCL) is an open-source library of algorithms for point cloud processing tasks and 3D geometry processing, such as occur in three-dimensional computer vision. The library contains algorithms for filtering, feature estimation, surface reconstruction, 3D registration, model fitting, object recognition, and segmentation. Each module is implemented as a smaller library that can be compiled separately. PCL has its own data format for storing point clouds - PCD, but also allows datasets to be loaded and saved in many other formats. It is written in C++ and released under the BSD license.
Differential dynamic programming (DDP) is an optimal control algorithm of the trajectory optimization class. The algorithm was introduced in 1966 by Mayne and subsequently analysed in Jacobson and Mayne's eponymous book. The algorithm uses locally-quadratic models of the dynamics and cost functions, and displays quadratic convergence. It is closely related to Pantoja's step-wise Newton's method.
Coordinate descent is an optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function. At each iteration, the algorithm determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane while fixing all other coordinates or coordinate blocks. A line search along the coordinate direction can be performed at the current iterate to determine the appropriate step size. Coordinate descent is applicable in both differentiable and derivative-free contexts.
In computer vision, pattern recognition, and robotics, point-set registration, also known as point-cloud registration or scan matching, is the process of finding a spatial transformation that aligns two point clouds. The purpose of finding such a transformation includes merging multiple data sets into a globally consistent model, and mapping a new measurement to a known data set to identify features or to estimate its pose. Raw 3D point cloud data are typically obtained from Lidars and RGB-D cameras. 3D point clouds can also be generated from computer vision algorithms such as triangulation, bundle adjustment, and more recently, monocular image depth estimation using deep learning. For 2D point set registration used in image processing and feature-based image registration, a point set may be 2D pixel coordinates obtained by feature extraction from an image, for example corner detection. Point cloud registration has extensive applications in autonomous driving, motion estimation and 3D reconstruction, object detection and pose estimation, robotic manipulation, simultaneous localization and mapping (SLAM), panorama stitching, virtual and augmented reality, and medical imaging.
Cloud robotics is a field of robotics that attempts to invoke cloud technologies such as cloud computing, cloud storage, and other Internet technologies centered on the benefits of converged infrastructure and shared services for robotics. When connected to the cloud, robots can benefit from the powerful computation, storage, and communication resources of modern data center in the cloud, which can process and share information from various robots or agent. Humans can also delegate tasks to robots remotely through networks. Cloud computing technologies enable robot systems to be endowed with powerful capability whilst reducing costs through cloud technologies. Thus, it is possible to build lightweight, low-cost, smarter robots with an intelligent "brain" in the cloud. The "brain" consists of data center, knowledge base, task planners, deep learning, information processing, environment models, communication support, etc.
In computer vision, rigid motion segmentation is the process of separating regions, features, or trajectories from a video sequence into coherent subsets of space and time. These subsets correspond to independent rigidly moving objects in the scene. The goal of this segmentation is to differentiate and extract the meaningful rigid motion from the background and analyze it. Image segmentation techniques labels the pixels to be a part of pixels with certain characteristics at a particular time. Here, the pixels are segmented depending on its relative movement over a period of time i.e. the time of the video sequence.
Gérard G. Medioni is a computer scientist, author, academic and inventor. He is a vice president and distinguished scientist at Amazon and serves as emeritus professor of Computer Science at the University of Southern California.
