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Iterative Closest Point
Iterative closest point (ICP) is an algorithm employed to minimize the difference between two clouds of points. ICP is often used to reconstruct 2D or 3D surfaces from different scans, to localize robots and achieve optimal path planning (especially when wheel odometry is unreliable due to slippery terrain), to co-register bone models, etc. Overview The Iterative Closest Point algorithm keeps one point cloud, the reference or target, fixed, while transforming the other, the source, to best match the reference. The transformation (combination of translation and rotation) is iteratively estimated in order to minimize an error metric, typically the sum of squared differences between the coordinates of the matched pairs. ICP is one of the widely used algorithms in aligning three dimensional models given an initial guess of the rigid transformation required. The ICP algorithm was first introduced by Chen and Medioni, and Besl and McKay. The Iterative Closest Point algorithm contras ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Idea Closest Point Algorithm
In common usage and in philosophy, ideas are the results of thought. Also in philosophy, ideas can also be mental representational images of some object. Many philosophers have considered ideas to be a fundamental ontological category of being. The capacity to create and understand the meaning of ideas is considered to be an essential and defining feature of human beings. In a popular sense, an idea arises in a reflexive, spontaneous manner, even without thinking or serious reflection, for example, when we talk about the ''idea'' of a person or a place. A new or an original idea can often lead to innovation. Etymology The word ''idea'' comes from Greek ἰδέα ''idea'' "form, pattern," from the root of ἰδεῖν ''idein'', "to see." History The argument over the underlying nature of ideas is opened by Plato, whose exposition of his theory of forms--which recurs and accumulates over the course of his many dialogs--appropriates and adds a new sense to the Greek word for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Method
In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''n''-th approximation is derived from the previous ones. A specific implementation of an iterative method, including the Algorithm#Termination, termination criteria, is an algorithm of the iterative method. An iterative method is called convergent if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common. In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors, direct methods would deliver an exact solution (for example, solving a linear system of equations A\mathbf=\mathbf by Gaussian elimination). Iterative methods are often the only cho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Set Registration
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 (''e.g.,'' scaling, rotation and translation) that aligns two point clouds. The purpose of finding such a transformation includes merging multiple data sets into a globally consistent model (or coordinate frame), 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 registratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Insight Segmentation And Registration Toolkit
__NOTOC__ ITK is a cross-platform, open-source application development framework widely used for the development of image segmentation and image registration programs. Segmentation is the process of identifying and classifying data found in a digitally sampled representation. Typically the sampled representation is an image acquired from such medical instrumentation as CT or MRI scanners. Registration is the task of aligning or developing correspondences between data. For example, in the medical environment, a CT scan may be aligned with an MRI scan in order to combine the information contained in both. ITK was developed with funding from the National Library of Medicine (U.S.) as an open resource of algorithms for analyzing the images of the Visible Human Project. ITK stands for The Insight Segmentation and Registration Toolkit. The toolkit provides leading-edge segmentation and registration algorithms in two, three, and more dimensions. ITK uses the CMake build environment to ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PCL (Point Cloud Library)
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 (for example, libpcl_filters, libpcl_features, libpcl_surface, ...). PCL has its own data format for storing point clouds - PCD (Point Cloud Data), but also allows datasets to be loaded and saved in many other formats. It is written in C++ and released under the BSD license. These algorithms have been used, for example, for perception in robotics to filter outliers from noisy data, stitch 3D point clouds together, segment relevant parts of a scene, extract keypoints and compute descriptors to recognize objects in the world based on their geometric appearance, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CloudCompare
CloudCompare is a 3D point cloud processing software (such as those obtained with a laser scanner). It can also handle triangular meshes and calibrated images. Originally created during a collaboration between Telecom ParisTech and the R&D division of EDF, the CloudCompare project began in 2003 with the PhD of Daniel Girardeau-Montaut on ''Change detection on 3D geometric data''. At that time, its main purpose was to quickly detect changes in 3D high density point clouds acquired with laser scanners in industrial facilities (such as power plants) or building sites. Afterwards it evolved towards a more general and advanced 3D data processing software. It is now an independent open source project and a free software. CloudCompare provides a set of basic tools for manually editing and rendering 3D points clouds and triangular meshes. It also offers various advanced processing algorithms, among which methods for performing: * projections (axis-based, cylinder or a cone ''unrolling'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MeshLab
MeshLab is a 3D mesh processing software system that is oriented to the management and processing of unstructured large meshes and provides a set of tools for editing, cleaning, healing, inspecting, rendering, and converting these kinds of meshes. MeshLab is free and open-source software, subject to the requirements of the GNU General Public License (GPL), version 2 or later, and is used as both a complete package and a library powering other software. It is well known in the more technical fields of 3D development and data handling. Overview MeshLab is developed by the ISTI - CNR research center; initially MeshLab was created as a course assignment at the University of Pisa in late 2005. It is a general-purpose system aimed at the processing of the typical not-so-small unstructured 3D models that arise in the 3D scanning pipeline. The automatic mesh cleaning filters includes removal of duplicated, unreferenced vertices, non-manifold edges, vertices, and null faces. Remeshing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-d Tree
In computer science, a ''k''-d tree (short for ''k-dimensional tree'') is a space-partitioning data structure for organizing points in a ''k''-dimensional space. ''k''-d trees are a useful data structure for several applications, such as searches involving a multidimensional search key (e.g. range searches and nearest neighbor searches) and creating point clouds. ''k''-d trees are a special case of binary space partitioning trees. Description The ''k''-d tree is a binary tree in which ''every'' node is a ''k''-dimensional point. Every non-leaf node can be thought of as implicitly generating a splitting hyperplane that divides the space into two parts, known as half-spaces. Points to the left of this hyperplane are represented by the left subtree of that node and points to the right of the hyperplane are represented by the right subtree. The hyperplane direction is chosen in the following way: every node in the tree is associated with one of the ''k'' dimensions, with the hyper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Procrustes Problem
The orthogonal Procrustes problem is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices A and B and asked to find an orthogonal matrix \Omega which most closely maps A to B. Specifically, :R = \arg\min_\Omega\, \Omega A-B\, _F \quad\mathrm\quad \Omega^T \Omega=I, where \, \cdot\, _F denotes the Frobenius norm. This is a special case of Wahba's problem (with identical weights; instead of considering two matrices, in Wahba's problem the columns of the matrices are considered as individual vectors). Another difference is, that Wahba's problem tries to find a proper rotation matrix, instead of just an orthogonal one. The name Procrustes refers to a bandit from Greek mythology who made his victims fit his bed by either stretching their limbs or cutting them off. Solution This problem was originally solved by Peter Schönemann in a 1964 thesis, and shortly after appeared in the journal Psychometrika. This problem is equivalent to find ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kabsch Algorithm
The Kabsch algorithm, named after Wolfgang Kabsch, is a method for calculating the optimal rotation matrix that minimizes the RMSD ( root mean squared deviation) between two paired sets of points. It is useful in graphics, cheminformatics to compare molecular structures, and also bioinformatics for comparing protein structures (in particular, see root-mean-square deviation (bioinformatics)). The algorithm only computes the rotation matrix, but it also requires the computation of a translation vector. When both the translation and rotation are actually performed, the algorithm is sometimes called partial Procrustes superimposition (see also orthogonal Procrustes problem). Description The algorithm for the rotation of into starts with two sets of paired points, and . Each set of points can be represented as an matrix. The first row is the coordinates of the first point, the second row is the coordinates of the second point, the th row is the coordinates of the th point. Chec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Transformation
In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space. (A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a proper rigid transformation, or rototranslation. Any proper rigid transformation can be decomposed into a rotation followed by a translation, while any improper rigid transformation can be decomposed into an improper rotation followed by a translation, or into a sequence of reflections. Any object wil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
