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In applied mathematics, k-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition approach. k-SVD is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to better fit the data.
Point set registration is the process of aligning two point sets. Here, the blue fish is being registered to the red fish. 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.
In linear algebra, the generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition (SVD).The two versions differ because one version decomposes two matrices (somewhat like the higher-order or tensor SVD) and the other version uses a set of constraints imposed on the left and right singular vectors of a single-matrix SVD.
The strategy for computing the Multilinear SVD and the M-mode SVD was introduced in the 1960s by L. R. Tucker, [3] further advocated by L. De Lathauwer et al., [5] and by Vasilescu and Terzopulous. [ 8 ] [ 6 ] The term HOSVD was coined by Lieven De Lathauwer, but the algorithm typically referred to in the literature as HOSVD was introduced by ...
Top: The action of M, indicated by its effect on the unit disc D and the two canonical unit vectors e 1 and e 2. Left: The action of V ⁎, a rotation, on D, e 1, and e 2. Bottom: The action of Σ, a scaling by the singular values σ 1 horizontally and σ 2 vertically.
In linear algebra, two-dimensional singular-value decomposition (2DSVD) computes the low-rank approximation of a set of matrices such as 2D images or weather maps in a manner almost identical to SVD (singular-value decomposition) which computes the low-rank approximation of a single matrix (or a set of 1D vectors).
PCL (Point Cloud Library) is an open-source framework for n-dimensional point clouds and 3D geometry processing. It includes several variants of the ICP algorithm. [9] Open source C++ implementations of the ICP algorithm are available in VTK, ITK and Open3D libraries.
A simple example is fitting a line in two dimensions to a set of observations. Assuming that this set contains both inliers, i.e., points which approximately can be fitted to a line, and outliers, points which cannot be fitted to this line, a simple least squares method for line fitting will generally produce a line with a bad fit to the data including inliers and outliers.