|
Thin Plate Splines
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. They were introduced to geometric design by Duchon. They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and shortly known as the TPS-RPM algorithm. Physical analogy The name ''thin plate spline'' refers to a physical analogy involving the bending of a thin sheet of metal. Just as the metal has rigidity, the TPS fit resists bending also, implying a penalty involving the smoothness of the fitted surface. In the physical setting, the deflection is in the z direction, orthogonal to the plane. In order to apply this idea to the problem of coordinate transformation, one interprets the lifting of the plate as a displacement of the x or y coordinates within the plane. In 2D cases, given a set of K corresponding points, the TPS warp is described by 2(K+3) parameters which include 6 global affine motion parameters and 2K coefficients for corre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline (mathematics)
In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. In the computer science subfields of computer-aided design and computer graphics, the term ''spline'' more frequently refers to a piecewise polynomial ( parametric) curve. Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes. Introduction The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Distance Weighting
Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points. This method can also be used to create spatial weights matrices in spatial autocorrelation analyses (e.g. Moran's ''I''). The name given to this type of method was motivated by the weighted average applied, since it resorts to the inverse of the distance to each known point ("amount of proximity") when assigning weights. Definition of the problem The expected result is a discrete assignment of the unknown function u in a study region: :u(x): x \to \mathbb, \quad x \in \mathbf \sub \mathbb^n, where \mathbf is the study region. The set of N known data points can be described as a list of tuples: : x_1, u_1), (x_2, u_2), ..., (x_N, u_N) The function is to be "smooth" (continuous and once differentiable), to be exact (u(x_i) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Society For Industrial And Applied Mathematics
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics. SIAM is one of the four member organizations of the Joint Policy Board for Mathematics. Membership Membership is open to both individuals and organizations. By the end of its first full year of operation, SIAM had 130 memb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grace Wahba
Grace Goldsmith Wahba (born August 3, 1934) is an American statistician and now-retired I. J. Schoenberg-Hilldale Professor of Statistics at the University of Wisconsin–Madison. She is a pioneer in methods for smoothing noisy data. Best known for the development of generalized cross-validation and "Wahba's problem", she has developed methods with applications in demographic studies, machine learning, DNA microarrays, risk modeling, medical imaging, and climate prediction. Biography Grace Wahba had an interest in science from an early age, when she was in Junior High she was given a chemistry set. At this time she also interested in becoming an engineer. Wahba studied at Cornell University for her undergraduate degree. When she was there women were severely restricted in their privileges, for example she was required to live in a dorm and had a curfew. She received her bachelor's degree from Cornell University in 1956 and a master's degree from the University of Maryland, Col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hubert Mara
Hubert Mara is an Austrian Computer Scientist who specializes in Archaeoinformatics and the application of methods from computer science to the humanities, and thus a combination of these fields. Education and career Hubert Mara graduated (matura) in electrical engineering from the HTBLuVA in Wiener Neustadt and studied computer science at the TU Wien, graduating in 2006. Already during his studies he participated in excavations in Israel and Peru, where he learned to combine methods of computer science and humanities. Early on, he participated in the development of new methods here, such as for 3D recording of ancient pottery for the Austrian Corpus Vasorum Antiquorum. After graduation, he received a Marie Curie Fellowship, with the help of which he went to the University of Florence, where he joined the ''Cultural Heritage Informatics Research Oriented Network'' (CHIRON) was involved in the development of the ''London Charter for the Computational Visualization of Cultural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diamantis Panagiotopoulos
Diamantis Panagiotopoulos (born 6 July 1967, Athens, Greece) is an Aegean Bronze Age archaeologist and Director of the Institute of Classical Archaeology at the University of Heidelberg. Education Diamantis Panagiotopoulos studied Classical Archaeology, History, Prehistory and Art History at the University of Athens, where he finished his diploma in 1989. 1990 he became PhD at the University of Heidelberg. There he added Egyptology and Ancient Near Eastern Studies to his expertise. 1996 he received his doctor's degree at the Ruprecht-Karls University of Heidelberg, with the title: "Das Tholosgrab E in der Nekropole von Phourni (Archanes). Studien zu einem nördlichen Außenposten der Mesara-Bestattungskultur". Seven years later Panagiotopoulos promoted to professor for Classical Archaeology with "Untersuchungen zur mykenischen Siegelpraxis" at the Philosophical Institute at the Paris Lodron University of Salzburg. 1997 he participated as scientific contributor for the Heraklion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Object Identifier
A digital object identifier (DOI) is a persistent identifier or handle used to uniquely identify various objects, standardized by the International Organization for Standardization (ISO). DOIs are an implementation of the Handle System; they also fit within the URI system ( Uniform Resource Identifier). They are widely used to identify academic, professional, and government information, such as journal articles, research reports, data sets, and official publications. DOIs have also been used to identify other types of information resources, such as commercial videos. A DOI aims to resolve to its target, the information object to which the DOI refers. This is achieved by binding the DOI to metadata about the object, such as a URL where the object is located. Thus, by being actionable and interoperable, a DOI differs from ISBNs or ISRCs which are identifiers only. The DOI system uses the indecs Content Model for representing metadata. The DOI for a document remains fixed over t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Longin Zeller
Karl Longin Zeller (December 28, 1924, Šiauliai, Lithuania – July 20, 2006, Tübingen) was a German mathematician and computer scientist who worked in numerical analysis and approximation theory.. He is the namesake of Zeller operators. Zeller was drafted into the Wehrmacht, and lost his right arm on the Soviet front of World War II. He earned his Ph.D. from the University of Tübingen in 1950, under the supervision of Konrad Knopp and Erich Kamke, and remained at Tübingen for most of his career as a professor and as director of the computer center. He left Tübingen in 1959 for a professorship in Stuttgart but returned to Tübingen in 1960 with a personal chair in "the mathematics of supercomputer facilities" (german: Mathematik der Hochleistungsrechenanlagen), making him one of the founders of computer science in Germany. He has over 200 academic descendants. In 1993, he was given an honorary doctorate by the University of Siegen The University of Siegen (german: Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subdivision Surface
In the field of 3D computer graphics, a subdivision surface (commonly shortened to SubD surface) is a curved surface represented by the specification of a coarser polygon mesh and produced by a recursive algorithmic method. The curved surface, the underlying ''inner mesh'', can be calculated from the coarse mesh, known as the ''control cage'' or ''outer mesh'', as the functional limit of an iterative process of subdividing each polygonal face into smaller faces that better approximate the final underlying curved surface. Less commonly, a simple algorithm is used to add geometry to a mesh by subdividing the faces into smaller ones without changing the overall shape or volume. Overview A subdivision surface algorithm is recursive in nature. The process starts with a base level polygonal mesh. A refinement scheme is then applied to this mesh. This process takes that mesh and subdivides it, creating new vertices and new faces. The positions of the new vertices in the mesh are compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline (mathematics)
In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. In the computer science subfields of computer-aided design and computer graphics, the term ''spline'' more frequently refers to a piecewise polynomial ( parametric) curve. Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes. Introduction The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoothing Spline
Smoothing splines are function estimates, \hat f(x), obtained from a set of noisy observations y_i of the target f(x_i), in order to balance a measure of goodness of fit of \hat f(x_i) to y_i with a derivative based measure of the smoothness of \hat f(x). They provide a means for smoothing noisy x_i, y_i data. The most familiar example is the cubic smoothing spline, but there are many other possibilities, including for the case where x is a vector quantity. Cubic spline definition Let \ be a set of observations, modeled by the relation Y_i = f(x_i) + \epsilon_i where the \epsilon_i are independent, zero mean random variables (usually assumed to have constant variance). The cubic smoothing spline estimate \hat f of the function f is defined to be the minimizer (over the class of twice differentiable functions) of : \sum_^n \^2 + \lambda \int \hat f''(x)^2 \,dx. Remarks: * \lambda \ge 0 is a smoothing parameter, controlling the trade-off between fidelity to the data and roughnes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radial Basis Function
A radial basis function (RBF) is a real-valued function \varphi whose value depends only on the distance between the input and some fixed point, either the origin, so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ), or some other fixed point \mathbf, called a ''center'', so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf-\mathbf\right\, ). Any function \varphi that satisfies the property \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ) is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection \_k which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they were originally applied to machine learning, in work by David Broomhead and David Lowe in 1988, which st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.png "Click for more on -> Subdivision Surface")
