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Large Deformation Diffeomorphic Metric Mapping
Large deformation diffeomorphic metric mapping (LDDMM) is a specific suite of algorithms used for diffeomorphic mapping and manipulating dense imagery based on diffeomorphic metric mapping within the academic discipline of computational anatomy, to be distinguished from its precursor based on diffeomorphic mapping. The distinction between the two is that diffeomorphic metric maps satisfy the property that the length associated to their flow away from the identity induces a metric on the group of diffeomorphisms, which in turn induces a metric on the orbit of shapes and forms within the field of Computational Anatomy. The study of shapes and forms with the metric of diffeomorphic metric mapping is called diffeomorphometry. A diffeomorphic mapping system is a system designed to map, manipulate, and transfer information which is stored in many types of spatially distributed medical imagery. Diffeomorphic mapping is the underlying technology for mapping and analyzing information m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Anatomy
Computational anatomy is an interdisciplinary field of biology focused on quantitative investigation and modelling of anatomical shapes variability. It involves the development and application of mathematical, statistical and data-analytical methods for modelling and simulation of biological structures. The field is broadly defined and includes foundations in anatomy, applied mathematics and pure mathematics, machine learning, computational mechanics, computational science, biological imaging, neuroscience, physics, probability, and statistics; it also has strong connections with fluid mechanics and geometric mechanics. Additionally, it complements newer, interdisciplinary fields like bioinformatics and neuroinformatics in the sense that its interpretation uses metadata derived from the original sensor imaging modalities (of which magnetic resonance imaging is one example). It focuses on the anatomical structures being imaged, rather than the medical imaging devices. It is similar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neuroinformatics
Neuroinformatics is the field that combines informatics and neuroscience. Neuroinformatics is related with neuroscience data and information processing by artificial neural networks. There are three main directions where neuroinformatics has to be applied: * the development of computational models of the nervous system and neural processes. * the development of tools for analyzing and modeling neuroscience data, * the development of tools and databases for management and sharing of neuroscience data at all levels of analysis, Neuroinformatics is related with philosophy (computational theory of mind), psychology (information processing theory), computer science (natural computing, bio-inspired computing), among others. Neuroinformatics doesn't deal with matter or energy, so it can be seen as a branch of neurobiology that studies various aspects of nervous systems. The term ''neuroinformatics'' seems to be used synonymously with cognitive informatics, described by ''Journal of Biome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faisal Beg LDDMM Algorithnm
Faisal, Faisel, Fayçal or Faysal ( ar, فيصل) is an Arabic given name. Faisal, Fayçal or Faysal may also refer to: People * King Faisal (other) ** Faisal I of Iraq and Syria (1885–1933), leader during the Arab Revolt ** Faisal II of Iraq (1935–1958), last King of the Kingdom of Iraq ** Faisal of Saudi Arabia (1906–1975), third King of Saudi Arabia * Faisal al-Duwaish (1882–1931), Arabian tribe sheik * Faisal Karami (born 1971), Lebanese politician * Faisal bin Abdullah Al Saud (born 1950), Saudi royal * Faisal bin Bandar Al Saud (born 1945), Saudi government official * Faisal bin Bandar Al Saud, Saudi royal and businessman * Faisal bin Khalid Al Saud (born 1973), Saudi government official * Faisal bin Mishaal Al Saud (born 1959), Saudi government official * Faisal bin Musaid Al Saud, Saudi royal * Faisal bin Sattam Al Saud (born 1970), Saudi ambassador to Italy * Faisal bin Turki Al Saud, Saudi royal * Faisal bin Turki I Al Saud (1920–1968), Saudi roya ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sobolev Space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, i.e. a Banach space. Intuitively, a Sobolev space is a space of functions possessing sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function. Sobolev spaces are named after the Russian mathematician Sergei Sobolev. Their importance comes from the fact that weak solutions of some important partial differential equations exist in appropriate Sobolev spaces, even when there are no strong solutions in spaces of continuous functions with the derivatives understood in the classical sense. Motivation In this section and throughout the article \Omega is an open subset of \R^n. There are many c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamilton's Principal Of Least Action
The stationary-action principle – also known as the principle of least action – is a variational principle that, when applied to the ''action'' of a mechanical system, yields the equations of motion for that system. The principle states that the trajectories (i.e. the solutions of the equations of motion) are ''stationary points'' of the system's ''action functional''. The term "least action" is a historical misnomer since the principle has no minimality requirement: the value of the action functional need not be minimal (even locally) on the trajectories. The principle can be used to derive Newtonian, Lagrangian and Hamiltonian equations of motion, and even general relativity (see Einstein–Hilbert action). In relativity, a different action must be minimized or maximized. The classical mechanics and electromagnetic expressions are a consequence of quantum mechanics. The stationary action method helped in the development of quantum mechanics. In 1933, the physicist Paul Dir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid-body Kinematics
In physics, a rigid body (also known as a rigid object) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light. In quantum mechanics, a rigid body is usually thought of as a collection of point masses. For instance, molecules (consisting of the point masses: electrons and nuclei) are often seen as rigid bodies (see classification of molecules as rigid rotors). Kinematics Linear and angular position The position of a rigid body is the position of all the particles of which it is composed. To simplify the description of this position, we exploit the property that the body is rigid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian And Eulerian Specification Of The Flow Field
__NOTOC__ In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an individual parcel through time gives the pathline of the parcel. This can be visualized as sitting in a boat and drifting down a river. The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. This can be visualized by sitting on the bank of a river and watching the water pass the fixed location. The Lagrangian and Eulerian specifications of the flow field are sometimes loosely denoted as the Lagrangian and Eulerian frame of reference. However, in general both the Lagrangian and Eulerian specification of the flow field can be applied in any observer's frame of reference, and in any coordinate system used within the chosen fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffeomorphisms
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable. Definition Given two manifolds M and N, a differentiable map f \colon M \rightarrow N is called a diffeomorphism if it is a bijection and its inverse f^ \colon N \rightarrow M is differentiable as well. If these functions are r times continuously differentiable, f is called a C^r-diffeomorphism. Two manifolds M and N are diffeomorphic (usually denoted M \simeq N) if there is a diffeomorphism f from M to N. They are C^r-diffeomorphic if there is an r times continuously differentiable bijective map between them whose inverse is also r times continuously differentiable. Diffeomorphisms of subsets of manifolds Given a subset X of a manifold M and a subset Y of a manifold N, a function f:X\to Y is said to be smooth if for all p in X there is a neighborhood ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morphome
Morphome is one of the omes in biology to map and classify all the morphological features of species. Morphome is different from phenome in that it is the totality of morphological variants while phenome includes non-morphological variants. See also * Genome * Proteome * Interactome In molecular biology, an interactome is the whole set of molecular interactions in a particular cell. The term specifically refers to physical interactions among molecules (such as those among proteins, also known as protein–protein interactions, ... References * Automotive morphome analysis of medical-biological images. Pishak, Vasyl P.; Tymochko, K. B.; Antoniuk, O. P. Proc. SPIE Vol. 4607, p. 411-413, Selected Papers from Fifth International Conference on Correlation Optics, ; Ed. * Strategies for the physiome project. Bassingthwaighte JB. Ann Biomed Eng. 2000 Aug;28(8):1043-58. Review. Comparative anatomy {{biology-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brown University
Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providence Plantations. Brown is one of nine colonial colleges chartered before the American Revolution. Admissions at Brown is among the most selective in the United States. In 2022, the university reported a first year acceptance rate of 5%. It is a member of the Ivy League. Brown was the first college in the United States to codify in its charter that admission and instruction of students was to be equal regardless of their religious affiliation. The university is home to the oldest applied mathematics program in the United States, the oldest engineering program in the Ivy League, and the third-oldest medical program in New England. The university was one of the early doctoral-granting U.S. institutions in the late 19th century, adding masters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulf Grenander
Ulf Grenander (23 July 1923 – 12 May 2016) was a Swedish statistician and professor of applied mathematics at Brown University. His early research was in probability theory, stochastic processes, time series analysis, and statistical theory (particularly the order-constrained estimation of cumulative distribution functions using his sieve estimator). In recent decades, Grenander contributed to computational statistics, image processing, pattern recognition, and artificial intelligence. He coined the term pattern theory to distinguish from pattern recognition. Honors In 1966 Grenander was elected to the Royal Academy of Sciences of Sweden, and in 1996 to the US National Academy of Sciences. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. He received an honorary doctorate in 1994 from the University of Chicago, and in 2005 from the Royal Institute of Technology of Stockholm, Sweden. Schooling Grenander earned his undergraduate degree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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