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Morphological Image Processing
Mathematical morphology (MM) is a theory and technique for the analysis and processing of geometrical structures, based on set theory, lattice theory, topology, and random functions. MM is most commonly applied to digital images, but it can be employed as well on graphs, surface meshes, solids, and many other spatial structures. Topological and geometrical continuous-space concepts such as size, shape, convexity, connectivity, and geodesic distance, were introduced by MM on both continuous and discrete spaces. MM is also the foundation of morphological image processing, which consists of a set of operators that transform images according to the above characterizations. The basic morphological operators are erosion, dilation, opening and closing. MM was originally developed for binary images, and was later extended to grayscale functions and images. The subsequent generalization to complete lattices is widely accepted today as MM's theoretical foundation. History Mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Processing
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensional picture, that resembles a subject. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term “image” may refer specifically to a 2D image. An image does not have to use the entire visual system to be a visual representation. A popular example of this is of a greyscale image, which uses the visual system's sensitivity to brightness across all wavelengths, without taking into account different colors. A black and white visual representation of something is still an image, even though it does not make full use of the visual system's capabilities. Images are typically still, but in some cases can be moving or animated. Characteristics Images may be two or three-dimensional, such as a pho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thesis
A thesis ( : theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144: DocumentationPresentation of theses and similar documents International Organization for Standardization, Geneva, 1986. In some contexts, the word "thesis" or a cognate is used for part of a bachelor's or master's course, while "dissertation" is normally applied to a doctorate. This is the typical arrangement in American English. In other contexts, such as within most institutions of the United Kingdom and Republic of Ireland, the reverse is true. The term graduate thesis is sometimes used to refer to both master's theses and doctoral dissertations. The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, and the required minimum study period may thus vary significantly in d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pacific and Indian Oceans. Its Metropolitan France, metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea; overseas territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean. Due to its several coastal territories, France has the largest exclusive economic zone in the world. France borders Belgium, Luxembourg, Germany, Switzerland, Monaco, Italy, Andorra, and Spain in continental Europe, as well as the Kingdom of the Netherlands, Netherlands, Suriname, and Brazil in the Americas via its overseas territories in French Guiana and Saint Martin (island), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
École Des Mines De Paris
Mines Paris - PSL, officially École nationale supérieure des mines de Paris (until May 2022 Mines ParisTech, also known as École des mines de Paris, ENSMP, Mines de Paris, les Mines, or Paris School of Mines), is a French grande école and a constituent college of PSL Research University. It was originally established in 1783 by King Louis XVI. Mines Paris is distinguished for the outstanding performance of its research centers and the quality of its international partnerships with other prestigious universities in the world, which include Massachusetts Institute of Technology (MIT), California Institute of Technology (Caltech), Harvard John A. Paulson School of Engineering and Applied Sciences (Harvard SEAS), Shanghai Jiao Tong University, University of Hong Kong, National University of Singapore (NUS), Novosibirsk State University, Pontifical Catholic University of Chile, and Tokyo Tech. Mines Paris also publishes a world university ranking based on the number of alumni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Serra
Jean Paul Frédéric Serra (born 1940 in Algeria) is a French mathematician and engineer, and known as one of the co-founders (together with Georges Matheron) of mathematical morphology. Biography Education Serra received a scientific baccalauréat in 1957, and an engineering degree from the École Nationale Supérieure des Mines de Nancy in 1962. He also obtained a Bachelor's degree in philosophy/psychology, from the University of Nancy, in 1965. He obtained a PhD in Mathematical Geology from the University of Nancy in 1967, and a ''doctorat d'etat'' in Mathematics, from the Pierre and Marie Curie University, Paris, in 1986. He speaks French, Russian, English, and Spanish. Mathematical morphology From 1962 to 1966, while a research engineer at the '' Institut de recherche de la sidérurgie'', France, Serra was a PhD student under the supervision of Georges Matheron. The subject of his thesis was " stochastic modeling of the iron deposit of Lorraine, at various scales," on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georges Matheron
Georges François Paul Marie Matheron (2 December 1930 – 7 August 2000) was a French mathematician and civil engineer of mines, known as the founder of geostatistics and a co-founder (together with Jean Serra) of mathematical morphology. In 1968, he created the Centre de Géostatistique et de Morphologie Mathématique at the Paris School of Mines in Fontainebleau. He is known for his contributions on Kriging and mathematical morphology. His seminal work is posted for study and review to the Online Library of the ''Centre de Géostatistique'', Fontainebleau, France. Early career Matheron graduated from ''École Polytechnique'' and later ''Ecole des Mines de Paris'', where he studied mathematics, physics and probability theory (as a student of Paul Lévy). From 1954 to 1963, he worked with the French Geological Survey in Algeria and France, and was influenced by the works of Krige, Sichel, and de Wijs, from the South African school, on the gold deposits of the Witwatersrand. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Lattice
In mathematics, a complete lattice is a partially ordered set in which ''all'' subsets have both a supremum (join) and an infimum (meet). A lattice which satisfies at least one of these properties is known as a ''conditionally complete lattice.'' Specifically, every non-empty finite lattice is complete. Complete lattices appear in many applications in mathematics and computer science. Being a special instance of lattices, they are studied both in order theory and universal algebra. Complete lattices must not be confused with complete partial orders (''cpo''s), which constitute a strictly more general class of partially ordered sets. More specific complete lattices are complete Boolean algebras and complete Heyting algebras (''locales''). Formal definition A partially ordered set (''L'', ≤) is a ''complete lattice'' if every subset ''A'' of ''L'' has both a greatest lower bound (the infimum, also called the ''meet'') and a least upper bound (the supremum, also called the ''j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grayscale
In digital photography, computer-generated imagery, and colorimetry, a grayscale image is one in which the value of each pixel is a single sample representing only an ''amount'' of light; that is, it carries only intensity information. Grayscale images, a kind of black-and-white or gray monochrome, are composed exclusively of shades of gray. The contrast ranges from black at the weakest intensity to white at the strongest. Grayscale images are distinct from one-bit bi-tonal black-and-white images, which, in the context of computer imaging, are images with only two colors: black and white (also called ''bilevel'' or '' binary images''). Grayscale images have many shades of gray in between. Grayscale images can be the result of measuring the intensity of light at each pixel according to a particular weighted combination of frequencies (or wavelengths), and in such cases they are monochromatic proper when only a single frequency (in practice, a narrow band of frequencies) is ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Image
A binary image is one that consists of pixels that can have one of exactly two colors, usually black and white. Binary images are also called ''bi-level'' or ''two-level'', Pixelart made of two colours is often referred to as ''1-Bit'' or ''1bit''. This means that each pixel is stored as a single bit—i.e., a 0 or 1. The names ''black-and-white'', ''B&W'', monochrome or monochromatic are often used for this concept, but may also designate any images that have only one sample per pixel, such as grayscale images. In Photoshop parlance, a binary image is the same as an image in "Bitmap" mode. Binary images often arise in digital image processing as masks or thresholding, and dithering. Some input/output devices, such as laser printers, fax machines, and bilevel computer displays, can only handle bilevel images. A binary image can be stored in memory as a bitmap, a packed array of bits. A 640×480 image requires 37.5 KiB of storage. Because of the small size of the image file ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closing (morphology)
In mathematical morphology, the closing of a set (binary image) ''A'' by a structuring element ''B'' is the erosion (morphology), erosion of the dilation (morphology), dilation of that set, :A\bullet B = (A\oplus B)\ominus B, \, where \oplus and \ominus denote the dilation and erosion, respectively. In image processing, closing is, together with opening (morphology), opening, the basic workhorse of morphological signal noise, noise removal. Opening removes small objects, while closing removes small holes. Properties * It is idempotent, that is, (A\bullet B)\bullet B=A\bullet B. * It is increasing, that is, if A\subseteq C, then A\bullet B \subseteq C\bullet B. * It is ''extensive'', i.e., A\subseteq A\bullet B. * It is Translational invariance, translation invariant. See also *Mathematical morphology *Dilation (morphology), Dilation *Erosion (morphology), Erosion *Opening (morphology), Opening *Top-hat_transform, Top-hat transformation Bibliography * ''Image Analysis and Mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
