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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] |
Algeria
) , image_map = Algeria (centered orthographic projection).svg , map_caption = , image_map2 = , capital = Algiers , coordinates = , largest_city = capital , religion = , official_languages = , languages_type = Other languages , languages = Algerian Arabic (Darja) French , ethnic_groups = , demonym = Algerian , government_type = Unitary semi-presidential republic , leader_title1 = President , leader_name1 = Abdelmadjid Tebboune , leader_title2 = Prime Minister , leader_name2 = Aymen Benabderrahmane , leader_title3 = Council President , leader_name3 = Salah Goudjil , leader_title4 = Assembly President , leader_name4 = Ibrahim Boughali , legislature = Parliament , upper_house = Council of the Nation , lower_house ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a ''stochastic process'' is also referred to as a ''random process''. Stochasticity is used in many different fields, including the natural sciences such as biology, chemistry, ecology, neuroscience, and physics, as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography, and telecommunications. It is also used in finance, due to seemingly random changes in financial markets as well as in medicine, linguistics, music, media, colour theory, botany, manufacturing, and geomorphology. Etymology The word ''stochastic'' in English was originally used as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Granulometry (morphology)
:merge with Optical granulometry In mathematical morphology, granulometry is an approach to compute a size distribution of grains in binary images, using a series of morphological opening operations. It was introduced by Georges Matheron in the 1960s, and is the basis for the characterization of the concept of ''size'' in mathematical morphology. Granulometry generated by a structuring element Let ''B'' be a structuring element in a Euclidean space or grid ''E'', and consider the family \, k=0,1,\ldots, given by: :B_k=\underbrace_, where \oplus denotes morphological dilation. By convention, B_0 is the set containing only the origin of ''E'', and B_1=B. Let ''X'' be a set (i.e., a binary image in mathematical morphology), and consider the series of sets \, k=0,1,\ldots, given by: :\gamma_k(X)=X\circ B_k, where \circ denotes the morphological opening. The ''granulometry function'' G_k(X) is the cardinality (i.e., area or volume, in continuous Euclidean space, or number of ... [...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] |
Opening (morphology)
In mathematical morphology, opening is the dilation of the erosion of a set A by a structuring element B: :A\circ B = (A\ominus B)\oplus B, \, where \ominus and \oplus denote erosion and dilation, respectively. Together with closing, the opening serves in computer vision and image processing as a basic workhorse of morphological noise removal. Opening removes small objects from the foreground (usually taken as the bright pixels) of an image, placing them in the background, while closing removes small holes in the foreground, changing small islands of background into foreground. These techniques can also be used to find specific shapes in an image. Opening can be used to find things into which a specific structuring element can fit (edges, corners, ...). One can think of ''B'' sweeping around the inside of the boundary of ''A'', so that it does not extend beyond the boundary, and shaping the ''A'' boundary around the boundary of the element. Properties * Opening is idempotent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dilation (morphology)
Dilation (usually represented by ⊕) is one of the basic operations in mathematical morphology. Originally developed for binary images, it has been expanded first to grayscale images, and then to complete lattices. The dilation operation usually uses a structuring element for probing and expanding the shapes contained in the input image. Binary dilation In binary morphology, dilation is a shift-invariant (translation invariant) operator, equivalent to Minkowski addition. A binary image is viewed in mathematical morphology as a subset of a Euclidean space R''d'' or the integer grid Z''d'', for some dimension ''d''. Let ''E'' be a Euclidean space or an integer grid, ''A'' a binary image in ''E'', and ''B'' a structuring element regarded as a subset of R''d''. The dilation of ''A'' by ''B'' is defined by ::A \oplus B = \bigcup_ A_b, where ''A''''b'' is the translation of ''A'' by ''b''. Dilation is commutative, also given by A \oplus B = B\oplus A = \bigcup_ B_a. If ''B'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erosion (morphology)
Erosion (usually represented by ⊖) is one of two fundamental operations (the other being dilation) in morphological image processing from which all other morphological operations are based. It was originally defined for binary images, later being extended to grayscale images, and subsequently to complete lattices. The erosion operation usually uses a structuring element for probing and reducing the shapes contained in the input image. Binary erosion In binary morphology, an image is viewed as a subset of a Euclidean space \mathbb^d or the integer grid \mathbb^d, for some dimension ''d''. The basic idea in binary morphology is to probe an image with a simple, pre-defined shape, drawing conclusions on how this shape fits or misses the shapes in the image. This simple "probe" is called structuring element, and is itself a binary image (i.e., a subset of the space or grid). Let ''E'' be a Euclidean space or an integer grid, and ''A'' a binary image in ''E''. The erosion of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hit-or-miss Transform
In mathematical morphology, hit-or-miss transform is an operation that detects a given configuration (or pattern) in a binary image, using the morphological erosion operator and a pair of disjoint structuring elements. The result of the hit-or-miss transform is the set of positions where the first structuring element fits in the foreground of the input image, and the second structuring element misses it completely. Mathematical definition In binary morphology, an image is viewed as a subset of a Euclidean space \mathbb^d or the integer grid \mathbb^d, for some dimension ''d''. Let us denote this space or grid by ''E''. A structuring element is a simple, pre-defined shape, represented as a binary image, used to probe another binary image, in morphological operations such as erosion, dilation, opening, and closing. Let C and D be two structuring elements satisfying C\cap D=\emptyset. The pair (''C'',''D'') is sometimes called a ''composite structuring element''. The hit-or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross Section (geometry)
In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation. In technical drawing a cross-section, being a projection of an object onto a plane that intersects it, is a common tool used to depict the internal arrangement of a 3-dimensional object in two dimensions. It is traditionally crosshatched with the style of crosshatching often indicating the types of materials being used. With computed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structuring Element
In mathematical morphology, a structuring element is a shape, used to probe or interact with a given image, with the purpose of drawing conclusions on how this shape fits or misses the shapes in the image. It is typically used in morphological operations, such as dilation, erosion, opening, and closing, as well as the hit-or-miss transform. According to Georges Matheron, knowledge about an object (e.g., an image) depends on the manner in which we probe (observe) it.See ( Dougherty 1992), chapter 1, page 1. In particular, the choice of a certain structuring element for a particular morphological operation influences the information one can obtain. There are two main characteristics that are directly related to structuring elements: * Shape. For example, the structuring element can be a "ball" or a line; convex or a ring, etc. By choosing a particular structuring element, one sets a way of differentiating some objects (or parts of objects) from others, according to their shape or spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petrographic
Petrography is a branch of petrology that focuses on detailed descriptions of rocks. Someone who studies petrography is called a petrographer. The mineral content and the textural relationships within the rock are described in detail. The classification of rocks is based on the information acquired during the petrographic analysis. Petrographic descriptions start with the field notes at the outcrop and include macroscopic description of hand specimens. The most important petrographer's tool is the petrographic microscope. The detailed analysis of minerals by optical mineralogy in thin section and the micro-texture and structure are critical to understanding the origin of the rock. Electron microprobe or atom probe tomography analysis of individual grains as well as whole rock chemical analysis by atomic absorption, X-ray fluorescence, and laser-induced breakdown spectroscopy are used in a modern petrographic lab. Individual mineral grains from a rock sample may also be analyz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
