* Dilation ( morphology ), an operation in mathematical morphology

The PiCCO algorithm is dependent on blood pressure waveform morphology ( i. e. mathematical analysis of the PP waveform ) and calculates continuous Q as described by Wesseling and co-workers.

* Transforming digitized representations of objects, for example ( A ) into simplified shapes such as ( i ) skeletons, by repeated removal of simple points such that the digital topology of an image does not change, or ( ii ) medial axis, by calculating local maxima in a distance transform of the given digitized object representation, or ( B ) into modified shapes using mathematical morphology.

* Opening ( morphology ), an operator in mathematical morphology

And his 1957 book Vorlesungen über Inhalt, Oberfläche und Isoperimetrie was foundational for the theory of Minkowski functionals, used in mathematical morphology.

Dilation is one of the basic operations in mathematical morphology.

A binary image is viewed in mathematical morphology as a subset of a Euclidean space R < sup > d </ sup > or the integer grid Z < sup > d </ sup >, 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.

In mathematical morphology, opening is the dilation of the erosion of a set A by a structuring element B:

In mathematical morphology, the closing of a set ( binary image ) A by a structuring element B is the erosion of the dilation of that set,

* Introduction to mathematical morphology

In mathematical morphology, a structuring element ( s. e.

She has worked in syntax, phonetics, phonology, morphology, historical and comparative linguistics, Romance studies, structure of Japanese, structure of American Sign Language, poetics, writing for ESL students, and mathematical and linguistic analysis of folk dance.

The goal is to produce a virtual liver, a dynamic mathematical model that represents human liver physiology, morphology and function.

Haralick's work in shape analysis and extraction uses the techniques of mathematical morphology.

The pruning algorithm is a technique used in digital image processing based on mathematical morphology.

However, a second definition and usage has historically been in practice in many fields of computer science and information technology, which defines the prefix kilo when used with byte or bit units of data as 1024 ( 2 < sup > 10 </ sup >); this is due to the mathematical coincidence that Thus, in these fields 1 kilobyte is equal to 1 kibibyte, a new unit standardized as part of the binary prefixes to resolve the ambiguity.

IST is an extension of Zermelo-Fraenkel set theory ( ZF ) in that alongside the basic binary membership relation, it introduces a new unary predicate standard which can be applied to elements of the mathematical universe together with some axioms for reasoning with this new predicate.

In mathematical terms, Hamming codes are a class of binary linear codes.

Reflected binary codes were applied to mathematical puzzles before they became known to engineers.

The Indian scholar Pingala ( around 5th – 2nd centuries BC ) developed mathematical concepts for describing prosody, and in doing so presented the first known description of a binary numeral system .< ref >

It is a fundamental property of many binary operations, and many mathematical proofs depend on it.

Two's complement is a mathematical operation on binary numbers, as well as a representation of signed binary numbers based on this operation.

One theme Stephenson explores in Quicksilver is the advancement of mathematical sciences which in turn led to important applications: Leibniz's theory of binary mathematic became the foundation upon which to develop computers.

In mathematical terms, the extended binary Golay code consists of a 12-dimensional subspace W of the space V = F < sub > 2 </ sub >< sup > 24 </ sup > of 24-bit words such that any two distinct elements of W differ in at least eight coordinates.

When describing base in mathematical notation, the letter b is generally used as a symbol for this concept, so, for a binary system, b equals 2.

Since a binary call is a mathematical derivative of a vanilla call with respect to strike, the price of a binary call has the same shape as the delta of a vanilla call, and the delta of a binary call has the same shape as the gamma of a vanilla call.

In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory T is cointerpretable in another such theory S, when the language of S can be translated into the language of T in such a way that S proves every formula whose translation is a theorem of T. The " translation " here is required to preserve the logical structure of formulas.

It may be placed over a mathematical expression to indicate that it is to be considered grouped together, or alternatively it may function as a binary connective between arguments appearing above and below it.

The order of the hexadecimal digits in each pair, and the mapping between the hexadecimal digits and the bits of the octet value, are derived by interpreting the bits of the octet value as a binary numeral using the normal mathematical rules for digit significance .” ( See hexadecimal ).

This appears from the context of the IEEE Standard 802-2001 to be another term for the ' Hexadecimal Representation ' – i. e., “ by interpreting the bits of the octet value as a binary numeral using the normal mathematical rules for digit significance .”

The order of the hexadecimal digits in each pair, and the mapping between the hexadecimal digits and the bits of the octet value, are derived by reversing the order of the bits in the octet value and interpreting the resulting bit sequence as a binary numeral using the normal mathematical rules for digit significance .”

* Adicity / Arity of a mathematical relation or function ( dyadic relations are usually called binary relations )

While based on C, NWScript does not have many functions from the C family, excluding logical and binary / ternary operators and some mathematical functions.

* Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors.

Peter Mansfield, a physicist and professor at the university, then developed a mathematical technique that would allow scans to take seconds rather than hours and produce clearer images than Lauterbur had.

Vector graphics is the use of geometrical primitives such as points, lines, curves, and shapes or polygon ( s ), which are all based on mathematical expressions, to represent images in computer graphics.

The two-dimensional images taken at different rotations are converted into a three-dimensional model of the density of electrons within the crystal using the mathematical method of Fourier transforms, combined with chemical data known for the sample.

2D graphics models may combine geometric models ( also called vector graphics ), digital images ( also called raster graphics ), text to be typeset ( defined by content, font style and size, color, position, and orientation ), mathematical functions and equations, and more.

As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including – but certainly not limited to – audio signals and images.

They are optimized for the visualization and manipulation of different types of complex data such as 3D mechanical design, engineering simulation ( e. g. computational fluid dynamics ), animation and rendering of images, and mathematical plots.

In contrast to authors who identify language and cognition, he describes his own mathematical thinking as largely wordless, often accompanied by mental images that represent the entire solution to a problem.

The first images are of scientific interest, showing mathematical and physical quantities, the solar system and its planets, DNA, and human anatomy and reproduction.

In 1989 Franke referred to " generative mathematics " as " the study of mathematical operations suitable for generating artistic images.

A set of eigenfaces can be generated by performing a mathematical process called principal component analysis ( PCA ) on a large set of images depicting different human faces.

Iris recognition biometric systems apply mathematical pattern-recognition techniques to images of the iris ( anatomy ) | irises of an individual's eyes.

Iris recognition is an automated method of biometric identification that uses mathematical pattern-recognition techniques on video images of the irides of an individual's eyes, whose complex random patterns are unique and can be seen from some distance.

Vector images resulted from mathematical geometry ( vector ).

Psychologist Zenon Pylyshyn theorized that the human mind processes mental images by decomposing them into an underlying mathematical proposition.

The authors of these studies concluded that while the neural processes they studied rely on mathematical and computational underpinnings, the brain also seems optimized to handle the sort of mathematics that constantly computes a series of topologically-based images rather than calculating a mathematical model of an object.

His paper " Artificial Evolution for Computer Graphics " described the application of genetic algorithms to generate abstract 2D images from complex mathematical formulae, evolved under the guidance of a human.

The images of the individual object-plane impulse functions are called point spread functions, reflecting the fact that a mathematical point of light in the object plane is spread out to form a finite area in the image plane ( in some branches of mathematics and physics, these might be referred to as Green's functions or impulse response functions ).

It consists of fast-paced visions or cutscenes often characterized by false-color images that integrate his analogies and mathematical models, usually followed by him rushing off to tell Don about his new insights.

' CharlieVision ' is not to be confused with " audience visions ," in which Charlie's voice uses an analogy to simplify a mathematical concept while corresponding images are flashed on screen.

The book Catoptrics attributed to Euclid covered the mathematical theory of mirrors, particularly the images formed by plane and spherical concave mirrors.