Category: Digital geometry

Discrete tomography
Discrete tomography focuses on the problem of reconstruction of binary images (or finite subsets of the integer lattice) from a small number of their projections. In general, tomography deals with the
Digital manifold
In mathematics, a digital manifold is a special kind of combinatorial manifold which is defined in digital space i.e. grid cell space. A combinatorial manifold is a kind of manifold which is a discret
Summed-area table
A summed-area table is a data structure and algorithm for quickly and efficiently generating the sum of values in a rectangular subset of a grid. In the image processing domain, it is also known as an
Bresenham's line algorithm
Bresenham's line algorithm is a line drawing algorithm that determines the points of an n-dimensional raster that should be selected in order to form a close approximation to a straight line between t
Euler operator (digital geometry)
In solid modeling and computer-aided design, the Euler operators modify the graph of connections to add or remove details of a mesh while preserving its topology. They are named by Baumgart after the
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 ori
In applied mathematics, lambda-connectedness (or λ-connectedness) deals with partial connectivity for a discrete space. Assume that a function on a discrete space (usually a graph) is given. A degree
Minkowski addition
In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B, i.e., the set Analogously,
Shape analysis (digital geometry)
This article describes shape analysis to analyze and process geometric shapes.
Pruning (morphology)
The pruning algorithm is a technique used in digital image processing based on mathematical morphology. It is used as a complement to the skeleton and thinning algorithms to remove unwanted parasitic
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 oft
Morphological skeleton
In digital image processing, morphological skeleton is a skeleton (or medial axis) representation of a shape or binary image, computed by means of morphological operators. Morphological skeletons are
Reeve tetrahedron
In geometry, the Reeve tetrahedron is a polyhedron, in three-dimensional space with vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0) and (1, 1, r) where r is a positive integer. It is named after , who use
Digital Morse theory
In mathematics, digital Morse theory is a digital adaptation of continuum Morse theory for scalar volume data. This is not about the Samuel Morse's Morse code of long and short clicks or tones used in
In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest addressable element in an all points addressable display de
Canberra distance
The Canberra distance is a numerical measure of the distance between pairs of points in a vector space, introduced in 1966and refined in 1967 by Godfrey N. Lance and William T. Williams. It is a weigh
Taxicab geometry
A taxicab geometry or a Manhattan geometry is a geometry in which the usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is th
Principal geodesic analysis
In geometric data analysis and statistical shape analysis, principal geodesic analysis is a generalization of principal component analysis to a non-Euclidean, non-linear setting of manifolds suitable
Azriel Rosenfeld
Azriel Rosenfeld (February 19, 1931 – February 22, 2004) was an American Research Professor, a Distinguished University Professor, and Director of the Center for Automation Research at the University
Gradually varied surface
In mathematics, a gradually varied surface is a special type of digital surfaces. It is a function from a 2D digital space (see digital geometry) to an ordered set or a chain. A gradually varied funct
Midpoint circle algorithm
In computer graphics, the midpoint circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. Bresenham's circle algorithm is derived from the midpoint circle algor
Cutting sequence
In digital geometry, a cutting sequence is a sequence of symbols whose elements correspond to the individual grid lines crossed ("cut") as a curve crosses a square grid. Sturmian words are a special c
Controlled image base
Controlled image base or CIB is unclassified digital imagery, produced to support mission planning and command, control, communications, and intelligence systems. CIB is used as a map substitute for e
Raster graphics
In computer graphics and digital photography, a raster graphic represents a two-dimensional picture as a rectangular matrix or grid of square pixels, viewable via a computer display, paper, or other d
Closing (morphology)
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, where and denote the dilation and erosion, respectively. In ima
Digital image
A digital image is an image composed of picture elements, also known as pixels, each with finite, discrete quantities of numeric representation for its intensity or gray level that is an output from i
LCD crosstalk
LCD crosstalk is a visual defect in an LCD screen which occurs because of interference between adjacent pixels. Owing to the way rows and columns in the display are addressed, and charge is pushed aro
Top-hat transform
In mathematical morphology and digital image processing, top-hat transform is an operation that extracts small elements and details from given images. There exist two types of top-hat transform: the w
Heat kernel signature
A heat kernel signature (HKS) is a feature descriptor for use in deformable shape analysis and belongs to the group of spectral shape analysis methods. For each point in the shape, HKS defines its fea
SPHARM-PDM toolbox is a shape correspondence software package developed by the at the University of North Carolina at Chapel Hill. SPHARM-PDM is a tool that computes point-based models using a paramet
Distance transform
A distance transform, also known as distance map or distance field, is a derived representation of a digital image. The choice of the term depends on the point of view on the object in question: wheth
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 compl
Mathematical morphology
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 common
Pick's theorem
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was
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 str
Nonograms, also known as Hanjie, Paint by Numbers, Picross, Griddlers, and Pic-a-Pix, and by various other names, are picture logic puzzles in which cells in a grid must be colored or left blank accor
Thinning (morphology)
Thinning is the transformation of a digital image into a simplified, but topologically equivalent image. It is a type of topological skeleton, but computed using mathematical morphology operators.
Spectral shape analysis
Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami
Morphological gradient
In mathematical morphology and digital image processing, a morphological gradient is the difference between the dilation and the erosion of a given image. It is an image where each pixel value (typica
Topological skeleton
In shape analysis, skeleton (or topological skeleton) of a shape is a thin version of that shape that is equidistant to its boundaries. The skeleton usually emphasizes geometrical and topological prop
Pixel aspect ratio
Pixel aspect ratio (often abbreviated PAR) is a mathematical ratio that describes how the width of a pixel in a digital image compares to the height of that pixel. Most digital imaging systems display
Digital geometry
Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean space. Simply put, digitizing is replacing an o