Gradually Varied Surface

	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 function is a function from a digital space \Sigma to \ where A_1< \cdots and $A_i$ are real numbers. This function possesses the following property: If ''x'' and ''y'' are two adjacent points in $\Sigma$ , assume $f(x)=A_$ , then $f(y)=A_$ , $f(x)=A_$ , or $A_$ . The concept of the continuous function in digital space (can be called digitally continuous functions) was proposed by Azriel Rosenfeld in 1986. It is a function in which the value (an integer) at a digital point is the same or almost the same as its neighbors. In other words, if ''x'' and ''y'' are two adjacent poi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Digital Surface 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 object by a discrete set of its points. The images we see on the TV screen, the raster display of a computer, or in newspapers are in fact digital images. Its main application areas are computer graphics and image analysis. Main aspects of study are: * Constructing digitized representations of objects, with the emphasis on precision and efficiency (either by means of synthesis, see, for example, Bresenham's line algorithm or digital disks, or by means of digitization and subsequent processing of digital images). * Study of properties of digital sets; see, for example, Pick's theorem, digital convexity, digital straightness, or digital planarity. * Transforming digitized representations of objects, for example (A) into simplified shapes such as (i) skeletons, by repeated removal of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	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 object by a discrete set of its points. The images we see on the TV screen, the raster display of a computer, or in newspapers are in fact digital images. Its main application areas are computer graphics and image analysis. Main aspects of study are: * Constructing digitized representations of objects, with the emphasis on precision and efficiency (either by means of synthesis, see, for example, Bresenham's line algorithm or digital disks, or by means of digitization and subsequent processing of digital images). * Study of properties of digital sets; see, for example, Pick's theorem, digital convexity, digital straightness, or digital planarity. * Transforming digitized representations of objects, for example (A) into simplified shapes such as (i) skeletons, by repeated removal of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	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 of Maryland, College Park, Maryland, where he also held affiliate professorships in the Departments of Computer Science, Electrical Engineering, and Psychology, and a talmid chochom. He held a Ph.D. in mathematics from Columbia University (1957), rabbinic ordination (1952) and a Doctor of Hebrew Literature degree (1955) from Yeshiva University, honorary Doctor of Technology degrees from Linkoping University (1980) and Oulu University (1994), and an honorary Doctor of Humane Letters degree from Yeshiva University (2000); he was awarded an honorary Doctor of Science degree from the Technion (2004, conferred posthumously). He was a Fellow of the Association for Computing Machinery (1994). Rosenfeld was a leading researcher in the field of computer image analysis. Over a period of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Graph Homomorphism In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a function between the vertex sets of two graphs that maps adjacent vertices to adjacent vertices. Homomorphisms generalize various notions of graph colorings and allow the expression of an important class of constraint satisfaction problems, such as certain scheduling or frequency assignment problems. The fact that homomorphisms can be composed leads to rich algebraic structures: a preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs). The computational complexity of finding a homomorphism between given graphs is prohibitive in general, but a lot is known about special cases that are solvable in polynomial time. Boundaries between tractable and intractable cases have been an active area of research. Definitions In this article, unless stated otherwise, ''graphs'' are fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]