
	Where results make sense

Topic: Minkowski addition

Related Topics

Mathematical morphology

Morphology

In the News (Wed 11 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Addition Encyclopedia (Site not responding. Last check: )
		Addition is also fundamental to the operation of digital computers, where the efficiency of addition, in particular the carry mechanism, is an important limitation to overall performance.
		In modern digital computers, integer addition is typically the fastest arithmetic instruction, yet it has the largest impact on performance, since it underlies all the floating-point operations as well as such basic tasks as address generation during memory access and fetching instructions during branching.
		Addition of cardinal numbers, however, is a commutative operation closely related to the disjoint union operation.
	www.hallencyclopedia.com /topic/Addition.html (5577 words)

	Bob Gardner's "Relativity and Black Holes" Special Relativity
		Minkowski, in fact, was one of Albert Einstein's mathematics professors at the Zurich Politechnikum in 1900.
		As a sad footnote, Hermann Minkowski died of appendicitis in 1909 at the age of 45.
		Minkowski is honored today by the fact that his spacetime is often called Minkowski spacetime or the Minkowski vector space.
	www.etsu.edu /physics/plntrm/relat/spactim.htm (940 words)

	Minkowski addition - Biocrawler
		In geometry, the Minkowski sum of two sets A and B in Euclidean space is the result of adding every element of A to every element of B, i.e.
		for a convex symmetric set containing 0, where the left-hand side is the Minkowski sum and the right-hand side the enlargement by a factor of 2.
		Minkowski addition is also called the binary dilation of A by B. Minkowski addition plays a central role in mathematical morphology.
	www.biocrawler.com /encyclopedia/Minkowski_addition (240 words)

	Minkowski, mathematiciens, and the mathematical theory of relativity (Site not responding. Last check: )
		Minkowski's 1908 Cologne lecture "Raum und Zeit" (Minkowski 1909) may be understood as an effort to extend the disciplinary frontier of mathematics to include the principle of relativity.
		Minkowski openly recognized the role-albeit a heuristic one-of experimental physics in the discovery of the principle of relativity.
		Minkowski was ultimately unable to detach his theory from that of Einstein, because even if he convinced some mathematicians that his work stood alone, the space-time theory came to be understood by most German physicists as a purely formal development of Einstein's theory.
	www.univ-nancy2.fr /DepPhilo/walter/papers/mmmh.xml (12692 words)

	Minkowski's addition of convex shapes
		We may even justify such an apparent sloppiness by expanding the operation to addition of sets and showing that the shape of the result does not depend on the selection of the origin.
		In other words, to find Minkowski's sum of two sets one must consider the totality of all possible sums of a point from one set and a point from the other.
		The applet demonstrates Minkowski's addition of two polygons with the number of sides between 3 and 9, inclusive.
	www.cut-the-knot.org /Curriculum/Geometry/PolyAddition.shtml (274 words)

	PlanetPhysics: Minkowski's Four-Dimensional Space (Site not responding. Last check: )
		But the discovery of Minkowski, which was of importance for the formal development of the theory of relativity, does not lie here.
		It is to be found rather in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space.
		This is version 3 of Minkowski's Four-Dimensional Space, born on 2006-03-11, modified 2006-03-24.
	planetphysics.org /encyclopedia/MinkowskisFourDimensionalSpace.html (675 words)

	Learning Image Morphology (Site not responding. Last check: )
		Minkowski Addition, also known as Dilation, consists of taking a set known as a structuring element and applying it to each member in the source set.
		In the continuous case Minkowski addition can be thought of as a way to grow the members of source set by a method of psuedoconvolution.
		The modification for Minkowski subtraction is is similar to that for Minkowski Addition except that the lesser of the two compared values is written to the output image.
	cobb.ee.psu.edu /users/greg/morphology.html (371 words)

	Hermann Minkowski Summary
		Minkowski was born in Alexotas, Russia on June 22, 1864, of German parents.
		Hermann Minkowski was born in Aleksotas (a suburb of Kaunas, Lithuania) to a family of German, Polish, and Jewish descent.
		Minkowski explored the arithmetic of quadratic forms, especially concerning n variables, and his research into that topic led him to consider certain geometric properties in a space of n dimensions.
	www.bookrags.com /Hermann_Minkowski (2901 words)

	Alexandre Minkowski, specialist on babies - The Boston Globe
		In addition to being noted for his work with newborns, Dr. Minkowski is known for his service with the Resistance during World War II.
		Minkowski directed the center for neonatal research at the Cochin-Port-Royal maternity ward in Paris from 1958 to 1987.
		Minkowski went on to serve as an adviser to the government, and in the 1990s he had a brief stint as an elected official for a Green party in the Paris area's regional council.
	www.boston.com /news/globe/obituaries/articles/2004/05/09/alexandre_minkowski_specialist_on_babies (220 words)

	Staircase Wit
		Since the velocity transformations leave the laws of physics unchanged, Minkowski reasoned, they ought to correspond to some invariant physical quantity, and their determinants ought to be unity.
		It seems likely that Minkowski was influenced by Klein’s Erlanger program, which sought to interpret various kinds of geometry in terms of the invariants under a specific group of transformations.
		It is certainly true that we are led toward the Lorentz transformations as soon as we consider the group of velocity transformations and attempt to identify a physically meaningful invariant corresponding to these transformations.
	www.mathpages.com /rr/s1-07/1-07.htm (3537 words)

	Search Results for Minkowski
		Minkowski's doctoral thesis, submitted in 1885, was a continuation of this prize winning work involving his natural definition of the genus of a form.
		Minkowski's original mathematical interests were in pure mathematics and he spent much of his time investigating quadratic forms and continued fractions.
		Minkowski's problem is to construct a convex surface in three dimensional space that realises a given curvature as a function of the direction of the normal.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Minkowski&CONTEXT=1 (2019 words)

	The Theorem of Barbier
		The algebraic concept fundamental to the proof is Minkowski's addition of convex sets.
		With a fixed origin O, the sum of two shapes is the collection of all endpoints of vectors OA+OB, where A ranges over one set, B over the other.
		Several important properties of Minkowski's addition could be discerned with the help of the following applet that shows the sum of two ("Left" and "Right") polygons.
	www.maa.org /editorial/knot/Barbier.html (1101 words)

	Some Aspects in Emil Wiechert
		In addition to this activity, Wiechert continued to be interested in the great Problems of theoretical physies.
		Wiechert, Minkowski and Sommerfeld belonged to the co-founders of electrodynamics in the form of electron theory (Wiechert), relativistic electrodynamics moving bodies (Minkowski) and quantum electrodynamics (Sommerfeld).
		The special relativistic form of electrodynamics was founded by Einstein (1905) and by Minkowski (1907) and these established the connection to Lorentz' study from 1895.
	verplant.org /history-geophysics/Wiechert.htm (2330 words)

	Null Coordinates
		The singularity of the Lorentz transformation is most clearly expressed in terms of the underlying Minkowski pseudo-metric. Recall that the invariant space time interval dt between the events (t,x) and (t+dt, x+dx) is given by
		Pictorially, the locus of points whose squared distance from the origin is ±1 consists of the two hyperbolas labeled +1 and -1 in the figure below.
		In terms of the usual orthogonal spacetime coordinates, we specify the coordinates (T,X,Y,Z) of event P relative to the observer O at the origin in terms of the coordinates of four events I
	www.mathpages.com /rr/s1-09/1-09.htm (973 words)

	Euclidean Relativity
		Euclidean relativity, both special and general, is gaining attention as a viable alternative to the Minkowski framework.
		A fractal-like universe is described where the four forces of nature together with their fermions and bosons are ordered hierarchically through their number of dimensions.
		The velocity addition formula shows a deviation from the standard one; an analysis and justification is given for that.
	www.euclideanrelativity.com (419 words)

	4 Relativistic Addition of Velocities
		It appears that the Euclidean approach as used in the previous Section does not yield the same equation for relativistic addition of velocities as used in special relativity.
		Although this particular point may be a serious obstacle to the acceptation of this proposal, it obviously is necessary to point it out.
		Virtually all practical situations that require the velocity addition formula to be used exist under such circumstances, which indicates that a deviation from the classical graph is likely to remain unnoticed.
	www.euclideanrelativity.com /dimensionshtml/node4.html (988 words)

	Talk_Ghosh
		We observe that the resemblance between the integer number system with multiplication & division and the system of convex objects with Minkowski addition & decomposition is really striking.
		Now, to view multiplication and division as a single operation it became necessary to extend the integer number system to the rational number system.
		A nonconvex object may be viewed as a mixture of ordinary convex object and negative object.
	www.hip.atr.co.jp /departments/Dept2/Talk_Ghosh.html (339 words)

	Papers
		In this paper we introduce and investigate similarity measures for convex polyhedra based on Minkowski addition and inequalities for the mixed volume and volume related to the Brunn-Minkowski theory.
		All measures considered are invariant under translations; furthermore, some of them are also invariant under subgroups of the affine transformation group.
		In most cases, these works may not be reposted without the explicit permission of the copyright holder.
	www.cs.rug.nl /~roe/publications/simpoly.html (244 words)

	CiteULike: Similarity measures for convex polyhedra based on Minkowski addition
		Similarity measures for convex polyhedra based on Minkowski addition
		Numerical implementations of the proposed approach are not discussed.
		@article{citeulike:773437, abstract = {In this paper we introduce and investigate similarity measures for convex polyhedra based on Minkowski addition and inequalities for the mixed volume and volume related to the Brunn-Minkowski theory.
	www.citeulike.org /user/ngoncalves/article/773437 (372 words)

	The Modular Group and Fractals
		Besides the four basic operations on the real numbers (addition, subtraction, multiplication, division), there is a fifth basic operation which is rarely taught in primary school and under-appreciated at higher levels, namely, "Farey Addition" or, expressed correctly, group multiplication in SL(2,Z).
		Chapter 3: The Minkowski Question Mark and the Modular Group SL(2,Z) (40 pages) shows that the distribution of Farey Fractions transforms under the dyadic representation of the Modular Group.
		It constructs the Minkowski Question Mark Function as a set-theoretic representation of (a subset of) the Modular Group.
	www.linas.org /math/sl2z.html (1771 words)

	IngentaConnect Convex Set Symmetry Measurement via Minkowski Addition (Site not responding. Last check: )
		For the case of rotation symmetry we use as a symmetrization transformation a generalization of the Minkowski symmetric set (a difference body) for a cyclic group of rotations.
		The first one is rotationally symmetrical and the second one is completely asymmetrical in the sense that it does not allow such a decomposition.
		Minkowski addition of two sets is reduced to the convolution of their characteristic functions.
	www.ingentaconnect.com /content/klu/jmiv/1997/00000007/00000001/00121047 (357 words)

	[No title] (Site not responding. Last check: )
		Minkowski Opearators, being used in Mathematical Morpholgy for a pretty long time, recently have also made its necessity quite high in the field of Virtual Sculpting.
		Minkowski Addition was taken as the mode of Pasting tool in our present virtual sculpting tool 'Sirpi'.
		Presently we are working with the addition of objects on a curved swept volume.
	members.rediff.com /pritha/research.html (155 words)

	pgmminkowski
		The Minkowski integrals mathematically characterize the shapes in the image and hence are the basis of "morphological image analysis." Hadwiger’s theorem has it that these integrals are the only motion- invariant, additive and conditionally continuous functions of a two- dimensional image, which means that they are preserved under certain kinds of deformations of the image.
		Basically, the Minkowski integrals are the area, total perimeter length, and the Euler characteristic of the image, where these metrics apply to the foreground image, not the rectangular PGM image itself.
		For a grayscale image, there is some threshold of intensity applied to categorize pixels into fl and white, and the Minkowski integrals are calculated as a function of this threshold value.
	linuxcommand.org /man_pages/pgmminkowski1.html (383 words)

	Pgmminkowski User Manual (Site not responding. Last check: )
		The Minkowski integrals mathematically characterize the shapes in the image and hence are the basis of "morphological image analysis."
		Hadwiger's theorem has it that these integrals are the only motion-invariant, additive and conditionally continuous functions of a two-dimensional image, which means that they are preserved under certain kinds of deformations of the image.
		The total surface area refers to the number of white pixels in the PGM and the perimeter is the sum of perimeters of each closed white region in the PGM.
	netpbm.sourceforge.net /doc/pgmminkowski.html (368 words)

	Real Algebraic and Analytic Geometry
		Support functions, projections and Minkowski addition of Legendrian cycles.
		It is shown that there is a partial ring structure on $\mathcal{LC}(\R^n \times S^{n-1})$, the multiplication being a generalized Minkowski addition.
		An example of non-existence of the Minkowski sum is given, but it is shown that the Minkowski sum does exist after changing one of the summands by an arbitrarily small linear map.
	www.uni-regensburg.de /Fakultaeten/nat_Fak_I/RAAG/preprints/0125.html (164 words)

Try your search on: Qwika (all wikis)