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Topic: Chessboard distance

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	Encyclopedia: Metric space (Site not responding. Last check: 2007-11-06)
		In mathematics a metric or distance is a function which assigns a distance to elements of a set.
		In information theory, the Levenshtein distance or edit distance between two strings is given by the minimum number of operations needed to transform one string into the other, where an operation is an insertion, deletion, or substitution.
		If (M, d) is a metric space, S is a subset of M and x is a point of M, we define the distance from x to S as In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are particularly nice kinds of topological spaces.
	www.nationmaster.com /encyclopedia/metric-space (4072 words)

	Casino Encyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, a metric space is a set where a notion of distance between elements of the set is defined.
		The Chessboard distance, the number of moves a chess king would take to travel from x to y.
		The Levenshtein distance, also called character edit distance, is a measure of the similarity between two strings u and v.
	www.casinoencyclopedia.com /index.php?title=Metric_space (1482 words)

	Morphology - Distance Transform
		Note that we are using the `chessboard' distance metric.
		There are several different sorts of distance transform depending upon which distance metric is being used to determine the distance between pixels.
		The distance transform is very closely linked to both the medial axis transform and to skeletonization.
	www.cee.hw.ac.uk /hipr/html/distance.html (880 words)

	Paper: Springer v2 :: huangj (Site not responding. Last check: 2007-11-06)
		Distance fields are scalar fields, with each element in the 3D volume representing the minimal distance to a certain shape.
		Distance fields are also applied to concurrent engineering [17] where simulations and analysis involving the interior of geometries, such as die-casting simulation or thickness analysis of parts [23], are routine.
		The distance contours (shown in red, perpoint shaded) are extracted with an error tolerance of 1/500 of the longest dimension of the models.
	computing.breinestorm.net /distance+field+complete+surface+adaptively (8048 words)

	Morphological Operations (Image Processing Toolbox) (Site not responding. Last check: 2007-11-06)
		The distance transform provides a metric or measure of the separation of points in the image.
		The Euclidean distance is the straight-line distance between two pixels.
		The Chessboard distance metric measures the path between the pixels based on an 8-connected neighborhood.
	www.phys.ufl.edu /docs/matlab/toolbox/images/morph14.html (223 words)

	Encyclopedia: Distance field (Site not responding. Last check: 2007-11-06)
		A distance transform, also known as distance map or distance field, is a representation of a digital image.
		The choice of the term depends on the point of view on the object in question: whether the initial image is transformed into another representation, or it is simply endowed with an additional map or field.
		For example, one may speak of Manhattan distance transform, if the underlying metric is manhattan distance.
	www.nationmaster.com /encyclopedia/Distance-field (188 words)

	20.7 Distance transforms (Site not responding. Last check: 2007-11-06)
		Distance transforms are used to calculate the minimum distance from each element of an object to the background.
		calculates the exact euclidean distance transform of the input, by replacing each object element (defined by values larger than zero) with the shortest euclidean distance to the background (all non-object elements).
		uses a brute-force algorithm to calculate the distance transform of the input, by replacing each object element (defined by values larger than zero) with the shortest distance to the background (all non-object elements).
	keres.colorado.edu /numarray/node91.html (596 words)

	Patent 6040835: System for depicting surfaces using volumetric distance maps
		Note that: 1) the gradient vector of this distance map points in the direction of the surface normal; 2) a zero distance map value indicates the presence of a surface; and 3) a positive distance value indicates that the sample is inside the object.
		The distance to the nearest surface point varies linearly in the direction normal to a surface, and varies slowly in the direction parallel to the surface as long as the surface is relatively smooth.
		In the subject invention, this distance is used to detect the presence of a surface and to estimate its normal direction.
	www.freepatentsonline.com /6040835.html (3924 words)

	Citations: Distance Transformations in Arbitrary Dimensions - Borgefors (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Each distance function is associated with a mask defined by a square matrix which is splitted into a pair of half masks.
		A value that represents the distance from the nearest edge of the 3 D shape is assigned to every point of the distance map.
		....distance maps on W described by and, we have to define initial estimate 0 and 0 such that the initial surfaces S and D are represented through a level set of 0 and 0.
	citeseer.lcs.mit.edu /context/6398/0 (4903 words)

	Re: Chessboard knight metric?
		But now we know an upper bound for the distance between any two pairs of squares.
		Since your metric clearly is integer and non-negative there must be a unique answer to the minimum distance for any pair of squares.
		But the existence or otherwise of an easy formula does not detract from the existence of the distance function and the fact that it is a metric.
	www.usenet.com /newsgroups/sci.math/msg10731.html (564 words)

	MORPH_DISTANCE (Site not responding. Last check: 2007-11-06)
		The distance map is useful for a variety of morphological operations: thinning, erosion and dilation by discs of radius "r", and granulometry.
		Each neighbor is assigned a distance corresponding to the number of pixels to be visited when travelling from the current pixel to the neighbor.
		Thresholding the result distance operator with a value of "n" produces the equivalent of eroding the thresholded image with a disc of radius "n".
	idlastro.gsfc.nasa.gov /idl_html_help/M41.html (318 words)

	[No title]
		Note that we are using the `chessboard' \ref{metric}{distance metric}.} \target{dual}{There} is a dual to the distance transform described above which produces the distance transform for the background region rather than the foreground region.
		The example shown in \figref{distance} uses the `chessboard' distance metric but both the Euclidean and `city block' metrics can be used as well.
		A 3\times^3 square element gives the `chessboard' distance transform, a cross shaped element gives the `city block' distance transform, and a disc shaped element gives the Euclidean distance transform.
	www.cee.hw.ac.uk /hipr/src/distance.hpr (946 words)

	ASTR 135 Course Notes (Site not responding. Last check: 2007-11-06)
		Edwin Hubble was measuring the distances to distant objects, like the galaxies in the Virgo and Perseus clusters, and discovered that they are receding away from us.
		The velocity of recession increased with increasing distance - this observation is compatible with an expanding universe.
		The distance between the corners of the board is still 8 squares.
	astro.wsu.edu /allen/courses/astr135/Notes/cosmology.html (2777 words)

	distance_transform
		= 'city-block', the distance is calculated from the shortest path from the point to the border of the region, where only horizontal and vertical ``movements'' are allowed.
		= 'chessboard', the distance is calculated from the shortest path to the border, where horizontal, vertical, and diagonal ``movements'' are allowed.
		To normalize the distances, the resulting distance image is divided by 3.
	mvtec.com /halcon/packages/distance/hdevelop/distance_transform.html (434 words)

	mm090distance - Distance.
		The second condition says that the distance for going from one point to another is the same as returning distance.
		A distance n from a point or region can be determined by dilating the point or region by the str.
		The 8-connected distance (chessboard) can be generated by the elementary 3x3 square.
	www.mmorph.com /mmtutor1.0/html/mmtutor/mm090distance.html (560 words)

	Solutions for exercises "C" in February, 2002 (Site not responding. Last check: 2007-11-06)
		In how many different ways is it possible to select two fields of a 8x8 chessboard, such that the midpoint of the segment joining the centres of the two fields should also be the centre of a field?
		On the ray AP, mark the two points whose distances from A are equal to FB ' and FB, and on the ray AB, mark the point whose distance from A is K ' B '.
		Thus the distance of the two tangents is the double of the distance of the contact point of the second parabola from the line y = x.
	www.komal.hu /verseny/2002-02/C.e.shtml (940 words)

	Bandwidth Market, Ltd (Site not responding. Last check: 2007-11-06)
		When the distances between the ending points of the two pairs are both shorter than the distance between the beginning points, the core is defined to have a certain value of features to be classified into the Whorl.
		Euclidean distance, "city block" distance or "chessboard" distance can be used, for example, according to definitions described in a document entitled, "Image Analysis Handbook," by Takagi, et al., published by Tokyo University Press, (1991).
		14 shows an example of an area with a chessboard distance d from a ridge end E1 that is expressed as a square area with an extent of 2 d.times.2 d wherein are comprised valley bifurcations B1 and B2.
	www.bandwidthnews.com /resources/patents/data7/5901239.html (10351 words)

	Morphology - Distance Transform (Site not responding. Last check: 2007-11-06)
		A 3×3 square element gives the `chessboard' distance transform, a cross shaped element gives the `city block' distance transform, and a disk shaped element gives the Euclidean distance transform.
		Of course it is not actually possible to generate a good disk shaped element on a discrete grid on a small scale, but there are algorithms that vary the structuring element on each erosion so as to approximate a circular element.
		when a distance transform is applied (scaled by a factor of 5).
	www.ccit.edu.tw /~taoi/hipr/distance.htm (907 words)

	Knight's Tour Notes, Part Cc: Chronology 1900 to Present
		The chessboard knight's tour problem is mentioned on p.37 (#132) and two symmetric tours are diagrammed on p.218.
		Knight's tours of smaller boards are mentioned on p.151 (#484) where it is stated, wrongly, that "on a 4×4 board, wherever you start, either four or six squares will be omitted from your tour" (the minimum is 1 for an open tour, 2 for a closed tour).
		Refers to the 4×16 circular chessboard tour in Twiss 1789 and gives two further examples of his own showing symmetry, which is impossible on the rectangular board.
	www.ktn.freeuk.com /cc.htm (7807 words)

	Definition of Metric space
		A metric space M is a set of points with an associated distance function (also called a metric) d : M � M
		For example, that the distance between distinct points is positive and the distance from x to y is the same as the distance from y to x.
		The name alludes to the tendency of railway journeys to always proceed via London, which is identified with the origin.
	www.wordiq.com /definition/Metric_space (1745 words)

	342.1.6.1 Mosaicking Options
		There are two different feathering methods for overlap areas: Linear and Non-Linear, both of which weight how the image cell values are changed in the overlap area as a function of their distance from the overlapping edge.
		Generally, this distance should equal one half of the overlap distance.
		The Chessboard method produces a chessboard effect by utilizing sets of raster values from each of the overlapping rasters.
	www.microimages.com /refman/xhtml/PROCE018.HTM (3710 words)

	VIGRA - Distance Transform
		Perform a distance transform using either the Euclidean, Manhattan, or chessboard metrics.
		For all background pixels, calculate the distance to the nearest object or contour.
		In the destination image, all pixels corresponding to background will be assigned the their distance value, all pixels corresponding to objects will be assigned 0.
	kogs.informatik.uni-hamburg.de /~koethe/vigra/doc/vigra/group__DistanceTransform.html (286 words)

	Glossary - Distance Metrics (Site not responding. Last check: 2007-11-06)
		It is often useful in image processing to be able to calculate the distance between two pixels in an image, but this is not as straightforward as it seems.
		The presence of the pixel grid makes several so-called distance metrics possible which often give different answers to each other for the distance between the same pair of points.
		This is the familiar straight line distance that most people are familiar with.
	www.dai.ed.ac.uk /HIPR2/metric.htm (192 words)

	ipps,10th International Parallel Processing Symposium (IPPS '96)
		The distance transform (DT) and the medial axis transform (MAT) are two image computation tools used to extract information about the shape and position of foreground pixels relative to each other.
		Finding the DT with respect to the Euclidean distance metric is easier to use, but rather time-consuming, so many approximate Euclidean DTs (EDTs) are also widely used in the computer vision and image processing fields.
		The chessboard DT (CDT) is one kind of DT, which converts an image based on the chessboard distance metric.
	csdl.computer.org /comp/proceedings/ipps/1996/7255/00/72550424abs.htm (315 words)

	Even babies can have optical illusions
		He gurgles contentedly and tugs inquisitively at the white curtain in front of his nose, until it is lifted up by an invisible force.
		Now Samuel is looking at a chessboard which is drawn in such a way that it seems to be receding into the distance away from him.
		Due to the perspective figures which are fixed higher up and near the horizon appear further away than rubber toys which are a little lower down � although this is only the case if the observer covers over one eye.
	www.eurekalert.org /pub_releases/2005-04/uob-ebc041205.php (606 words)

	Distance-map software downloads (Site not responding. Last check: 2007-11-06)
		Mac PDF Measure It is an Acrobat plug-in tool, it enables accurate measure ment of the distance and angle between two points on a page.
		All you do is type in a ZIP Code, specify the radius distance in miles, and within seconds, a list of ZIP Code s that fall within that radius is displayed.
		Calculate the distance ranges between different ZIP Code locations, look up area codes and all cities and towns located within the specified ZIP Code location.
	www.freedownloadsoft.com /distance-map.html (578 words)

	Papers (Site not responding. Last check: 2007-11-06)
		A new general algorithm for computing distance transforms of digital images is presented.
		The algorithm can be used for the computation of the exact Euclidean, Manhattan (L_1 norm), and chessboard distance (L_\infty norm) transforms.
		However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the publisher.
	www.cs.rug.nl /users/roe/publications/dt.html (243 words)

	The Geometry Junkyard: All Topics (Site not responding. Last check: 2007-11-06)
		Distances on the surface of a rectangular box, illustrated using colored wavefronts in this Java applet by Henry Bottomley.
		Infinite sets of points with rational distances are known, from which arbitrarily large finite sets of points with integer distances can be constructed; however it is open whether there are even seven points at integer distances in general position (no three in a line and no four on a circle).
		Maximizing the minimum distance of N points on a sphere, ray-traced by Hugo Pfoertner.
	www.ics.uci.edu /~eppstein/junkyard/all.html (9731 words)

	55:148 Dig. Image Proc. Chapter 2, Part 3 (Site not responding. Last check: 2007-11-06)
		The distance between two pixels in a digital image is a significant quantitative measure.
		The distance between points with co-ordinates (i,j) and (h,k) may be defined in several different ways;
		Border R is the set of pixels within the region that have one or more neighbors outside R...
	www.icaen.uiowa.edu /~dip/LECTURE/ImageProperties3.html (721 words)

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