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Topic: Distance transforms

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	Distance Fields and Distance Transforms
		This has led to methods such as chamfer distance transforms and vector distance transforms which propagate known distances throughout the image, and latterly these methods have been extended into 3D for the calculation of distance volumes.
		Ideally the distance to the closest point on the object of interest (S) should be stored for each point (p) within a distance field (D).
		Our research has included more accurate distance transforms, and a new process whereby the distance transform is used to give a starting point for the correct sub-voxel distance calculation.
	www.swan.ac.uk /compsci/research/graphics/vg/distance/index.html (504 words)

	[Distance Transforms] - A New Kind of Science: The NKS Forum
		Distance transforms are simple 2 dimensional rules where points are labeled by their closest distance to a set of seed points.
		A distance transform is equivalent to a rule on a directed acylic network, and vice versa.
		A generalized distance transform can be thought of as having two rules, one to update the network, or distance increments, and one to update the color of the pixels, or perhaps as one rule with two purposes.
	forum.wolframscience.com /archive/topic/379-1.html (2765 words)

	21.8 Distance transforms
		Distance transforms are used to calculate the minimum distance from each element of an object to the background.
		uses a chamfer type 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).
		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).
	stsdas.stsci.edu /numarray/numarray-1.5.html/node96.html (596 words)

	Proof that Classical Action is Invariant in a Galilean Transformation—by Miles Mathis
		The current interpretation as the limit of the Lorentz transformation as the velocity of light approaches infinity (or, as some see it, a contraction of the Lorentz transformation) is incorrect because the action of a free particle is not invariant under such a transformation.
		The author argues that the correct transformation is a static translation in space rather than one that moves with the frame of a moving inertial observer.
		The Lorentz transformation transforms events and can be used to compare the description of the motion of a particle as observed with respect to two reference frames in uniform relative motion.
	geocities.com /mileswmathis/gal.html (5970 words)

	References on Euclidean Distance Transforms
		A distance map is an image where the value of each pixel is the distance from this pixel to the nearest pixel belonging to a given set or object.
		Because geodesic distances are based on the notion of paths, a trade-off has to be introduced between the accuracy with which straight lines are represented and the way curves of the domain are followed.
		The distance transform is an operation that converts an image consisting of fl and white pixels to an image where each pixel has a value or coordinate that represents the distance or location to the nearest fl pixel.
	www.lems.brown.edu /vision/people/leymarie/Refs/CompVision/DT/EDT.html (2076 words)

	20.7 Distance transforms (Site not responding. Last check: 2007-10-04)
		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)

	Representing and Analyzing 3D Digital Shape Using Distance Information
		In Paper I, distance transforms using from one to six steps in a 5x5x5 neighbourhood of a voxel are presented.
		The distance transforms are all semi-regular, i.e., a straight path is a minimal path, which is a condition necessary but not sufficient for the distance transform to indicate a metric.
		In Paper IV, a general framework for thinning the distance transform of the object to a surface skeleton is presented.
	www.cb.uu.se /~stina/PhDthesis (1395 words)

	Educational Services - K-12 - Distance Learning - Programs and Resources
		The Distance Education and Training Council (formerly the National Home Study Council) is a non profit educational association located in Washington, D.C. DETC serves as a clearinghouse of information about the distance study/correspondence field and sponsors a nationally recognized accrediting agency called the Accrediting Commission of the Distance Education and Training Council.
		The American Distance Education Consortium, ADEC is an international consortium of state universities and land grant institutions providing high quality and economic distance education programs and services via the latest and most appropriate information technologies.
		Distance Learning at The Cleveland Museum of Art allows students to connect with the CMA through interactive videoconferencing, and discover works of art from the collection without having to leave their school.
	www.wviz.org /edsvcs/k_12/distance_learning/links.asp (967 words)

	Paper Title: Accelerated Volume Ray Casting
		The result of this initialization phase is a distance map where voxels on the surface of non-transparent regions are initialized to the minimum distance.
		A wavefront (represented as a queue) of distances is grown from each foreground voxel until voxels in the distance queue reach the maximum distance or a border.
		In Section 3.2, standard distance transforms which had previously been used to encode empty space distances, were used to compute distance transforms for homogeneous regions.
	home.pacbell.net /freundj/volume/vis97 (3949 words)

	The Chronicle: Information Technology: May 26, 2000
		"Distance education is going to be very competitive in the future," says Dan Daniel, chief information officer for NYUonline, which is seeking a company to provide 24-7 support for its courses.
		Beyond their efforts in distance education, colleges are also struggling to provide on-campus students with more technical support, because those students, too, are using computers more and more.
		But distance education seems to be moving more quickly toward the 24-7 model.
	www.chronicle.com /free/v46/i38/38a04901.htm (1977 words)

	Morphology - Distance Transform
		The result of the transform is a greylevel image that looks similar to the input image except that the greylevel intensity of points inside foreground regions are changed to show the distance to the closest boundary from each point.
		There is a dual to the distance transform described above which produces the distance transform for the background region rather than the foreground region.
		There are several different sorts of distance transform depending upon which distance metric is being used to determine the distance between pixels.
	www.cee.hw.ac.uk /hipr/html/distance.html (880 words)

	Chamfer Matching
		Then, the distance transform of the obtained edges is determined.
		distance transform image is proportional to the distance of that pixel to the edge pixel closest to it.
		distances at the model pixels is determined and the shift position producing the smallest sum is
	www.imgfsr.com /ifsr_ir_cm.html (242 words)

	4.2 Depth of Field (Site not responding. Last check: 2007-10-04)
		Normal viewing transforms act like a perfect pinhole camera; everything visible is in focus, regardless of how close or how far the objects are from the viewer.
		When computing depth of field transforms, however, we only use shear instead of rotation, and sample a number of viewpoints, not just two, along an axis perpendicular to the view direction.
		The closer an object is to the fusion distance, the less it shifts, and the sharper it appears.
	www.opengl.org /resources/code/samples/sig99/advanced99/notes/node27.html (203 words)

	mmdist
		The distances available are based on the Euclidean metrics and on metrics generated by a a regular graph, that is characterized by a connectivity rule defined by the structuring element
		To generate useful Distance transforms, the structuring elements must be symmetric and have the origin included.
		The Euclidean distance transform is rounded to the nearest integer, since it is represented as an unsigned integer image.
	www.mmorph.com /pymorphpro/morph/morph/mmdist.html (157 words)

	String Similarity Metrics for Information Integration
		This is similar to the basic edit distance metric, Levenshtein distance, this adds an variable cost adjustment to the cost of a gap, i.e.
		Again similar to the to Levenshtein distance, this was developed to identify optimal allignments between related DNA and protein sequencies.
		This distance is often incorrectly reffered to as an implementation of the Smith-Waterman distance approach.
	www.dcs.shef.ac.uk /%7Esam/stringmetrics.html (3865 words)

	Distance Maps - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-10-04)
		The manhattan distance from the white points can be found in linear time by using a wave propagation algorith, like flood filling an area.
		Also when doing this, you need to know the point you're calculating euclidian distance from, so that can be stored along with the points (maybe this is useful information too?) or it can be stored in the queue alongside the corresponding point.
		I came across one paper that described a method to perform the distance transform in 2d in linear time, and it said there was a non-trivial way to expand it to 3d, but the algorithm was complicated so I didn't take the time to try to understand it.
	www.gamedev.net /community/forums/topic.asp?topic_id=426784 (950 words)

	Nando de Freitas
		A distance transform of a binary image specifies for each 0-valued pixel the distance to the nearest 1-valued pixel (or vice versa).
		These algorithms are applicable to computing classical distance transforms of binary images as well as to solving a broad class of minimization problems involving a cost function with both local and spatial terms.
		The fast Gauss transform has been applied to the kernel density estimation (KDE), to the mean shift algorithm for clustering, where it improves the quadratic complexity of each iteration, and to kernel machines.
	www.cs.ubc.ca /~nando/nipsfast/abstracts.html (1032 words)

	a4iL: Other transforms of 3d images.
		The Euclidean distance of each pixel to the foreground is approximated by chamfering with a 5x5x5 mask.
		The Euclidean distance of each pixel to the foreground is approximated by chamfering with a 3x3x3 mask.
		The weighted distance of each pixel to the foreground is approximated by chamfering with a 3x3x3 mask.
	www.itwm.fhg.de /mab/projects/MAVI/a4iLDoku/html/group__dt3d.html (893 words)

	disparity_to_distance
		Transform a disparity value into a distance value in a rectified binocular stereo system.
		transforms a disparity value into a distance of an object point to the binocular stereo system.
		The distance to the subset plane z=0 which is parallel to the rectified image plane and contains the optical centers of both cameras is returned in
	www.halcon.us /download/documentation/reference/c/disparity_to_distance.html (197 words)

	Distance Transforms
		Brute force distance calculations are very expensive, since for each voxel of the field the distance to the nearest surface point has to be evaluated by inspecting all objects of the scene.
		Their main idea is to replace the global distance computation by a local propagation of distances in a small neighborhood.
		Traditionally, the distance computation issues from a segmented binary data, where the object surface voxel positions are confined to fixed grid point coordinates.
	www.cg.tuwien.ac.at /studentwork/CESCG/CESCG-2002/MSramek/node1.html (250 words)

	Distance Transforms
		Brute force distance calculations are very expensive, since for each voxel of the field the distance to the nearest surface point has to be evaluated by inspecting all objects of the scene.
		Their main idea is to replace the global distance computation by a local propagation of distances in a small neighborhood.
		Traditionally, the distance computation issues from a segmented binary data, where the object surface voxel positions are confined to fixed grid point coordinates.
	www.cescg.org /CESCG-2002/MSramek/node1.html (250 words)

	System for depicting surfaces using volumetric distance maps - Patent 6040835
		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 one embodiment, the distance is positive inside of the object, negative outside of the object and zero on the object surface.
	www.freepatentsonline.com /6040835.html (3935 words)

	4.1.2 Computing the Transforms
		Computationally, the stereo viewing transforms happen last, after the viewing transform has been applied to put the viewer at the origin.
		Move fusion distance along the viewing direction from the viewer position, and use that point for the center of interest of both eyes.
		An alternative, but less correct, method of implementing stereo transforms is to translate the views left and right by half of the interocular distance, then rotate by the inverse tangent of the ratio between the fusion distance and half of the interocular distance:
	www.opengl.org /resources/code/samples/sig99/advanced99/notes/node26.html (263 words)

	Environment and Planning B abstract (Site not responding. Last check: 2007-10-04)
		This raises the question as to how distances should be measured in such cases and to what extent these relate to continuous space metrics.
		In this paper I show that a set of image processing algorithms known as distance transforms (DTs) may be applied to such datasets and can be extended to solve a wide range of 2D and 3D optimisation problems.
		Sample pseudo-code for the transforms discussed is included in an appendix.
	www.envplan.com /epb/abstracts/b31/b29123.html (253 words)

	NKS 2006 Conference & Minicourse: Distance Transforms
		Distance transforms can be defined as cellular automata on directed acylic networks on a grid.
		Examples include the time evolution of 1D cellular automata, and more general cases where the network connections and shape of the front are generated by the rule.
		An efficient algorithm for distance transforms runs in O(n logn) time where n is the number of grid points, which compares to worst case O(n-cubed) runtime when using a standard 2D cellular automata implementation.
	www.wolframscience.com /conference/2006/presentations/scott.html (116 words)

	Distance Transformations
		To see what a distance transform will do to an image click on the sample input images.
		I have written a program that applies a "distance transform" to grey-scale images and outputs distance transformed copy of that image, also a grey-scale image.
		The point of a distance transform is to assign a value to each pixel according to its depth within an image.
	cgm.cs.mcgill.ca /~godfried/student_projects/scottyb_DistTrans (649 words)

	[gagvani98] notes page (Site not responding. Last check: 2007-10-04)
		It can be computed using topological thinning operators or a distance transform based method (which they use).
		The distance transform of a voxel is the minimum distance from that voxel to the boundary.
		Their distance is the minimum of all applicable values.
	www.cs.princeton.edu /~min/meshclass/shape/notes.cgi?key=gagvani98 (283 words)

	Distance transform of Wardrop’s velocity field model
		Distance transforms compute the distance of every pixel in a binary image, or every cell in a lattice dataset, to the nearest point in an object set – the object set may be a single point, in which case the distance contours should be circular if the transform is strictly Euclidean.
		However, distance transforms often use approximations to Euclidean distance for speed of processing (so-called chamfer metrics).
		In the first example (Wardrop’s model), a Least Cost Distance Transform (LCDT) is shown, where cost is a function of traffic velocity.
	www.desmith.net /MJdS/DT1.htm (282 words)

	Chamfer Distance Transforms Object Detection Recognition Shape Matching Hausdorff
		A major advantage is the hierarchical approach of the system (in both shape and transformation space); it results in substantial efficiency gains compared to an equivalent brute-force template matching method.
		edge detection) and the so-called distance transform; this results in a distance image, where pixels contain the distances to closest data pixels in the feature image.
		Matching consists of translating and positioning the template at various locations of the distance image; the matching measure is determined by the pixel values of the distance image which lie under the data pixels of the transformed template.
	www.gavrila.net /Computer_Vision/Research/Chamfer_System/chamfer_system.html (627 words)

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