7.3.7 Distance Transforms, Distance Functions, Distance Measures

Rosenfeld, A., and Pfaltz, J.L.,
Distance Functions on Digital Pictures,
PR(1), No. 1, July 1968, pp. 33-61.
WWW Version. BibRef 6807

Jackson, D.M.[David M.], White, L.J.[Lee J.],
Effect of random errors on generalized distance computations,
PR(4), No. 3, October 1972, pp. 263-273.
WWW Version. 0309 BibRef

Fischler, M.A.,
Fast Algorithms for Two Maximal Distance Problems with Applications to Image Analysis,
PR(12), No. 1, 1980, pp. 35-40.
WWW Version. BibRef 8000

Yokoi, S., Toriwaki, J.I., and Fukumura, T.,
On Generalized Distance Transformation of Digitized Pictures,
PAMI(3), No. 4, July 1981, pp. 424-443. BibRef 8107
Earlier:
Generalized Distance Transformation on Digitized Binary Images,
ICPR80(1201-1203). BibRef

Toriwaki, J.I., Naruse, T., and Fukumura, T.,
Fundamental Properties of the Grey Weighted Distance Transformation of Grey Pictures,
IECE(60), 1977, pp. 1101-1108. BibRef 7700

Toriwaki, J.I., Tanaka, M., and Fukumura, T.,
A Generalized Distance Transformation of a Line Pattern with Grey Values and Its Application,
CGIP(20), 1982, pp. 319-346. BibRef 8200
Earlier: ICPR80(35-37). BibRef

Danielsson, P.E.,
Euclidean Distance Mapping,
CGIP(14), No. 3, November 1980, pp. 227-248. How far is a point to some feature. BibRef 8011

Danielsson, P.E., Kruse, B.,
Distance Checking Algorithms,
CGIP(11), No. 4, December 1979, pp. 349-376.
WWW Version. BibRef 7912

Roberts, S.J., Hanka, R.,
An interpretation of Mahalanobis distance in the dual space,
PR(15), No. 4, 1982, pp. 325-333.
WWW Version. 0309 BibRef

Krusinska, E.,
A valuation of state of object based on weighted Mahalanobis distance,
PR(20), No. 4, 1987, pp. 413-418.
WWW Version. 0309 BibRef

Samet, H.,
Distance Transform for Images Represented by Quadtrees,
PAMI(4), No. 3, May 1982, pp. 298-303. BibRef 8205

Chazelle, B.,
An Improved Algorithm for the Fixed-Radius Neighbor Problem,
IPL(16), 1983, pp. 193-198. BibRef 8300

Bhattacharya, B.K., Toussaint, G.T.,
Efficient Algorithms for Computing the Maximum Distance,
Algorithms(4), 1983, pp. 121-126. BibRef 8300

Soille, P.,
Spatial Distributions from Contour Lines: An Efficient Methodology Based on Distance Transformations,
JVCIR(2), 1991, pp. 138-150. BibRef 9100

Soille, P.[Pierre],
Constrained Connectivity for Hierarchical Image Decomposition and Simplification,
PAMI(30), No. 7, July 2008, pp. 1132-1145.
WWW Version. 0806 BibRef
Earlier:
On Genuine Connectivity Relations Based on Logical Predicates,
CIAP07(487-492).
WWW Version. 07092 pixels are connected if the meet certain constraints, gray level differences over the connecting path. BibRef

Klein, F., and Kubler, O.,
Euclidean Distance Transformations and Model-Guided Image Interpretation,
PRL(5), 1987, pp. 19-29. BibRef 8700

Das, P.P., Chakrabarti, P.P., and Chatterji, B.N.,
Distance Functions in Digital Geometry,
IS(42), 1987, pp. 113-136. BibRef 8700

Das, P.P., Chatterji, B.N.,
Hyperspheres In Digital Geometry,
IS(50), 1990, pp. 73-91. BibRef 9000

Das, P.P., Chatterji, B.N.,
Knight's Distance in Digital Geometry,
PRL(7), 1988, pp. 215-226. BibRef 8800

Das, P.P.,
Counting Minimal Paths in Digital Geometry,
PRL(12), 1991, pp. 595-603. BibRef 9100
And:
An Algorithm for Computing the Number of the Minimal Paths in Digital Images,
PRL(9), 1989, pp. 107-116. BibRef

Das, P.P., Mukherjee, J.,
Metricity of Super-Knight's Distance in Digital Geometry,
PRL(11), 1990, pp. 601-604. BibRef 9000

Das, P.P., Chatterji, B.N.,
Octagonal Distances For Digital Pictures,
IS(50), 1990, pp. 123-150. BibRef 9000

Das, P.P., Chatterji, B.N.,
A Note on 'Distance Transformations in Arbitrary Dimensions',
CVGIP(43), No. 3, September 1988, pp. 368-385.
WWW Version. BibRef 8809

Das, P.P.,
Lattice of Octagonal Distances in Digital Geometry,
PRL(11), 1990, pp. 663-667. BibRef 9000

Das, P.P.,
More on Path Generated Digital Metrics,
PRL(10), 1989, pp. 25-31. BibRef 8900

Das, P.P.,
Metricity Preserving Transforms,
PRL(10), 1989, pp. 73-76. BibRef 8900

Rosenfeld, A.,
A Note on Average Distances in Digital Sets,
PRL(5), 1987, pp. 281-283. BibRef 8700

Borgefors, G.,
Distance Transformations in Digital Images,
CVGIP(34), No. 3, June 1986, pp. 344-371. BibRef 8606
Earlier:
A New Distance Transformation Approximating the Euclidean Distance,
ICPR86(336-338). BibRef
And:
Another Comment on 'A Note on 'Distance Transformations in Digital Images'',
CVGIP(54), No. 2, September 1991, pp. 301-306.
WWW Version. BibRef

Borgefors, G., Hartmann, T., and Tanimoto, S.L.,
Parallel Distance Transforms on Pyramid Machines: Theory and Implementation,
SP(21), 1990, pp. 61-86. BibRef 9000

Vossepoel, A.M.,
A Note on 'Distance Transformations in Digital Images',
CVGIP(43), No. 1, July 1988, pp. 88-97.
WWW Version. BibRef 8807

Vossepoel, A.M.,
Estimating the size of circular pre-images from coarsely digitized representations,
ICPR92(III:365-368).
WWW Version. 9208probability of disks in set of pixels. BibRef

Beckers, A.L.D., Smeulders, A.W.M.,
A Comment on 'A Note on 'Distance Transformations in Digital Images'',
CVGIP(47), No. 1, July 1989, pp. 89-91.
WWW Version. BibRef 8907

Yamashita, M., Honda, N.,
Distance Functions Defined by Variable Neighborhood Sequences,
PR(17), No. 5, 1984, pp. 509-513.
WWW Version. 9611 BibRef

Yamashita, M., Ibaraki, T.,
Distances Defined By Neighborhood Sequences,
PR(19), No. 3, 1986, pp. 237-246.
WWW Version. BibRef 8600

Piper, J., Granum, E.,
Computing Distance Transformations in Convex and Non-Convex Domains,
PR(20), No. 6, 1987, pp. 599-615.
WWW Version. BibRef 8700

Verwer, B.J.H., Verbeek, P.W., and Dekker, S.T.,
An Efficient Uniform Cost Algorithm Applied to Distance Transforms,
PAMI(11), No. 4, April 1989, pp. 425-429.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 8904

Shih, F.Y., Wu, H.,
Optimization on Euclidean Distance Transformation Using Grayscale Morphology,
JVCIR(3), 1992, pp. 104-114. BibRef 9200

Shih, F.Y.[Frank Y.], Liu, J.J.[Jenny J.],
Size-invariant four-scan Euclidean distance transformation,
PR(31), No. 11, November 1998, pp. 1761-1766.
WWW Version. BibRef 9811

Shih, F.Y.[Frank Y.], Wu, Y.T.[Yi-Ta],
Fast Euclidean Distance Transformation in Two Scans Using a 3X3 Neighborhood,
CVIU(93), No. 2, February 2004, pp. 195-205.
WWW Version. 0402Record relative X and Y and achieve distance in only 2 scans. See also Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods. BibRef

Shih, F.Y.[Frank Y.], Wu, Y.T.[Yi-Ta],
The Efficient Algorithms for Achieving Euclidean Distance Transformation,
IP(13), No. 8, August 2004, pp. 1078-1091.
WWW Version. 0409 BibRef

Paglieroni, D.W.[David W.],
Distance Transforms: Properties and Machine Vision Applications,
GMIP(54), No. 1, January 1992, pp. 56-74. BibRef 9201

Paglieroni, D.W.,
A Unified Distance Transform Algorithm and Architecture,
MVA(5), 1992, pp. 47-55. BibRef 9200

Wang, X.L.[Xiao-Li], Bertrand, G.,
Some Sequential Algorithms for a Generalized Distance Transformation Based on Minkowski Operations,
PAMI(14), No. 11, November 1992, pp. 1114-1121.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9211
An Algorithm for a Generalized Distance Transformation Based on Minkowski Operations,
ICPR88(II: 1164-1168).
WWW Version.
IEEE Top Reference. BibRef

Ragnemalm, I.[Ingemar],
Neighborhoods for Distance Transformations Using Ordered Propagation,
CVGIP(56), No. 3, November 1992, pp. 399-409.
WWW Version. BibRef 9211

Borgefors, G., Ragnemalm, I.[Ingemar], and Sanniti di Baja, G.[Gabriella],
Feature Extraction of the Euclidean Distance Transform,
CIAP91(115-122). BibRef 9100

Ragnemalm, I.,
The Euclidean Distance Transform in Arbitrary Dimensions,
PRL(14), 1993, pp. 883-888. BibRef 9300

Ragnemalm, I.,
Fast Erosion and Dilation by Contour Processing and Thresholding of Distance Maps,
PRL(13), 1992, pp. 161-166. BibRef 9200

Starovoitov, V.V., Ablameyko, S.V., Ishikawa, S., Kawaguchi, E.,
Binary Texture Border Extraction on Line Drawings Based on Distance Transform,
PR(26), No. 8, August 1993, pp. 1165-1176.
WWW Version. BibRef 9308

Breu, H., Gil, J., Kirkpatrick, D., Werman, M.,
Linear-Time Euclidean Distance Transform Algorithms,
PAMI(17), No. 5, May 1995, pp. 529-533.
IEEE Abstract. IEEE Top Reference.
WWW Version. One theoretical algorithm and one practical algorithm, derive transform from a Voronoi diagram. BibRef 9505

Embrechts, H.[Hugo], Roose, D.[Dirk],
A Parallel Euclidean Distance Transformation Algorithm,
CVIU(63), No. 1, January 1996, pp. 15-26.
WWW Version. BibRef 9601
Earlier:
Parallel algorithms for the distance transformation,
ECCV92(387-391).
WWW Version. 9205 BibRef

Starovoitov, V.V.,
A Clustering Technique Based on the Distance Transform,
PRL(17), No. 3, March 6 1996, pp. 231-239. BibRef 9603

Toivanen, P.J.,
New Geodesic Distance Transforms for Gray-Scale Images,
PRL(17), No. 5, May 1 1996, pp. 437-450. 9606 BibRef
And: Correction: PRL(17), No. 13, November 25 1996, pp. 1411-1411. BibRef

Eggers, H.,
Parallel Euclidean Distance Transformations in Z(G)(N),
PRL(17), No. 7, June 10 1996, pp. 751-757. 9607 BibRef

Eggers, H.[Hinnik],
Two Fast Euclidean Distance Transformations in Z2 Based on Sufficient Propagation,
CVIU(69), No. 1, January 1998, pp. 106-116.
WWW Version. BibRef 9801

Kiselman, C.O.,
Regularity Properties of Distance Transformations in Image-Analysis,
CVIU(64), No. 3, November 1996, pp. 390-398. 9612
WWW Version. BibRef

Chaudhuri, D., Murthy, C.A., Chaudhuri, B.B.,
A Modified Metric to Compute Distance,
PR(25), No. 7, July 1992, pp. 667-677.
WWW Version. BibRef 9207

Huang, C.T.[C. Tony], and Mitchell, O.R.[O. Robert],
A Euclidian Distance Transform Using Grayscale Morphology Decomposition,
PAMI(16), No. 4, April 1994, pp. 443-448.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9404
Earlier:
Rapid Euclidean Distance Transform Using Grayscale Morphology Decomposition,
CVPR91(695-697).
IEEE Abstract. IEEE Top Reference. See also Threshold Decomposition of Gray-Scale Morphology into Binary Morphology. BibRef

Arcelli, C., Ramella, G.,
Sketching a Grey-Tone Pattern from Its Distance Transform,
PR(29), No. 12, December 1996, pp. 2033-2045.
WWW Version. 9701 BibRef

Coquin, D., and Bolon, P.,
Discrete Distance Operator on Rectangular Grids,
PRL(16), 1995, pp. 911-923. BibRef 9500

Toivanen, P.J.,
Image Compression by Selecting Control Points Using Distance Function on Curved Space,
PRL(14), 1993, pp. 475-482. BibRef 9300

Rhodes, F.[Frank],
On the metrics of Chaudhuri, Murthy and Chaudhuri,
PR(28), No. 5, May 1995, pp. 745-752.
WWW Version. 0401considers the approximation of Euclidean distance in n-dimensional space by linear combinations of the L1 and L-inf metrics. See also Modified Metric to Compute Distance, A. BibRef

Rhodes, F.,
Some Characterizations of the Chessboard Metric and the City Block Metric,
PRL(11), 1990, pp. 669-675. BibRef 9000

Melter, R.A.,
Some Characterizations of City Block Distance,
PRL(6), 1987, pp. 235-240. BibRef 8700

Brown, R.L.,
The Fringe Distance Measure: An Easily Calculated Image Distance Measure with Recognition Results Comparable to Gaussian Blurring,
SMC(24), 1994, pp. 111-115. BibRef 9400

Lee, Y.H., Horng, S.J., Kao, T.W., Chen, Y.J.,
Parallel Computation of the Euclidean Distance transform on the Mesh of Trees and the Hypercube Computer,
CVIU(68), No. 1, October 1997, pp. 109-119. 9710
WWW Version. BibRef

Lee, Y.H.[Yu-Hua], Horng, S.J.[Shi-Jinn],
Optimal Computing the Chessboard Distance Transform on Parallel Processing Systems,
CVIU(73), No. 3, March 1999, pp. 374-390.
WWW Version. BibRef 9903

Juffs, P., Beggs, E., Deravi, F.,
A Multiresolution Distance Measure for Images,
SPLetters(5), No. 6, June 1998, pp. 138-140.
IEEE Top Reference. 9806 BibRef

Butt, M.A., Maragos, P.,
Optimum Design of Chamfer Distance Transforms,
IP(7), No. 10, October 1998, pp. 1477-1484.
WWW Version. BibRef 9810

Kaijser, T.,
Computing the Kantorovich Distance for Images,
JMIV(9), No. 2, September 1998, pp. 173-191.
WWW Version. 9811 BibRef

Pennec, X., Ayache, N.,
Uniform Distribution, Distance and Expectation Problems for Geometric Features Processing,
JMIV(9), No. 1, July 1998, pp. 49-67.
WWW Version. 9807 BibRef

Maekawa, T.,
An overview of offset curves and surfaces,
CAD(31), No. 3, March 1999, pp. 165-173. BibRef 9903

Maekawa, T., and Patrikalakis, N.M.,
Computation of singularities and intersections of offsets of planar curves,
CAGD(10), No. 5, 1993, pp. 407-429. BibRef 9300

Marchand-Maillet, S.[Stephane], Sharaiha, Y.M.[Yazid M.],
Euclidean Ordering via Chamfer Distance Calculations,
CVIU(73), No. 3, March 1999, pp. 404-413.
WWW Version. BibRef 9903
And:
A Graph-Theoretic Algorithm for the Exact Generation of Euclidean Distance Maps,
SCIA97(xx-yy) 9705
HTML Version. BibRef

Takala, J.H.[Jarmo H.], Viitanen, J.O.[Jouko O.],
Distance Transform Algorithm for Bit-Serial SIMD Architectures,
CVIU(74), No. 2, May 1999, pp. 150-161.
WWW Version. BibRef 9905
Earlier: A2, A1:
SIMD parallel calculation of distance transformations,
ICIP94(III: 645-649).
WWW Version. 9411 BibRef

Bloch, I.[Isabelle],
On fuzzy distances and their use in image processing under imprecision,
PR(32), No. 11, November 1999, pp. 1873-1895.
WWW Version. See also Fuzzy Connectivity and Mathematical Morphology. BibRef 9911

Bloch, I.[Isabelle],
Geodesic balls in a fuzzy set and fuzzy geodesic mathematical morphology,
PR(33), No. 6, June 2000, pp. 897-905.
WWW Version. 0004 BibRef

Bloch, I.[Isabelle],
On links between mathematical morphology and rough sets,
PR(33), No. 9, September 2000, pp. 1487-1496.
WWW Version. 0005 BibRef

Ramponi, G.,
Warped Distance for Space-Variant Linear Image Interpolation,
IP(8), No. 5, May 1999, pp. 629-639.
WWW Version. BibRef 9905

Zhang, S., Karim, M.A.,
Euclidean Distance Transform by Stack Filters,
SPLetters(6), No. 10, October 1999, pp. 253.
IEEE Top Reference. BibRef 9910

Cuisenaire, O., Macq, B.,
Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods,
CVIU(76), No. 2, November 1999, pp. 163-172. 9911
WWW Version. Also use bucket sort. BibRef

Toivanen, P.J.[Pekka J.], Vepsäläinen, A.M.[Ari M.], Parkkinen, J.P.S.[Jussi P.S.],
Image Compression Using the Distance Transform on Curved Space (DTOCS) and Delaunay Triangulation,
PRL(20), No. 10, October 1999, pp. 1015-1026. 9911 BibRef
Earlier:
Image Compression Using the DTOCS and Delaunay Triangulation,
SCIA97(xx-yy) 9705
HTML Version. BibRef

Pan, Y., Hamdi, M., Li, K.,
Euclidean Distance Transform for Binary Images on Reconfigurable Mesh-Connected Computers,
SMC-B(30), No. 1, February 2000, pp. 240-243.
IEEE Top Reference. 0004 See also Improved Constant-Time Algorithm for Computing the Radon and Hough Transforms on a Reconfigurable Mesh, An. BibRef

Gomes, J.[José], Faugeras, O.D.[Olivier D.],
Reconciling Distance Functions and Level Sets,
JVCIR(11), No. 2, June 2000, pp. 209-223. 0008 BibRef
Earlier: ScaleSpace99(70-81). BibRef

Gomes, J.[José], Faugeras, O.D.[Olivier D.],
The Vector Distance Functions,
IJCV(52), No. 2-3, May-June 2003, pp. 161-187.
WWW Version. 0301 BibRef

Mukherjee, J., Das, P.P., Kumar, M.A.[M. Aswatha], Chatterji, B.N.,
On approximating Euclidean metrics by digital distances in 2D and 3D,
PRL(21), No. 6-7, June 2000, pp. 573-582. 0006 BibRef

Chang, C.C., Chou, J.S., Chen, T.S.,
An Efficient Computation of Euclidean Distance Using Approximated Look-Up Table,
CirSysVideo(10), No. 4, June 2000, pp. 594-599.
IEEE Top Reference. 0006 BibRef

Boxer, L.[Laurence], Miller, R.[Russ],
Efficient Computation of the Euclidean Distance Transform,
CVIU(80), No. 3, December 2000, pp. 379-383. 0012
WWW Version. BibRef
And: Corrigendum: CVIU(86), No. 2, May 2002, pp. 137-140.
WWW Version. 0301 BibRef

Sebe, N.[Nicu], Lew, M.S.[Michael S.], Huijsmans, D.P.[Dionysius P.],
Toward Improved Ranking Metrics,
PAMI(22), No. 10, October 2000, pp. 1132-1143.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0011 Evaluation. Distance Measures. Applied to contyent based retrieval, stereo matching and motion tracking. Comparison of various metrics (SSD, SAD, Cauchy, Kullback). Cauchy was better. BibRef

Satherley, R.[Richard], Jones, M.W.[Mark W.],
Vector-City Vector Distance Transform,
CVIU(82), No. 3, June 2001, pp. 238-254.
WWW Version. City-block chamfer distance transform. 0108 BibRef

Maurer, C.R.[Calvin R.], Qi, R.S.[Ren-Sheng], Raghavan, V.[Vijay],
A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions,
PAMI(25), No. 2, February 2003, pp. 265-270.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0301For k-dimensional images. Based on dimensionality reduction and partial Voronoi diagram reconstructions. BibRef

Saha, P.K.[Punam K.], Wehrli, F.W.[Felix W.], Gomberg, B.R.[Bryon R.],
Fuzzy Distance Transform: Theory, Algorithms, and Applications,
CVIU(86), No. 3, June 2002, pp. 171-190.
WWW Version. 0301 BibRef

Li, J.[Jun], Nekka, F.[Fahima],
The Hausdorff measure functions: A new way to characterize fractal sets,
PRL(24), No. 15, November 2003, pp. 2723-2730.
WWW Version. 0308 BibRef

Datta, A., Soundaralakshmi, S.,
Fast parallel algorithm for distance transform,
SMC-A(33), No. 4, July 2003, pp. 429-434.
IEEE Abstract. IEEE Top Reference. 0310 BibRef

Zhang, Y.G.[Yun Gang], Zhang, C.S.[Chang Shui], Zhang, D.[David],
Distance metric learning by knowledge embedding,
PR(37), No. 1, January 2004, pp. 161-163.
WWW Version. 0311 BibRef
And: Erratum: PR(37), No. 4, April 2004, pp. Page 855.
WWW Version. 0403 BibRef

Fernández García, N.L., Medina Carnicer, R., Carmona Poyato, A., Madrid Cuevas, F.J., Prieto Villegas, M.,
Characterization of empirical discrepancy evaluation measures,
PRL(25), No. 1, January 2004, pp. 35-47.
WWW Version. 0311 BibRef

Grevera, G.J.[George J.],
The 'dead reckoning' signed distance transform,
CVIU(95), No. 3, September 2004, pp. 317-333.
WWW Version. 0409Modification to Chamfer distance based loosely on dead reckoning navigation. More efficient and accurate. BibRef

Ikonen, L.[Leena], Toivanen, P.J.[Pekka J.],
Shortest routes on varying height surfaces using gray-level distance transforms,
IVC(23), No. 2, 1 February 2004, pp. 133-141.
WWW Version. 0412 BibRef

Ikonen, L.[Leena], Toivanen, P.J.[Pekka J.],
Distance and nearest neighbor transforms on gray-level surfaces,
PRL(28), No. 5, 1 April 2007, pp. 604-612.
WWW Version. 0703Distance transforms; Gray-level distance transforms; Nearest neighbor transforms; Geodesic distances; Minimal geodesics; Surface roughness BibRef

Ikonen, L.[Leena], Toivanen, P.J.[Pekka J.], Tuominen, J.[Janne],
Shortest Route on Gray-Level Map Using Distance Transform on Curved Space,
SCIA03(305-310).
WWW Version. 0310 BibRef

Ikonen, L.[Leena],
Priority pixel queue algorithm for geodesic distance transforms,
IVC(25), No. 10, 1 October 2007, pp. 1520-1529.
WWW Version. 0709Distance transforms; Gray-level distance transforms; Nearest neighbor transforms; Minimal geodesics; Pixel queue algorithms BibRef

Toivanen, P.J.[Pekka J.], Lenz, R.[Reiner],
On the Properties of Gray-scale Distance Transforms,
SCIA01(O-M4B). 0206 BibRef

Fouard, C.[Céline], Malandain, G.[Grégoire],
3-D chamfer distances and norms in anisotropic grids,
IVC(23), No. 2, 1 February 2004, pp. 143-158.
WWW Version. 0412 BibRef
Earlier:
Automatic calculation of chamfer mask coefficients for large masks and anisotropic images pages.,
INRIARR-4792, Mars 2003.
HTML Version. 0306 BibRef

Ong, E.J.[Eng-Jon], Bowden, R.[Richard],
Learning multi-kernel distance functions using relative comparisons,
PR(38), No. 12, December 2005, pp. 2653-2657.
WWW Version. 0510 BibRef

Ong, E.J.[Eng-Jon], Bowden, R.[Richard],
Learning Distances for Arbitrary Visual Features,
BMVC06(II:749).
PDF Version. 0609 BibRef

Miyazawa, M., Zeng, P.[Peifeng], Iso, N., Hirata, T.,
A Systolic Algorithm for Euclidean Distance Transform,
PAMI(28), No. 7, July 2006, pp. 1127-1134.
WWW Version. 0606Computes the Euclidean distance map of an NXN binary image in 3N clocks on 2N^2 processing cells. BibRef

Nayak, A.[Arvind], Trucco, E.[Emanuele], Thacker, N.A.[Neil A.],
When are Simple LS Estimators Enough? An Empirical Study of LS, TLS, and GTLS,
IJCV(68), No. 2, June 2006, pp. 203-216.
WWW Version. 0606least squares; total least squares; generalized total least squares. Study the various errors to determine whether simpler model can be used. BibRef

Guderlei, R., Klenk, S., Mayer, J., Schmidt, V., Spodarev, E.,
Algorithms for the computation of the Minkowski functionals of deterministic and random polyconvex sets,
IVC(25), No. 4, April 2007, pp. 464-474.
WWW Version. 0702Binary image; Intrinsic volume; Querma[ss] integral; Minkowski functional; Area; Boundary length; Euler-Poincare characteristic; Stationary random closed set; Random field; Volume fraction; Steiner formula; Principal kinematic formula; Parallel set BibRef

Lee, D.J.[Dah-Jye], Archibald, J.[James], Xu, X.[Xiaoqian], Zhan, P.C.[Peng-Cheng],
Using distance transform to solve real-time machine vision inspection problems,
MVA(18), No. 2, April 2007, pp. 85-93.
WWW Version. 0704 BibRef

Fouard, C.[Celine], Strand, R.[Robin], Borgefors, G.[Gunilla],
Weighted distance transforms generalized to modules and their computation on point lattices,
PR(40), No. 9, September 2007, pp. 2453-2474.
WWW Version. 0705Weighted distance; Distance transform; Chamfer algorithm; Non-standard grids BibRef

Rauber, T.W., Braun, T., Berns, K.,
Probabilistic distance measures of the Dirichlet and Beta distributions,
PR(41), No. 2, February 2008, pp. 637-645.
WWW Version. 0711Probabilistic distance measures; Chernoff distance; Bhattacharyya distance; Dirichlet distribution; Beta distribution BibRef

da Silva, M.A.H.B.[Moacyr A.H.B.], Teixeira, R.[Ralph], Pesco, S.[Sinésio], Craizer, M.[Marcos],
A Fast Marching Method for the Area Based Affine Distance,
JMIV(30), No. 1, January 2008, pp. 1-12.
WWW Version. 0801 BibRef

McCane, B.[Brendan], Albert, M.[Michael],
Distance functions for categorical and mixed variables,
PRL(29), No. 7, 1 May 2008, pp. 986-993.
WWW Version. 0804Categorical data; Mahalanobis distance; Distance functions BibRef

Fabbri, R.[Ricardo], Da Fontoura Costa, L.[Luciano], Torelli, J.C.[Julio C.], Bruno, O.M.[Odemir M.],
2D Euclidean distance transform algorithms: A comparative survey,
Surveys(40), No. 1, February 2008, pp. 1-44.
WWW Version. 0805 Survey, Distance Measures. BibRef

Solnon, C.[Christine], Jolion, J.M.[Jean-Michel],
Generalized vs Set Median Strings for Histogram-Based Distances: Algorithms and Classification Results in the Image Domain,
GbRPR07(404-414).
WWW Version. 0706 BibRef

Antón-Canalís, L.[Luis], Hernández-Tejera, M.[Mario], Sánchez-Nielsen, E.[Elena],
Analysis of Relevant Maxima in Distance Transform. An Application to Fast Coarse Image Segmentation,
IbPRIA07(I: 97-104).
WWW Version. 0706 BibRef

Felzenszwalb, P.F.[Pedro F.], Huttenlocher, D.P.[Daniel P.],
Distance Transforms of Sampled Functions,
Cornell2004, Computing and Information Science TR2004-1963. Code, Distance Transform.
WWW Version. BibRef 0400

Twining, C.J.[Carole J.], Taylor, C.J.,
Specificity as a Graph-Based Estimator of Cross-Entropy and KL Divergence,
BMVC06(II:59).
PDF Version. 0609 BibRef

Harker, M.J., O'Leary, P.L.,
First Order Geometric Distance (The Myth of Sampsonus),
BMVC06(I:87).
PDF Version. 0609 BibRef

Omer, I.[Ido], Werman, M.[Michael],
The Bottleneck Geodesic: Computing Pixel Affinity,
CVPR06(II: 1901-1907).
WWW Version. 0606Compute image specific measures for simmilarity of pixels. Path in histogram space that is short and dense. BibRef

Abdi, H., O'Toole, A.J., Valentin, D., Edelman, B.,
DISTATIS: The Analysis of Multiple Distance Matrices,
EEMCV05(III: 42-42).
WWW Version. 0507 BibRef

Lucet, Y.[Yves],
A Linear Euclidean Distance Transform Algorithm Based on the Linear-Time Legendre Transform,
CRV05(262-267).
WWW Version. 0505 BibRef

Zhang, B.[Bin], Srihari, S.,
Discovery of the tri-edge inequality with binary vector dissimilarity measures,
ICPR04(IV: 669-672).
WWW Version. 0409Triangle: sum of 2 sides greater than the third. Apply to distance measure analysis. BibRef

Schouten, T., van den Broek, E.,
Fast exact euclidean distance (FEED) transformation,
ICPR04(III: 594-597).
WWW Version. 0409 BibRef

Cardenes, R., Watfield, S.K., Macias, E., Ruiz-Alzolar, J.,
Occlusion points propagation geodesic distance transformation,
ICIP03(I: 361-364).
IEEE Abstract. IEEE Top Reference. 0312 BibRef

Chen, W.J.[Wei-Jun], Buhmann, J.M.[Joachim M.],
A New Distance Measure for Probabilistic Shape Modeling,
DAGM03(507-514).
HTML Version. 0310 BibRef

Manay, S., Yezzi, A.,
A second-order pde tecumque to construct distance functions with more accurate derivatives,
ICIP03(I: 873-876).
IEEE Abstract. IEEE Top Reference. 0312 BibRef

Donath, K.[Klaus], Wolf, M.[Matthias], Chrástek, R.[Radim], Niemann, H.[Heinrich],
A Hybrid Distance Map Based and Morphologic Thinning Algorithm,
DAGM03(354-361).
HTML Version. 0310 BibRef

Aujol, J.F.[Jean-Francois], Aubert, G.[Gilles],
Signed distance functions and viscosity solutions of discontinuous Hamilton-Jacobi Equations,
INRIARR-4507, July 2002.
HTML Version. 0211 BibRef

Giannopoulos, P.[Panos], Veltkamp, R.C.[Remco C.],
A Pseudo-Metric for Weighted Point Sets,
ECCV02(III: 715 ff.).
HTML Version. 0205 BibRef

Levina, E.[Elizaveta], Bickel, P.[Peter],
The Earth Mover's Distance is the Mallows Distance: Some Insights from Statistics,
ICCV01(II: 251-256).
WWW Version. 0106 See also Earth Mover's Distance as a Metric for Image Retrieval, The. BibRef

Gomes, J., Faugeras, O.D.,
Level Sets and Distance Functions,
ECCV00(I: 588-602).
WWW Version. 0003 BibRef

Cohen, S.D., Guibas, L.J.,
The Earth Mover's Distance under Transformation Sets,
ICCV99(1076-1083).
WWW Version. See also Earth Mover's Distance as a Metric for Image Retrieval, The. BibRef 9900

Gustin, V.[Veselko], Lapajne, A.[Ales], Kodric, R.[Rober], Zitko, T.[Tomislav],
Measurement of Ski-Jump Distances by the Use of Fuzzy Pattern Comparator,
CAIP99(462-471).
WWW Version. 9909 BibRef

Jang, J.H., Hong, K.S.,
Detection of Curvilinear Structures Using the Euclidean Distance Transform,
MVA98(xx-yy). BibRef 9800

Forsmoo, A.,
The distance transform algorithm on a two-processor computer,
CIAP99(114-118).
WWW Version. 9909 BibRef

Forsmoo, A.[Anders], and Borgefors, G.[Gunilla],
Parallel Distance Transform Algorithms on a General SIMD Computer,
SCIA97(xx-yy) 9705
HTML Version. BibRef

Baglietto, P.,
Euclidean distance transform on a dedicated architecture based on a reconfigurable mesh network,
CIAP99(235-240).
WWW Version. 9909 BibRef

Kwon, O.K.[Oh-Kyu], Sim, D.G.[Dong-Gyu], Park, R.H.[Rae-Hong],
New Hausdorff distances based on robust statistics for comparing images,
ICIP96(III: 21-24).
WWW Version. 9610 BibRef

Shih, F.Y., Yang, C.H.T.,
On solving exact Euclidean distance transformation with invariance to object size,
CVPR93(607-608).
IEEE Abstract. IEEE Top Reference. 0403 BibRef

Pridmore, T.P.[Tony P.], Ablameyko, S.V.[Sergey V.],
The distance transform for line patterns: Generalisation and development,
CAIP95(278-285).
WWW Version. 9509 BibRef

Buchowicz, A.,
Adaptive multichannel distance filter,
ICIP95(I: 175-178).
WWW Version. 9510 BibRef

Buchowicz, A., Pitas, I.,
Multichannel distance filters,
ICIP94(II: 575-579).
WWW Version. 9411 BibRef

Yang, D.L.[Dyi-Long], Chen, C.H.[Chin-Hsing],
A real-time systolic array for distance transformation,
ICPR94(C:342-344).
WWW Version. 9410 BibRef

Verbeek, F.J.,
Deformation correction using Euclidean contour distance maps,
ICPR92(III:347-351).
WWW Version. 9208 BibRef

Segawa, H., Ukita, T.,
A similarity value transformation method for probabilistic scoring,
ICPR88(II: 1225-1209).
WWW Version. 8811Turn similarity into probability. BibRef

Mouer, E., Schaerf, R.,
New Applications of Distance Transformation Methods for Effective Structural Image Analysis,
ICPR86(666-668). BibRef 8600

Okada, T., Kanade, T.,
Approximate Lengths Between Phalanges of Multijointed Fingers for Stable Grasping,
AAAI-83(301-305). BibRef 8300

Chapter on 2-D Feature Analysis, Extraction and Representations, Shape, Skeletons, Texture continues in
Three Dimensional Distance Transforms and Distance Functions .