7.3.7 Distance Transforms, Distance Functions, Distance Measures

Chapter Contents (Back)
Symmetry. Distance Function. Thinning Techniques. Distance Transform. Distance Map. 9605

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.[Jun-Ichiro], Tanaka, M.[Masahiko], Fukumura, T.[Teruo],
A Generalized Distance Transformation of a Line Pattern with Grey Values and Its Application,
CGIP(20), No. 4, December 1982, pp. 319-346.
WWW Version. BibRef 8212
Earlier: ICPR80(35-37). BibRef

Danielsson, P.E.,
Euclidean Distance Mapping,
CGIP(14), No. 3, November 1980, pp. 227-248.
WWW Version. 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.
IEEE DOI Link 0806
BibRef
Earlier:
On Genuine Connectivity Relations Based on Logical Predicates,
CIAP07(487-492).
IEEE DOI Link 0709
2 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.
WWW Version. 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).
IEEE DOI Link 9208
probability 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. 0402
Record 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.
IEEE DOI Link 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).
IEEE DOI Link
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).
Springer DOI Link 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.[Didier], Bolon, P.[Philippe],
Discrete Distance Operator on Rectangular Grids,
PRL(16), 1995, pp. 911-923. BibRef 9500

Coquin, D.[Didier], Bolon, P.[Philippe],
Lower and Upper Bounds for Scaling Factors Used for Integer Approximation of 3D Anisotropic Chamfer Distance Operator,
DGCI09(457-468).
Springer DOI Link 0909
BibRef

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. 0401
considers 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.
IEEE DOI Link 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).
IEEE DOI Link 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.
IEEE DOI Link 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. 0301
For 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. 0409
Modification 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. 0703
Distance 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. 0709
Distance 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.
IEEE DOI Link 0606
Computes 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.
Springer DOI Link 0606
least 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. 0702
Binary 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.Q.[Xiao-Qian], 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.
Springer DOI Link 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. 0705
Weighted 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. 0711
Probabilistic distance measures; Chernoff distance; Bhattacharyya distance; Dirichlet distribution; Beta distribution BibRef

Rauber, T.W., Conci, A., Braun, T., Berns, K.,
Bhattacharyya probabilistic distance of the Dirichlet density and its application to Split-and-Merge image segmentation,
WSSIP08(145-148).
IEEE DOI Link 0806
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.
Springer DOI Link 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. 0804
Categorical 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

Gavrilova, M.L.[Marina L.], Alsuwaiyel, M.H.[Muhammad H.],
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Li, J.[Jing], Lu, B.L.[Bao-Liang],
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PR(42), No. 3, March 2009, pp. 349-357.
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Lucet, Y.[Yves],
New sequential exact Euclidean distance transform algorithms based on convex analysis,
IVC(27), No. 1-2, January 2009, pp. 37-44.
WWW Version. 0811
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A Linear Euclidean Distance Transform Algorithm Based on the Linear-Time Legendre Transform,
CRV05(262-267).
IEEE DOI Link 0505
Distance transform; Euclidean distance; Feature transform; Fast Legendre transform; Legendre-Fenchel transform; Fenchel conjugate; Moreau envelope; Moreau-Yosida approximate; Computational convex analysis BibRef


Zhou, Z.Q.A.[Zhi-Qi-Ang], Wang, B.[Bo],
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Rangarajan, A.[Anand], Gurumoorthy, K.S.[Karthik S.],
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SSVM09(100-111).
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Joken, S.[Son], Inoue, N.[Naoya], Yamashita, Y.[Yukihiko],
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Coeurjolly, D.[David],
Distance transformation, reverse distance transformation and discrete medial axis on toric spaces,
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Gupta, M.D.[Mithun Das], Huang, T.S.[Thomas S.],
Bregman distance to L1 regularized logistic regression,
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Ebrahim, Y., Ahmed, M., Chau, S.C., Abdelsalam, W.,
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Shirdhonkar, S.[Sameer], Jacobs, D.W.[David W.],
Approximate earth mover's distance in linear time,
CVPR08(1-8).
IEEE DOI Link 0806
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Memoli, F.[Facundo],
Gromov-Hausdorff distances in Euclidean spaces,
NORDIA08(1-8).
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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).
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Antón-Canalís, L.[Luis], Hernández-Tejera, M.[Mario], Sánchez-Nielsen, E.[Elena],
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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.
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Twining, C.J.[Carole J.], Taylor, C.J.,
Specificity as a Graph-Based Estimator of Cross-Entropy and KL Divergence,
BMVC06(II:59).
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Harker, M.J., O'Leary, P.L.,
First Order Geometric Distance (The Myth of Sampsonus),
BMVC06(I:87).
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CVPR06(II: 1901-1907).
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Abdi, H., O'Toole, A.J., Valentin, D., Edelman, B.,
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Schouten, T., van den Broek, E.,
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Cardenes, R., Watfield, S.K., Macias, E., Ruiz-Alzolar, J.,
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Chen, W.J.[Wei-Jun], Buhmann, J.M.[Joachim M.],
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ICIP03(I: 873-876).
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Donath, K.[Klaus], Wolf, M.[Matthias], Chrástek, R.[Radim], Niemann, H.[Heinrich],
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Signed distance functions and viscosity solutions of discontinuous Hamilton-Jacobi Equations,
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A Pseudo-Metric for Weighted Point Sets,
ECCV02(III: 715 ff.).
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Levina, E.[Elizaveta], Bickel, P.[Peter],
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ICCV01(II: 251-256).
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Gomes, J., Faugeras, O.D.,
Level Sets and Distance Functions,
ECCV00(I: 588-602).
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Cohen, S.D., Guibas, L.J.,
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ICCV99(1076-1083).
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Gustin, V.[Veselko], Lapajne, A.[Ales], Kodric, R.[Rober], Zitko, T.[Tomislav],
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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).
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Forsmoo, A.[Anders], and Borgefors, G.[Gunilla],
Parallel Distance Transform Algorithms on a General SIMD Computer,
SCIA97(xx-yy) 9705

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Baglietto, P.,
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Buchowicz, A.,
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Buchowicz, A., Pitas, I.,
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Yang, D.L.[Dyi-Long], Chen, C.H.[Chin-Hsing],
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ICPR94(C:342-344).
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Verbeek, F.J.,
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Segawa, H., Ukita, T.,
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ICPR88(II: 1225-1209).
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Mouer, E., Schaerf, R.,
New Applications of Distance Transformation Methods for Effective Structural Image Analysis,
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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 .


Last update:Nov 16, 2009 at 19:35:14