메뉴 건너뛰기




Volumn 27, Issue 1-2, 2009, Pages 37-44

New sequential exact Euclidean distance transform algorithms based on convex analysis

Author keywords

Computational convex analysis; Distance transform; Euclidean distance; Fast Legendre transform; Feature transform; Fenchel conjugate; Legendre Fenchel transform; Moreau envelope; Moreau Yosida approximate

Indexed keywords

COMPUTATIONAL CONVEX ANALYSIS; DISTANCE TRANSFORM; EUCLIDEAN DISTANCE; FAST LEGENDRE TRANSFORM; FEATURE TRANSFORM; FENCHEL CONJUGATE; LEGENDRE-FENCHEL TRANSFORM; MOREAU ENVELOPE; MOREAU-YOSIDA APPROXIMATE;

EID: 54549090988     PISSN: 02628856     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.imavis.2006.10.011     Document Type: Article
Times cited : (29)

References (43)
  • 1
    • 84943347235 scopus 로고
    • Sequential operations in digital picture processing
    • Rosenfeld A., and Pfaltz J.L. Sequential operations in digital picture processing. J. ACM 13 4 (1966) 471-494
    • (1966) J. ACM , vol.13 , Issue.4 , pp. 471-494
    • Rosenfeld, A.1    Pfaltz, J.L.2
  • 2
    • 0019229539 scopus 로고    scopus 로고
    • P.-E. Danielsson, Euclidean distance mapping, Comput. Graph. Image Process. 14 (1980) 227-248.
    • P.-E. Danielsson, Euclidean distance mapping, Comput. Graph. Image Process. 14 (1980) 227-248.
  • 3
    • 0022927138 scopus 로고
    • Distance transformations in digital images
    • Borgefors G. Distance transformations in digital images. Comput. Vis. Graph. Image Process. 34 3 (1986) 344-371
    • (1986) Comput. Vis. Graph. Image Process. , vol.34 , Issue.3 , pp. 344-371
    • Borgefors, G.1
  • 4
    • 0024486272 scopus 로고
    • Distance transformations on hexagonal grids
    • Borgefors G. Distance transformations on hexagonal grids. PRL 9 (1989) 97-105
    • (1989) PRL , vol.9 , pp. 97-105
    • Borgefors, G.1
  • 5
    • 85000328579 scopus 로고    scopus 로고
    • O. Cuisenaire, Distance transformations: fast algorithms and applications to medical image processing, Ph.D. thesis, Université Catholique de Louvain, Louvain-la-Neuve, Belgium (Oct. 1999).
    • O. Cuisenaire, Distance transformations: fast algorithms and applications to medical image processing, Ph.D. thesis, Université Catholique de Louvain, Louvain-la-Neuve, Belgium (Oct. 1999).
  • 6
    • 85000284043 scopus 로고    scopus 로고
    • J. Toriwaki, K. Mori, Distance transformation and skeletonization of 3d pictures and their applications to medical images, in: R.K.E.G. Bertrand, A. Imiya (Eds.), Digital and Image Geometry: Advanced Lectures, Lecture Notes in Computer Science, vol. 2243/2001, Springer-Verlag Heidelberg, 2001, pp. 412-429.
    • J. Toriwaki, K. Mori, Distance transformation and skeletonization of 3d pictures and their applications to medical images, in: R.K.E.G. Bertrand, A. Imiya (Eds.), Digital and Image Geometry: Advanced Lectures, Lecture Notes in Computer Science, vol. 2243/2001, Springer-Verlag Heidelberg, 2001, pp. 412-429.
  • 7
    • 0036450711 scopus 로고    scopus 로고
    • S. Prohaska, H.C. Hege, Fast visualization of plane-like structures in voxel data, in: VIS '02: Proceedings of the Conference on Visualization '02, IEEE Computer Society, Boston, MA, 2002, pp. 29-36..
    • S. Prohaska, H.C. Hege, Fast visualization of plane-like structures in voxel data, in: VIS '02: Proceedings of the Conference on Visualization '02, IEEE Computer Society, Boston, MA, 2002, pp. 29-36..
  • 9
    • 0028467461 scopus 로고
    • A fast algorithm for Euclidean distance maps of a 2-d binary image
    • Chen L., and Chuang H.Y.H. A fast algorithm for Euclidean distance maps of a 2-d binary image. Inform. Process. Lett. 51 1 (1994) 25-29
    • (1994) Inform. Process. Lett. , vol.51 , Issue.1 , pp. 25-29
    • Chen, L.1    Chuang, H.Y.H.2
  • 10
    • 0037325736 scopus 로고    scopus 로고
    • A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions
    • Maurer Jr. C.R., Qi R., and Raghavan V.V. A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions. IEEE Trans. Pattern Anal. Mach. Intell. 25 2 (2003) 265-270
    • (2003) IEEE Trans. Pattern Anal. Mach. Intell. , vol.25 , Issue.2 , pp. 265-270
    • Maurer Jr., C.R.1    Qi, R.2    Raghavan, V.V.3
  • 11
    • 0742304570 scopus 로고    scopus 로고
    • Fast Euclidean distance transformation in two scans using a 3 × 3 neighborhood
    • Shih F.Y., and Wu Y.-T. Fast Euclidean distance transformation in two scans using a 3 × 3 neighborhood. Comput. Vis. Image Underst. 93 2 (2004) 195-205
    • (2004) Comput. Vis. Image Underst. , vol.93 , Issue.2 , pp. 195-205
    • Shih, F.Y.1    Wu, Y.-T.2
  • 12
    • 85000280588 scopus 로고    scopus 로고
    • L. Deniau, J. Blanc-Talon, Fractal analysis with Hausdorff distance under affine transformations, Tech. rep., ETCA-CREA-SP (1995).
    • L. Deniau, J. Blanc-Talon, Fractal analysis with Hausdorff distance under affine transformations, Tech. rep., ETCA-CREA-SP (1995).
  • 13
    • 85000301035 scopus 로고    scopus 로고
    • P.F. Felzenszwalb, D.P. Huttenlocher, Distance transforms of sampled functions, Tech. Rep. TR2004-1963, Cornell Computing and Information Science (Sep. 2004).
    • P.F. Felzenszwalb, D.P. Huttenlocher, Distance transforms of sampled functions, Tech. Rep. TR2004-1963, Cornell Computing and Information Science (Sep. 2004).
  • 14
    • 85000302994 scopus 로고    scopus 로고
    • M. Gavrilova, M.H. Alsuwaiyel, Two algorithms for computing the Euclidean distance transform, Tech. Rep. 2000-661-13, Computer Science Technical Reports, University of Calgary (2000).
    • M. Gavrilova, M.H. Alsuwaiyel, Two algorithms for computing the Euclidean distance transform, Tech. Rep. 2000-661-13, Computer Science Technical Reports, University of Calgary (2000).
  • 15
    • 0032629760 scopus 로고    scopus 로고
    • O. Cuisenaire, B. Macq, Fast and exact signed Euclidean distance transformation with linear complexity, in: Proc. of ICASSP'99, vol. 6, IEEE, Phoenix, AZ, USA, 1999, pp. 3293-3296, Int. Conference on Acoustics, Speech and Signal Processing.
    • O. Cuisenaire, B. Macq, Fast and exact signed Euclidean distance transformation with linear complexity, in: Proc. of ICASSP'99, vol. 6, IEEE, Phoenix, AZ, USA, 1999, pp. 3293-3296, Int. Conference on Acoustics, Speech and Signal Processing.
  • 16
    • 35048869565 scopus 로고    scopus 로고
    • D.G. Bailey, An efficient Euclidean distance transform, in: R. Klette, J. Žunić (Eds.), Combinatorial Image Analysis: 10th International Workshop, IWCIA 2004, Auckland, New Zealand, December 1-3, 2004. Proceedings, Lecture Notes in Computer Science, vol. 3322, Springer-Verlag GmbH, 2004, pp. 394-408.
    • D.G. Bailey, An efficient Euclidean distance transform, in: R. Klette, J. Žunić (Eds.), Combinatorial Image Analysis: 10th International Workshop, IWCIA 2004, Auckland, New Zealand, December 1-3, 2004. Proceedings, Lecture Notes in Computer Science, vol. 3322, Springer-Verlag GmbH, 2004, pp. 394-408.
  • 17
    • 85000302993 scopus 로고    scopus 로고
    • W. Hesselink, A linear-time algorithm for euclidean feature transform sets, http://www.cs.rug.nl/~wim/pub/mans.html/ (May 2005).
    • W. Hesselink, A linear-time algorithm for euclidean feature transform sets, http://www.cs.rug.nl/~wim/pub/mans.html/ (May 2005).
  • 18
    • 85000252223 scopus 로고    scopus 로고
    • S. Mauch, A fast algorithm for computing the closest point and distance transform, http://www.acm.caltech.edu/seanm/projects/cpt/cpt.pdf/ (Dec. 2000).
    • S. Mauch, A fast algorithm for computing the closest point and distance transform, http://www.acm.caltech.edu/seanm/projects/cpt/cpt.pdf/ (Dec. 2000).
  • 19
    • 0242424279 scopus 로고    scopus 로고
    • C. Sigg, R. Peikert, M. Gross, Signed distance transform using graphics hardware, in: Proceedings of IEEE Visualization '03, ETH Zürich, 2003.
    • C. Sigg, R. Peikert, M. Gross, Signed distance transform using graphics hardware, in: Proceedings of IEEE Visualization '03, ETH Zürich, 2003.
  • 20
    • 85000252221 scopus 로고    scopus 로고
    • Y. Lucet, Fast Moreau envelope computation I: Numerical algorithms, Tech. rep., University of British Columbia Okanagan (2005).
    • Y. Lucet, Fast Moreau envelope computation I: Numerical algorithms, Tech. rep., University of British Columbia Okanagan (2005).
  • 22
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, New york
    • Rockafellar R.T. Convex Analysis (1970), Princeton University Press, Princeton, New york
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 23
    • 85000331684 scopus 로고    scopus 로고
    • J.-B. Hiriart-Urruty, C. Lemaréchal, Convex Analysis and Minimization Algorithms, vol. 305-306 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 1993, vol I: Fundamentals, vol II: Advanced theory and bundle methods.
    • J.-B. Hiriart-Urruty, C. Lemaréchal, Convex Analysis and Minimization Algorithms, vol. 305-306 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 1993, vol I: Fundamentals, vol II: Advanced theory and bundle methods.
  • 24
    • 85000252226 scopus 로고    scopus 로고
    • K. Yosida, Functional analysis, Classics in Mathematics, Springer-Verlag, Berlin, 1995, reprint of the sixth (1980) edition.
    • K. Yosida, Functional analysis, Classics in Mathematics, Springer-Verlag, Berlin, 1995, reprint of the sixth (1980) edition.
  • 25
    • 1942434208 scopus 로고
    • Propriétés des applications "prox"
    • Moreau J.-J. Propriétés des applications "prox". C. R. Acad. Sci. Paris 256 (1963) 1069-1071
    • (1963) C. R. Acad. Sci. Paris , vol.256 , pp. 1069-1071
    • Moreau, J.-J.1
  • 26
    • 0000276924 scopus 로고
    • Proximité et dualité dans un espace Hilbertien
    • Moreau J.-J. Proximité et dualité dans un espace Hilbertien. Bull. Soc. Math. France 93 (1965) 273-299
    • (1965) Bull. Soc. Math. France , vol.93 , pp. 273-299
    • Moreau, J.-J.1
  • 28
    • 0001355283 scopus 로고
    • Un algorithme rapide pour le calcul de transformées de Legendre-Fenchel discrètes
    • Brenier Y. Un algorithme rapide pour le calcul de transformées de Legendre-Fenchel discrètes. C. R. Acad. Sci. Paris Sér. I Math. 308 (1989) 587-589
    • (1989) C. R. Acad. Sci. Paris Sér. I Math. , vol.308 , pp. 587-589
    • Brenier, Y.1
  • 29
    • 0000759411 scopus 로고    scopus 로고
    • Fast Legendre-Fenchel transform and applications to Hamilton-Jacobi equations and conservation laws
    • Corrias L. Fast Legendre-Fenchel transform and applications to Hamilton-Jacobi equations and conservation laws. SIAM J. Numer. Anal. 33 4 (1996) 1534-1558
    • (1996) SIAM J. Numer. Anal. , vol.33 , Issue.4 , pp. 1534-1558
    • Corrias, L.1
  • 30
    • 0030197212 scopus 로고    scopus 로고
    • A fast computational algorithm for the Legendre-Fenchel transform
    • Lucet Y. A fast computational algorithm for the Legendre-Fenchel transform. Comput. Optimizat. Appl. 6 1 (1996) 27-57
    • (1996) Comput. Optimizat. Appl. , vol.6 , Issue.1 , pp. 27-57
    • Lucet, Y.1
  • 31
    • 0028513617 scopus 로고
    • A fast Legendre transform algorithm and applications to the adhesion model
    • Noullez A., and Vergassola M. A fast Legendre transform algorithm and applications to the adhesion model. J. Scient. Comput. 9 3 (1994) 259-281
    • (1994) J. Scient. Comput. , vol.9 , Issue.3 , pp. 259-281
    • Noullez, A.1    Vergassola, M.2
  • 32
    • 6644224525 scopus 로고
    • The inviscid Burgers equation with initial data of brownian type
    • She Z.-S., Aurell E., and Frisch U. The inviscid Burgers equation with initial data of brownian type. Comm. Math. Phys. 148 3 (1992) 623-641
    • (1992) Comm. Math. Phys. , vol.148 , Issue.3 , pp. 623-641
    • She, Z.-S.1    Aurell, E.2    Frisch, U.3
  • 33
    • 0004879867 scopus 로고    scopus 로고
    • Faster than the fast legendre transform, the linear-time legendre transform
    • Lucet Y. Faster than the fast legendre transform, the linear-time legendre transform. Numer. Algorithms 16 2 (1997) 171-185
    • (1997) Numer. Algorithms , vol.16 , Issue.2 , pp. 171-185
    • Lucet, Y.1
  • 35
    • 0002447660 scopus 로고    scopus 로고
    • Burgulence
    • Lesieur A.M., and David E.F. (Eds), Springer EDP-Sciences
    • Frisch U., and Bec J. Burgulence. In: Lesieur A.M., and David E.F. (Eds). Les Houches 2000: New Trends in Turbulence (2001), Springer EDP-Sciences 341-383
    • (2001) Les Houches 2000: New Trends in Turbulence , pp. 341-383
    • Frisch, U.1    Bec, J.2
  • 36
    • 0035872959 scopus 로고    scopus 로고
    • Singularities and the distribution of density in the Burgers/adhesion model
    • Frisch U., Bec J., and Villone B. Singularities and the distribution of density in the Burgers/adhesion model. Phys. D 152-153 (2001) 620-635
    • (2001) Phys. D , vol.152-153 , pp. 620-635
    • Frisch, U.1    Bec, J.2    Villone, B.3
  • 37
    • 85000266647 scopus 로고    scopus 로고
    • A. Noullez, S.N. Gurbatov, E. Aurell, S.I. Simdyankin, The global picture of self-similar and not self-similar decay in Burgers turbulence, Tech. Rep. nlin.CD/0409022, arXiv.org eprint archive (Sep. 2004).
    • A. Noullez, S.N. Gurbatov, E. Aurell, S.I. Simdyankin, The global picture of self-similar and not self-similar decay in Burgers turbulence, Tech. Rep. nlin.CD/0409022, arXiv.org eprint archive (Sep. 2004).
  • 38
    • 85000266645 scopus 로고    scopus 로고
    • B. Koopen, Contact of bodies in 2D-space: Implementing the Discrete Legendre Transform, AI Master's thesis, Intelligent Autonomous Systems Group, University of Amsterdam (Feb. 2002).
    • B. Koopen, Contact of bodies in 2D-space: Implementing the Discrete Legendre Transform, AI Master's thesis, Intelligent Autonomous Systems Group, University of Amsterdam (Feb. 2002).
  • 39
    • 0038420934 scopus 로고    scopus 로고
    • T. Hisakado, K. Okumura, V. Vukadinovic, L. Trajkovic, Characterization of a simple communication network using Legendre transform, in: Proc. IEEE Int. Symp. Circuits and Systems, vol. 3, 2003, pp. 738-741.
    • T. Hisakado, K. Okumura, V. Vukadinovic, L. Trajkovic, Characterization of a simple communication network using Legendre transform, in: Proc. IEEE Int. Symp. Circuits and Systems, vol. 3, 2003, pp. 738-741.
  • 40
    • 84938566904 scopus 로고    scopus 로고
    • A linear Euclidean distance transform algorithm based on the Linear-time Legendre Transform
    • IEEE Computer Society Press, Victoria BC
    • Lucet Y. A linear Euclidean distance transform algorithm based on the Linear-time Legendre Transform. Proceedings of the Second Canadian Conference on Computer and Robot Vision (CRV 2005) (2005), IEEE Computer Society Press, Victoria BC
    • (2005) Proceedings of the Second Canadian Conference on Computer and Robot Vision (CRV 2005)
    • Lucet, Y.1
  • 41
    • 85000341823 scopus 로고    scopus 로고
    • P. Helluy, Simulation numérique des écoulements multiphasiques : De la théorie aux applications, Ph.D. thesis, Institut des Sciences de l'Ingenieur de Toulon et du Var, Laboratoire Modélisation Numérique et Couplages, BP 56, 83162 La Valette CEDEX, France, habilitation à Diriger des Recherches (Jan. 2005).
    • P. Helluy, Simulation numérique des écoulements multiphasiques : De la théorie aux applications, Ph.D. thesis, Institut des Sciences de l'Ingenieur de Toulon et du Var, Laboratoire Modélisation Numérique et Couplages, BP 56, 83162 La Valette CEDEX, France, habilitation à Diriger des Recherches (Jan. 2005).
  • 42
    • 23744515749 scopus 로고    scopus 로고
    • Variability of the Lagrangian turbulent diffusion in the lower stratosphere
    • Legras B., Pisso I., Berthet G., and Lefvre F. Variability of the Lagrangian turbulent diffusion in the lower stratosphere. Atmospheric Chem. Phys. 5 (2005) 1605-1622
    • (2005) Atmospheric Chem. Phys. , vol.5 , pp. 1605-1622
    • Legras, B.1    Pisso, I.2    Berthet, G.3    Lefvre, F.4
  • 43
    • 85000302020 scopus 로고    scopus 로고
    • R. Fabbri, Scilab image processing toolbox, 2005. http://siptoolbox.sourceforge.net/.
    • R. Fabbri, Scilab image processing toolbox, 2005. http://siptoolbox.sourceforge.net/.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.