메뉴 건너뛰기




Volumn 37, Issue 3, 2009, Pages 1172-1206

Does median filtering truly preserve edges better than linear filtering?

Author keywords

Image denoising; Kernel smoothing; Linear filtering; Median filtering; Minimax estimation; Nonparametric regression; Running median

Indexed keywords


EID: 68649110508     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS604     Document Type: Article
Times cited : (213)

References (38)
  • 3
    • 1442333087 scopus 로고
    • Deterministic properties of analog median filters
    • MR1134302
    • BOTTEMA, M. J. (1991). Deterministic properties of analog median filters. IEEE Trans. Inform. Theory 37 1629-1640. MR1134302
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1629-1640
    • BOTTEMA, M.J.1
  • 4
    • 0032217844 scopus 로고    scopus 로고
    • Cycles of medians
    • MR1658177
    • BRANDT, J. (1998). Cycles of medians. Util. Math. 54 111-126. MR1658177
    • (1998) Util. Math , vol.54 , pp. 111-126
    • BRANDT, J.1
  • 5
    • 0036045688 scopus 로고    scopus 로고
    • Recovering edges in ill-posed inverse problems: Optimality of curvelet frames
    • MR1922542
    • CANDÈS, E. J. and DONOHO, D. L. (2002). Recovering edges in ill-posed inverse problems: Optimality of curvelet frames. Ann. Statist. 30 784-842. MR1922542
    • (2002) Ann. Statist , vol.30 , pp. 784-842
    • CANDÈS, E.J.1    DONOHO, D.L.2
  • 6
    • 0036045688 scopus 로고    scopus 로고
    • Recovering edges in ill-posed inverse problems: Optimality of curvelet frames
    • MR1922542
    • CANDÈS, E. J. and DONOHO, D. L. (2002). Recovering edges in ill-posed inverse problems: Optimality of curvelet frames. Ann. Statist. 30 784-842. MR1922542
    • (2002) Ann. Statist , vol.30 , pp. 784-842
    • CANDÈS, E.J.1    DONOHO, D.L.2
  • 7
    • 0032210517 scopus 로고    scopus 로고
    • Partial differential equations and mathematical morphology
    • MR1656780
    • CAO, F. (1998). Partial differential equations and mathematical morphology. J. Math. Pures Appl. 77 909-941. MR1656780
    • (1998) J. Math. Pures Appl , vol.77 , pp. 909-941
    • CAO, F.1
  • 8
    • 0033893336 scopus 로고    scopus 로고
    • Vector median filters, inf-sup operations, and coupled PDEs: Theoretical connections
    • MR1745601
    • CASELLES, V., SAPIRO, G. and CHUNG, D. H. (2000). Vector median filters, inf-sup operations, and coupled PDEs: Theoretical connections. J. Math. Imaging Vision 12 109-119. MR1745601
    • (2000) J. Math. Imaging Vision , vol.12 , pp. 109-119
    • CASELLES, V.1    SAPIRO, G.2    CHUNG, D.H.3
  • 9
    • 0033248623 scopus 로고    scopus 로고
    • Wedgelets: Nearly minimax estimation of edges
    • MR1724034
    • DONOHO, D. L. (1999). Wedgelets: Nearly minimax estimation of edges. Ann. Statist. 27859-897. MR1724034
    • (1999) Ann. Statist , vol.27 , pp. 859-897
    • DONOHO, D.L.1
  • 10
    • 0032334093 scopus 로고    scopus 로고
    • Minimax estimation via wavelet shrinkage
    • MR1635414
    • DONOHO, D. L. and JOHNSTONE, I. M. (1998). Minimax estimation via wavelet shrinkage. Ann. Statist. 26 879-921. MR1635414
    • (1998) Ann. Statist , vol.26 , pp. 879-921
    • DONOHO, D.L.1    JOHNSTONE, I.M.2
  • 12
    • 0034345319 scopus 로고    scopus 로고
    • Nonlinear pyramid transforms based on medianinterpolation
    • MR1759198
    • DONOHO, D. L. and YU, T. P.-Y. (2000). Nonlinear pyramid transforms based on medianinterpolation. SIAM J. Math. Anal. 31 1030-1061. MR1759198
    • (2000) SIAM J. Math. Anal , vol.31 , pp. 1030-1061
    • DONOHO, D.L.1    YU, T.P.-Y.2
  • 13
    • 21844482638 scopus 로고
    • On curve estimation by minimizing mean absolute deviation and its implications
    • MR1292544
    • FAN, J. and HALL, P. (1994). On curve estimation by minimizing mean absolute deviation and its implications. Ann. Statist. 22 867-885. MR1292544
    • (1994) Ann. Statist , vol.22 , pp. 867-885
    • FAN, J.1    HALL, P.2
  • 15
    • 68649089160 scopus 로고    scopus 로고
    • GUICHARD, F. and MOREL, J.-M. (1997). Partial differential equations and image iterative filtering. In The State of the Art in Numerical Analysis (York, 1996). Inst. Math. Appl. Conf. Ser. New Ser. 63 525-562. Oxford Univ. Press, New York. MR1628359
    • GUICHARD, F. and MOREL, J.-M. (1997). Partial differential equations and image iterative filtering. In The State of the Art in Numerical Analysis (York, 1996). Inst. Math. Appl. Conf. Ser. New Ser. 63 525-562. Oxford Univ. Press, New York. MR1628359
  • 16
    • 0034860229 scopus 로고    scopus 로고
    • GUPTA, M. and CHEN, T. (2001). Vector color filter array demosaicing. In Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications. II (M. B. J. C. N. Sampat, ed.). Proceedings of the SPIE 4306 374-382. SPIE, Bellingham, WA.
    • GUPTA, M. and CHEN, T. (2001). Vector color filter array demosaicing. In Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications. II (M. B. J. C. N. Sampat, ed.). Proceedings of the SPIE 4306 374-382. SPIE, Bellingham, WA.
  • 18
    • 0003157339 scopus 로고
    • Robust estimation of a location parameter
    • MR0161415
    • HUBER, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Statist. 35 73-101. MR0161415
    • (1964) Ann. Math. Statist , vol.35 , pp. 73-101
    • HUBER, P.J.1
  • 19
    • 0019367783 scopus 로고    scopus 로고
    • JUSTUSSON, B. (1981). Median filtering: Statistical properties. In Two-Dimensional Digital Signal Processing. II (T. S. Huang, ed.). Topics in Applied Physics 43 161-196. Springer, Berlin. MR0688317
    • JUSTUSSON, B. (1981). Median filtering: Statistical properties. In Two-Dimensional Digital Signal Processing. II (T. S. Huang, ed.). Topics in Applied Physics 43 161-196. Springer, Berlin. MR0688317
  • 20
    • 0030364565 scopus 로고    scopus 로고
    • On the asymptotic performance of median smoothers in image analysis and nonparametric regression
    • MR1416654
    • KOCH, I. (1996). On the asymptotic performance of median smoothers in image analysis and nonparametric regression. Ann. Statist. 24 1648-1666. MR1416654
    • (1996) Ann. Statist , vol.24 , pp. 1648-1666
    • KOCH, I.1
  • 22
    • 68649110172 scopus 로고    scopus 로고
    • MALLOWS, C. L. (1979). Some theoretical results on Tukey's 3R smoother. In Smoothing Techniques for Curve Estimation (Proc. Workshop, Heidelberg, 1979). Lecture Notes in Math. 757 77-90. Springer, Berlin. MR0564253
    • MALLOWS, C. L. (1979). Some theoretical results on Tukey's 3R smoother. In Smoothing Techniques for Curve Estimation (Proc. Workshop, Heidelberg, 1979). Lecture Notes in Math. 757 77-90. Springer, Berlin. MR0564253
  • 23
    • 67650425421 scopus 로고
    • 2(0, 1)
    • MR0723743
    • 2(0, 1). Ann. Probab. 12 243-255. MR0723743
    • (1984) Ann. Probab , vol.12 , pp. 243-255
    • MASON, D.M.1
  • 24
    • 68649117777 scopus 로고    scopus 로고
    • MATHERON, G. (1975). Random Sets and Integral Geometry. Wiley, New York. MR0385969
    • MATHERON, G. (1975). Random Sets and Integral Geometry. Wiley, New York. MR0385969
  • 25
    • 84869722624 scopus 로고    scopus 로고
    • MOREL, J.-M. and SOLIMINI, S. (1995). Variational Methods in Image Segmentation. Birkhäuser Boston, Boston, MA. MR1321598
    • MOREL, J.-M. and SOLIMINI, S. (1995). Variational Methods in Image Segmentation. Birkhäuser Boston, Boston, MA. MR1321598
  • 26
    • 84990602490 scopus 로고
    • Optimal approximations by piecewise smooth functions and associated variational problems
    • MR0997568
    • MUMFORD, D. and SHAH, J. (1989). Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42 577-685. MR0997568
    • (1989) Comm. Pure Appl. Math , vol.42 , pp. 577-685
    • MUMFORD, D.1    SHAH, J.2
  • 27
    • 0025465145 scopus 로고
    • Scale-space and edge detection using anisotropic diffusion
    • PERONA, P. and MALIK, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12 629-639.
    • (1990) IEEE Trans. Pattern Anal. Mach. Intell , vol.12 , pp. 629-639
    • PERONA, P.1    MALIK, J.2
  • 28
    • 85040499916 scopus 로고
    • Median filtering of random processes
    • MR0776767
    • PITERBARG, L. I. (1984). Median filtering of random processes. Problemy Peredachi Informatsii 20 65-73. MR0776767
    • (1984) Problemy Peredachi Informatsii , vol.20 , pp. 65-73
    • PITERBARG, L.I.1
  • 29
    • 0002365998 scopus 로고
    • The remedian: A robust averaging method for large data sets
    • MR1137355
    • ROUSSEEUW, P. J. and BASSETT, G. W. JR. (1990). The remedian: A robust averaging method for large data sets. J. Amer. Statist. Assoc. 85 97-104. MR1137355
    • (1990) J. Amer. Statist. Assoc , vol.85 , pp. 97-104
    • ROUSSEEUW, P.J.1    BASSETT JR., G.W.2
  • 30
    • 0002365998 scopus 로고
    • The remedian: A robust averaging method for large data sets
    • MR1137355
    • ROUSSEEUW, P. J. and BASSETT, G. W. JR. (1990). The remedian: A robust averaging method for large data sets. J. Amer. Statist. Assoc. 85 97-104. MR1137355
    • (1990) J. Amer. Statist. Assoc , vol.85 , pp. 97-104
    • ROUSSEEUW, P.J.1    BASSETT JR., G.W.2
  • 31
    • 68649122743 scopus 로고    scopus 로고
    • SAPIRO, G. (2001). Geometric Partial Differential Equations and Image Analysis. Cambridge Univ. Press, Cambridge. MR1813971
    • SAPIRO, G. (2001). Geometric Partial Differential Equations and Image Analysis. Cambridge Univ. Press, Cambridge. MR1813971
  • 32
    • 0000404069 scopus 로고
    • Quasiconformal mappings and chord-arc curves
    • MR0927689
    • SEMMES, S. W. (1988). Quasiconformal mappings and chord-arc curves. Trans. Amer. Math. Soc. 306 233-263. MR0927689
    • (1988) Trans. Amer. Math. Soc , vol.306 , pp. 233-263
    • SEMMES, S.W.1
  • 33
    • 68649087983 scopus 로고    scopus 로고
    • SERRA, J. (1982). Image Analysis and Mathematical Morphology. Academic Press, London. MR0753649
    • SERRA, J. (1982). Image Analysis and Mathematical Morphology. Academic Press, London. MR0753649
  • 34
    • 68649109960 scopus 로고    scopus 로고
    • SETHIAN, J. A. (1999). Level Set Methods and Fast Marching Methods, 2nd ed. Cambridge Monographs on Applied and Computational Mathematics 3. Cambridge Univ. Press, Cambridge. MR1700751
    • SETHIAN, J. A. (1999). Level Set Methods and Fast Marching Methods, 2nd ed. Cambridge Monographs on Applied and Computational Mathematics 3. Cambridge Univ. Press, Cambridge. MR1700751
  • 35
    • 68649108045 scopus 로고    scopus 로고
    • SHORACK, G. R. and WELLNER, J. A. (1986). Empirical Processes with Aplications to Statistics. Wiley, New York. MR0838963
    • SHORACK, G. R. and WELLNER, J. A. (1986). Empirical Processes with Aplications to Statistics. Wiley, New York. MR0838963


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.