Erratum to "Adaptive Smoothing via Contextual and Local Discontinuities"
OCTOBER 2008 (Vol. 30, No. 10) pp. 1872
0162-8828/08/$31.00 © 2008 IEEE

Published by the IEEE Computer Society
Erratum to "Adaptive Smoothing via Contextual and Local Discontinuities"
Ke Chen
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The author of the paper "Adaptive Smoothing via Contextual and Local Discontinuities," which appeared in the IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 10, pp. 1552-1567, Oct. 2005, would like to point out that equation (9) on page 1555 in [ 1 ] should have been read as follows:


$$\eqalign{&D^+_{xy;ij} =\cr& \sum_{{(v,w) \in {\cal N} _{xy;ij}(x,y)\atop(v',w') \in {\cal N} _{xy;ij}(i,j)\atop s.t. x\!-\!v=i\!-\!v', y\!-\!w=j\!-\!w'}}\cr&\bigg [1 - \exp \bigg (\! -\! { {(d^+_{vw;v'w'})^2}\over{2\sigma_u^2}} \bigg ) \bigg ] \exp \bigg (\! -\! { {d_{xy;vw}^2}\over{2R_{xy;ij}^2}} \bigg ),}$$


(9a)





$$\eqalign{&D^-_{xy;ij} =\cr& \sum_{{(v,w) \in {\cal N} _{xy;ij}(x,y)\atop(v',w') \in {\cal N} _{xy;ij}(i,j)\atop s.t. x\!-\!v=i\!-\!v', y\!-\!w=j\!-\!w' }}\cr&\bigg [1 - \exp \bigg ( \!-\! { {(d^-_{vw;v'w'})^2}\over{2\sigma_u^2}} \bigg ) \bigg ] \exp \bigg (\! -\! { {d_{xy;vw}^2}\over{2R_{xy;ij}^2}} \bigg ),}$$


(9b)



where


$$\eqalign{&d^2_{xy;vw} = (x-v)^2 + (y-w)^2,\cr &d^+_{vw;v'w'} = \left\{\matrix{I_{(v,w)} - I_{(v',w')},& {\rm if}\;I_{(v,w)} - I_{(v',w')} > 0,\hfill\cr 0,\hfill&{\rm otherwise.}\hfill}\right.\cr &d^-_{vw;v'w'} = \left\{\matrix{I_{(v,w)} - I_{(v',w')},& {\rm if}\;I_{(v,w)} - I_{(v',w')} < 0,\cr 0,\hfill&{\rm otherwise.}\hfill}\right.}$$


The author is grateful to X. Hu for finding the typo by comparing the author's source code with the algorithm description in [ 1 ].

    The author is with the School of Computer Science, The University of Manchester, Manchester M13 9PL, UK.

    E-mail: chen@cs.manchester.ac.uk.

Manuscript received 18 Mar. 2008; accepted 15 July 2008.

Recommended for acceptance by Z. Ghahramani.

For information on obtaining reprints of this article, please send e-mail to: tpami@computer.org, and reference IEEECS Log Number TPAMI-2008-03-0155.

Digital Object Identifier no. 10.1109/TPAMI.2008.186.

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