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Issue No.10 - October (2008 vol.30)
pp: 1872
Published by the IEEE Computer Society
Ke Chen , The University of Manchester, Mancheter
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:

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


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



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

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.


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:, and reference IEEECS Log Number TPAMI-2008-03-0155.

Digital Object Identifier no. 10.1109/TPAMI.2008.186.


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