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Fast Correlation

 

Barnea and Silverman [5] introduced a class of sequential algorithms for fast image registration. They were designed to reduce computation in matching procedures using minimum dissimilarity measures like the sum of the absolute differences (SAD). Konecny and Pape [6] reviewed image correlation techniques according to photogrammetric and mathematical fundamentals.

Different similarity measures have been used in the literature [7, 8], and their performance and computation cost vary. It has also been shown that the zero mean normalized cross correlation and the zero mean sum of squared differences tend to give better results [9]. We will use the zero mean normalized cross-correlation (ZNCC) coefficient as the similarity measure of the candidate matching areas. The estimate is independent of differences in brightness and contrast due to the normalization with respect to mean and standard deviation.

Let tex2html_wrap_inline656 be the intensity value of an tex2html_wrap_inline658 image f at position (m,n), where f is to be box filtered into tex2html_wrap_inline666 , i.e. obtaining the mean of the original image within the box. We also have similar definition for a second image g. The normalized cross-correlation of two windows can be written as follows:

  equation112

where

  equation119

  equation131

equation141

and d is the shift along epipolar lines; K and L define the correlation window size. It can be seen from this equation that the co-variance between f and g and the variances of f and g at different positions in the image need to be evaluated.





Changming Sun
Wed Dec 31 11:53:12 EST 1997