Figure 2.13:<\/strong>
\nCorrelation based similarity – the window is shifted along the epipolar line<\/caption>\n

\n $\"Image$ <\/div>\n<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

\nThe similarity with the highest correlation is chosen. The correlation is defined as\n<\/p>\n\n

<\/p>\n\n\n

$\"$displaystyle$ <\/td>\n

\n(2.19)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

<\/p>\n\nwhere <\/p>\n\n

<\/p>\n\n\n

$\"begin{equation*}begin{aligned}sigma_l^2$ <\/td>\n<\/tr>\n<\/table>\n<\/div>\n

<\/p>\n\nare the variances of the intensity values of the left and right image and<\/p>\n\n

<\/p>\n\n\n

$\"$displaystyle$ <\/td>\n

\n(2.21)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

<\/p>\n\nis the covariance. The correlation is at its maximum if the variance is minimal and the covariance is maximal. A lower threshold $\"$$ is chosen, which decides whether the similarity is strong enough or not. Thus<\/p>\n\n

<\/p>\n\n\n

$\"$displaystyle$ <\/td>\n

\n(2.22)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

<\/p>\n\n

\nBecause correlation takes a lot of time to compute, the sum of squared difference (SSD) is often used instead. Equation 2.23<\/a> shows the equation of SSD.\n<\/p>\n\n

<\/p>\n\n\n

$\"$displaystyle$ <\/td>\n

\n(2.23)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

<\/p>\n\nIf the SSD is at its minimum, the best match has been found. In this case $\"$$ is an upper threshold and defines whether the result is small enough or not. <\/p>\n\n

<\/p>\n\n\n

$\"$displaystyle$ <\/td>\n

\n(2.24)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

<\/p>\n\n

\nIntensity differences in high contrast areas are more reliable than in low contrast areas. A possible solution is to normalize Equation 2.23<\/a> with the local variance. <\/p>\n<\/p>\n\n

<\/p>\n\n\n

$\"$displaystyle$ <\/td>\n

\n(2.25)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

<\/p>\n\n

\nAnother problem is that cameras often have different sensitivities. A solution for this problem is to normalize the image with variance and intensity. Equation 2.25<\/a> would look like\n<\/p>\n\n

<\/p>\n\n\n

$\"$displaystyle$ <\/td>\n

\n(2.26)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

<\/p>\n\n

\nSo far we assumed that we have a fixed window size $\"$$ (m $\"$$ n). The choice of $\"$$ influences the resulting disparity map. If $\"$$ is very small, many false matches can occur, especially if the images are noisy. If $\"$$ is very big, then the optimum is flattened and the computation time increases. Some approaches use adaptive window sizes to gain their results [KO94<\/a>]. After calculating disparity values for all pixels, the resulting disparity map should be convolved with a median filter so that single very unrepresentative pixel in a neighbour hood are deleted.<\/p>\n<\/p>\n\n

Next:<\/b> Phase Difference<\/a>
\n Up:<\/b> Intensity-based correspondence analysis<\/a>
\n<\/p>\n

<\/body><\/p>\n","protected":false},"excerpt":{"rendered":"