Comparing image regions

Image regions are typically compared using sum-of-square-differences (SSD) or normalized cross-correlation (NCC). Consider a window $W$ in image $I$ and a corresponding region ${\bf T}(W)$ in image $J$. The dissimilarity between two image regions based on SSD is given by

$$D=\int \int_W \left[ J({\bf T}(x,y)) -I(x,y)\right]^2 w(x,y) dx dy$$ (D1)

where $w(x,y)$ is a weighting function that is defined over W. Typically, $w(x,y)=1$ or it is a Gaussian. The similarity measure between two image regions based on NCC is given by

$$S=\frac{\int \int_W (J({\bf T}(x,y))-\bar{J}). (I(x,y)-\bar... ...d x d y}. \sqrt{\int \int_W (I(x,y)-\bar{I}) w(x,y) d x d y}}$$ (D2)

with $\bar{J}=\int \int_W J(T(x,y)) dx dy$ and $\bar{I}=\int \int_W I(x,y) dx dy$ the mean image intensity in the considered region. Note that this last measure is invariant to global intensity and contrast changes over the considered regions.