PhD thesis - Institute for Computer Graphics and Vision - Graz ...

48 Chapter 4. GPU-based Depth Map Estimation using Plane Sweeping
(a) CPU generated (b) GPU generated
Figure 4.2: NCC images calculated on the CPU (left) and on the GPU (right) using
integral images.. Darker pixels indicate smaller similarity values. The image computed on
the GPU has significant deviations especially in the lower right regions.
4.2.3 Sum of Absolute Differences and Variants
The sum of absolute differences (SAD) is a widely used image similarity function because
of its simple computation, the minimal precision requirements and its high performance:
SAD = �
|Xi − Yi|,
i∈W
where W denotes the aggregation window. It is not insensitive to illumination changes,
which results in limited use of the SAD for real-world application.
Lighting changes in the scene can be incorporated by subtracting the local mean from
the original image values yielding a zero-mean sum of absolute differences (ZSAD):
ZSAD = �
|(Xi − ¯ X) − (Yi − ¯ Y )|.
i∈W
In contrast to the correlation coefficient the subtracted local means cannot be moved
outside the absolute value bars. Hence a similar technique like the shifting theorem for
the correlation coefficient is not applicable and the ZSAD is not suitable for efficient
computation. In a first step we replace the true zero-mean intensity values Xi − ¯ X resp.
Yi − ¯ Y by the differences Xi − X σ i , where Xσ is a smoothed version of the image X. X σ
is typically generated by box-filtering the original image. The same applies to Y . The