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filtered 19.05.2009 5x5
filtered Dr. Pierre Elbischger - MIP1/ISAP'SS09 48 Rotating mask filter
Reduce the blurring on edges as it is the case in low-pass filtering
Idea: Search for the most homogeneous neighborhood and use this region to compute the gray
value for the pixel of interest.
Use the variance of the gray values in the mask for the homogeneous criteria. Algorithm 1) Place the mask with every possible position over the pixel of interest
2) Compute the variance using the current neighborhood
3) Choose the mask that gives the smallest variance 4) The pixel of interest is assigned to the mean gray value of the neighborhood
determined by the mask 1 19.05.2009 2 ... 7 Dr. Pierre Elbischger - MIP1/ISAP'SS09 8 9 49 E46 T9 Adaptive mean filter (1)
Make the filtering dependent on the local image structure in a way that discontinuities are better
preserved. Mean under
the mask Current gray value Variance under the
mask Variance of the
if no a priori information
about the noise is available
use the following estimate: Nb, Mb … size of the neighborhood
… size of the image In the case of a local variance that is below the expected noise
variance (e.g., in quite homogeneous regions), the quotient is
approximately ‘0’ and the pixel value in the output image is replaced
by the mean of the neighborhood. blending between the
two extreme states At locations with large local variance, an important object structure is assumed (e.g., edges). The
quotient becomes ‘1’ and, thus, the original image data is preserved.
19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 50 E15 Adaptive mean filter (2) Corrupted by Gaussian
variance=1000 original Mean filter Adaptive Filter (7x7 window) (7x7) 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 51 Degradation functions
Motion blur H ( u, v ) = sin (π (VxTu + VyTv) ) π (Vx u + Vy v) e − jπ (VxTu +VyTv ) a = VT moved distance
V moving velocity
T moving duration Atmospheric turbulences Out of focus H ( u, v ) = J1 ( ar )
r= u 2 + v 2
J1 1. orde...
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- Spring '09