Update: 08 January 2010

High Pass Filter

This high-pass filtering operation is a linear one. This operation ( named as convolution) sets every pixel of the final image a weighted sum of some pixels of its local neighborhood. The weights (or coefficients) are contained in a kernel, which size is the actual size of the neighborhood.
This filter aims in sharpening the image by attenuating the low spatial frequencies of the image (finer details), and by keeping inchanged the highest frequencies. The low frequencies attenuation increases with the kernel size.
The following kernel coefficients are valid when the efficiency coefficient is null (i.e. maximum efficiency).

3x3 kernel coefficients

-0.018-0.135-0.018
-0.135+1.615-0.135
-0.018-0.135-0.018

5x5 kernel coefficients

-0.000-0.007-0.018-0.007-0.000
-0.007-0.135-0.368-0.135-0.007
-0.018-0.368+3.141-0.368-0.018
-0.007-0.135-0.368-0.135-0.007
-0.000-0.007-0.018-0.007-0.000

7x7 kernel coefficients

-0.000-0.000-0.001-0.002-0.001-0.000-0.000
-0.000-0.005-0.036-0.069-0.036-0.005-0.000
-0.001-0.036-0.264-0.513-0.264-0.036-0.001
-0.002-0.069-0.513+4.712-0.513-0.069-0.002
-0.001-0.036-0.264-0.513-0.264-0.036-0.001
-0.000-0.005-0.036-0.069-0.036-0.005-0.000
-0.000-0.000-0.001-0.002-0.001-0.000-0.000

9x9 kernel coefficients

-0.000-0.000-0.000-0.000-0.000-0.000-0.000-0.000-0.000
-0.000-0.000-0.002-0.007-0.011-0.007-0.002-0.000-0.000
-0.000-0.002-0.018-0.082-0.135-0.082-0.018-0.002-0.000
-0.000-0.007-0.082-0.368-0.607-0.368-0.082-0.007-0.000
-0.000-0.011-0.135-0.607+6.283-0.607-0.135-0.011-0.000
-0.000-0.007-0.082-0.368-0.607-0.368-0.082-0.007-0.000
-0.000-0.002-0.018-0.082-0.135-0.082-0.018-0.002-0.000
-0.000-0.000-0.002-0.007-0.011-0.007-0.002-0.000-0.000
-0.000-0.000-0.000-0.000-0.000-0.000-0.000-0.000-0.000