Update: 08 January 2010
Low Pass Filter
This low-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 smoothing the image by attenuating the higher spatial frequencies of the image (finer details), and by keeping inchanged the lowest frequencies. The high 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
0.011 | 0.084 | 0.011 |
0.084 | 0.619 | 0.084 |
0.011 | 0.084 | 0.011 |
5x5 kernel coefficients
0.000 | 0.002 | 0.006 | 0.002 | 0.000 |
0.002 | 0.043 | 0.117 | 0.043 | 0.002 |
0.006 | 0.117 | 0.318 | 0.117 | 0.006 |
0.002 | 0.043 | 0.117 | 0.043 | 0.002 |
0.000 | 0.002 | 0.006 | 0.002 | 0.000 |
7x7 kernel coefficients
0.000 | 0.000 | 0.000 | 0.001 | 0.000 | 0.000 | 0.000 |
0.000 | 0.001 | 0.008 | 0.014 | 0.008 | 0.001 | 0.000 |
0.000 | 0.008 | 0.056 | 0.109 | 0.056 | 0.008 | 0.000 |
0.001 | 0.014 | 0.109 | 0.212 | 0.109 | 0.014 | 0.001 |
0.000 | 0.008 | 0.056 | 0.109 | 0.056 | 0.008 | 0.000 |
0.000 | 0.001 | 0.008 | 0.014 | 0.008 | 0.001 | 0.000 |
0.000 | 0.000 | 0.000 | 0.001 | 0.000 | 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 | 0.000 | 0.001 | 0.002 | 0.001 | 0.000 | 0.000 | 0.000 |
0.000 | 0.000 | 0.003 | 0.013 | 0.022 | 0.013 | 0.003 | 0.000 | 0.000 |
0.000 | 0.001 | 0.013 | 0.059 | 0.097 | 0.059 | 0.013 | 0.001 | 0.000 |
0.000 | 0.002 | 0.022 | 0.097 | 0.159 | 0.097 | 0.022 | 0.002 | 0.000 |
0.000 | 0.001 | 0.013 | 0.059 | 0.097 | 0.059 | 0.013 | 0.001 | 0.000 |
0.000 | 0.000 | 0.003 | 0.013 | 0.022 | 0.013 | 0.003 | 0.000 | 0.000 |
0.000 | 0.000 | 0.000 | 0.001 | 0.002 | 0.001 | 0.000 | 0.000 | 0.000 |
0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |