Gaussian blur
From Biocrawler, the free encyclopedia.
Gaussian blur is a widely used effect in graphics software such as Adobe Photoshop or The GIMP.
The gaussian blur is just the natural blur situation expressed in mathematic fomula. The equation of gaussian blur is
- Gr = e -[r/σ] ² / 2 / √(2πσ)
where r is the distance to the center. In fact, this is just a planar gaussian distribution concentric circles.
In practice, being relatively low value outside 3 * σ, program usually calculates effects only within 3 * σ distance, i.e., use only a
- [2 * ( 3 * σ ) + 1] * [2 * ( 3 * σ ) + 1];
two dimemsional array.
Apply the gaussian blur matrix which represent the intensity distribution to original photo will get a good smooth blurred photo.
The normalized matrix with σ = 1 is
- 0.00000067 0.00002292 0.00019117 0.00038771 0.00019117 0.00002292 0.00000067
- 0.00002292 0.00078633 0.00655965 0.01330373 0.00655965 0.00078633 0.00002292
- 0.00019117 0.00655965 0.05472157 0.11098164 0.05472157 0.00655965 0.00019117
- 0.00038771 0.01330373 0.11098164 0.22508352 0.11098164 0.01330373 0.00038771
- 0.00019117 0.00655965 0.05472157 0.11098164 0.05472157 0.00655965 0.00019117
- 0.00002292 0.00078633 0.00655965 0.01330373 0.00655965 0.00078633 0.00002292
- 0.00000067 0.00002292 0.00019117 0.00038771 0.00019117 0.00002292 0.00000067
Note that 0.22508352 (the central one) is 1177 times larger than 0.00019117 which is just outside 3 * σ.
The following 2 images show the effect of gaussian blur: Img. 2 is blurred by gaussian blur with σ = 2 from Img.1.
 Img. 1 The original  Img. 2 The blurred image |
