Gaussian Smoothing

averaging the color values of neighboring pixels
The spread, i.e. the amount of smoothing/blur is determined by the standard deviation σ of the Gaussian distribution used in the process.
- scale selection: selecting the required amount of scale - less important the scale, more the smoothing
- higher the standard deviation of the distribution, less important the center pixel becomes and so more blurry the image becomes
The image is convolved with a Gaussian kernel, which is a matrix representing the Gaussian Distribution.
Each pixel in the image is replaced with a weighted average of its neighboring pixels, with the weights determined by the Gaussian kernel.
Gaussian smoothing is also decomposable
Decomposable Kernels
- symmetric kernels are decomposable into 2 linear convolutions
- if the kernel 2D matrix can be written as the outer product of 2 vectors
  - n x n = n x 1 * 1 x n
  - convolving with nxn kernel is the same as 2 convolutions with n x 1 and 1 x n kernels
  - such convolutions are computationally cheaper
    - 2n multiplications instead of n² per pixel
Link to original
g(a, b) = A exp(-(a² + b² )/2σ²) = A * (exp(-(a² )/2σ²)) * (exp(-(b² )/2σ²))

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