# Binomial Filter

Difference with Gaussian Filter?

Gaussian is perfectly radial and isotropic, while a binomial filter has more “rectangular” response, filtering less of the diagonals.

A binomial filter approximates a gaussian distribution.

Binomial Filter

- Performs a smoothing
- Smoothing using an approximation of a Gaussian as the kernel function
- Discrete approximation due to pixels
- The decay of the weights approximates a Gaussian using the coefficients of a Binomial distribution $B(0.5,n)$
- Elements of the Pascal’s triangle

So when you apply a gaussian blur, it’s just applying the Binomial Kernel.

Degree of smoothing

- Box filter offers a stronger smoothing than the binomial filter.