Bilateral kernel parameter optimization by risk minimization

A statistical approach is presented for determining the optimal parameters of a bilateral filter for suppressing noise in an image. A closed-form solution to obtaining Stein´s unbiased estimate of the bilateral filter-based image estimation risk is derived. The values of the parameters are then determined by minimization of the estimated risk, which is equivalent to maximization of the estimated signal to noise ratio. Experimental results show that the method provides estimates of noise intensity that are close to the actual, and the performance of the bilateral filter, in terms of providing good tradeoff between noise suppression and edge preservation, is improved significantly by using the optimal parameters estimate.