An Extension to a Filter Implementation of a Local Quadratic Surface for Image Noise Estimation

Based on regression analysis this paper gives a description for simple image filter design. Specifically 3 3 filter implementations of a quadratic surface, residuals from this surface, gradients and the Laplacian are given. For the residual a 5 5 filter is given also. It is shown that the 3 3 filter for the residual gives low values for horizontal and vertical lines and edges as opposed to diagonal ones. Therefore an extension including a rotated version of the filter for the residual to ensure low values for lines and edges in all directions is suggested. It is also shown that the 5 5 filter for the residual does not give low values for lines and edges in any direction. The performance of six noise models including the ones mentioned above are compared. Based on visual inspection of results from an example using a generated image (with all directions and many spatial frequencies represented) it is concluded that if striping is to be considered as a part of the noise, the residual from a 3 3 median filter seems best. If we are interested in a salt-andpepper noise estimator the proposed extension to the 3 3 filter for the residual from a quadratic surface seems best. Simple statistics and autocorrelations in the estimated noise images support these findings.