Digital High-Pass Filters with Milder High-Pass Effect on Digital Images

Abstract

Image filtering consists of modifying the original image by logically "reimaging" it with a mathematical imaging device in which spatial response can be controlled by the user. Image filtering is performed by a mathematical operation called convolution, which is simply the successive replacement of each point in the original image by a new value produced by a weighted combination of the original point and its surrounding neighbour points. Filtering generally requires definition of a filtering kernel or small matrix; often a few filtering kernels are predefined in imaging computer systems. The filtering kernel is generally square with a matrix size of 3×3 pixels, 5×5 pixels or 7×7 pixels. We consider the use of two-dimensional, second-order derivatives for image enhancement. The approach basically consists of defining a discrete formulation of the second-order derivative and then constructing a filter mask based on that formulation. Ten spatial high-pass filters (masks) are developed, then implemented and tested in our laboratory by using programs that were written in Borland c⁺⁺ and visual Fortran. The results of the application of the developped Laplacian and Laplacian high-pass digital filters (masks) on digital images (either edge detection, sharpening of high frequency regions (fine details) accentuation), comparing between the effect of different dimensions filters 3×3 and 5×5 and milder high pass effect are presented and demonstrated. As the size of the filter (mask) gets larger and/or the weight of the center pixel of the kernel gets higher, the sharpenning effect becomes more and more. Second-order derivatives have a strong response to fine detail, such as thin lines and isolated points.