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.

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“…In Formula (9) above, m is a random number in [0.4, 0.9], 𝛽 is a random number in [−1, 1], and 𝑥 ⃗ * (𝑡) indicates the optimal location for the black widow spider. 𝑥 (𝑡) in (10) represents the random position of the Harris Eagle, 𝑥 (𝑡) represents the prey's position, and 𝑥 (𝑡) represents the average position. lb, ub, and r represent the lower limit The Harris Hawk algorithm has the disadvantage of easily falling into local optimization during the iterative process.…”

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