Introduction

The derivative operator is a useful tool in removing the low frequency components to enhance the details of an image Claerbout (1998a). However, the conventional derivative operator has a particular derivative direction. This is not desirable in some cases where the contour map has circular features, so what needed is a derivative operator without a specific direction. One isotropic alternative, the Laplacian operator, often cuts low frequencies too strongly.

The introduction of helical coordinate system Claerbout (1997) gives us the ability to solve the problem. The Kolmogoroff algorithm of spectral factorization Claerbout (1976) enables us to derive a helix derivative filter from its autocorrelation, the negative Laplacian operator Claerbout (1998b). The Wilson-Burg method of spectral factorization Sava et al. (1998) makes it more convenient to compute the coefficients of a finite-length helix derivative filter.

The helix low-cut filter is another operator useful in enhancing the digital images and also has the circularly symmetric spectrum. Unlike the helix derivative filter, the helix low-cut filter removes the frequency components below an adjustable cut-off frequency from the image, and has a flat response at high frequencies.

In this paper, I present the enhanced helix derivative and low-cut filters with more adjustable parameters. Then I analyze the influence on the filter spectrum for these parameters, and present guidelines for choosing the parameters for image processing, using the examples from GEE.