ANALYTICAL DESIGN AND APPLICATIONS OF 2D ANISOTROPIC FILTERS WITH ELLIPTICAL FREQUENCY RESPONSE

This paper describes an analytical design technique in the frequency domain for a particular class of two-dimensional zero-phase anisotropic filters, namely with an elliptical or circular frequency response. These filters may be low-pass, if their response contains the origin of the frequency plane, or band-pass. The elliptical filters are specified by their orientation angle and the lengths of its axes. Their synthesis begins from a Gaussian low-pass prototype with a given selectivity, its frequency response being a ratio of two factored, even order polynomials. A specific frequency transformation is next determined, which is applied to the 1D prototype, leading to the desired 2D elliptically-shaped filter. The frequency response of the obtained filter results in a factored, matrix form and it explicitly contains the imposed specifications. Thus the filter is parametric, it can be adjusted or tuned for various specifications, without the need to resume every time from the start the design procedure. The filters designed through this analytical method are accurate in shape and efficient, of relatively low order, and their frequency response results in a factored form, convenient for implementation. Some relevant examples of design using the proposed method and also some filtering tasks on various test images are provided, to show their capabilities in image processing applications.