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Journal ArticleDOI

Analytic design of directional and square-shaped 2D IIR filters based on digital prototypes

01 Oct 2019-Multidimensional Systems and Signal Processing (Springer US)-Vol. 30, Iss: 4, pp 2021-2043
TL;DR: An analytic design method for a class of 2D recursive filters, namely with directional and square-shaped frequency response, based on a specified 1D digital prototype filter and a complex frequency transformation which is determined using various rational approximations.
Abstract: This paper proposes an analytic design method for a class of 2D recursive filters, namely with directional and square-shaped frequency response. The design technique is based on a specified 1D digital prototype filter and a complex frequency transformation which is determined using various rational approximations. Several design examples are presented for given specifications. The resulted filters are efficient and adjustable, being at the same time of low complexity and relatively high selectivity. These filters may have useful applications in image processing, like detecting lines with a given orientation from an image, as shown through simulation results on test images. The novelty of the proposed method consists in deriving the transfer function of the desired 2D filter only by applying successive frequency transformations to a prototype filter. Its advantages over most state-of-the-art design methods, which generally use global optimization numerical algorithms, is the filter tunability, and also its versatility; since the filter parameters, namely orientation and selectivity appear explicitly in the 2D filter matrices, they result directly for any specified parameters, therefore the design procedure does not need to be resumed every time from the start.
Citations
More filters
Proceedings ArticleDOI
23 Sep 2020
TL;DR: This work proposes an analytic design method for a particular class of 2D filter banks, with circular shape in the frequency plane and a maximally-flat characteristic, and the designed filter bank is tested in filtering a given texture image.
Abstract: This work proposes an analytic design method for a particular class of 2D filter banks, with circular shape in the frequency plane and a maximally-flat characteristic. The circular filters comprising the filter bank result starting from a zerophase prototype by applying specific frequency mappings; they are efficient, of relatively low order and good selectivity. Their transfer functions can be expressed in a closed form and depend explicitly on a parameter given by specified number of filters, e.g. in the case of an uniform circular filter bank. A design example is provided for imposed specification and the designed filter bank is tested in filtering a given texture image.

4 citations


Cites methods from "Analytic design of directional and ..."

  • ...In [16], a class of Gaussian directional FIR filters were proposed, and in [17] two types of 2D IIR filters were developed, namely directional filters and square-shaped filrers, based on similar prototypes and designed using analytical techniques....

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Journal ArticleDOI
TL;DR: In this paper , the authors proposed an analytical design procedure for a class of 2D filters with a directional characteristic in the frequency plane, which can be scaled along the frequency axis, thus resulting narrower or wider.
Abstract: This paper proposes an analytical design procedure for a class of 2D filters with a directional characteristic in the frequency plane. The method starts from two types of low-pass prototypes, namely a Gaussian filter and a wide-band filter. The two prototypes and the resulted 2D filters are zero-phase, a very useful property in image processing tasks. The prototypes are parametric and can be scaled along the frequency axis, thus resulting narrower or wider. A 1D to 2D frequency mapping, based on accurate approximations, is derived and applied to each prototype, obtaining the desired directional 2D frequency response with specified selectivity and orientation. The designed filters are adjustable, with a frequency response in factored matrix form depending on specifications. The Gaussian prototype yields very selective directional filters, used in detecting oriented straight lines in images, as show simulation results on several test images. Using oriented wide-band filters, other useful 2D filters result, namely square and parallelogram filters. The designed filters have accurate frequency responses, good directional selectivity and high linearity at relatively low order. An advantage of this analytical approach is that the filter transfer function results in parametric form and allows for easy tunability.

2 citations

Proceedings ArticleDOI
15 Jul 2021
TL;DR: In this paper, an analytic design procedure for 2D filters with wedge-shaped frequency response is presented, where the overall frequency response of the wedge filter is determined in a factored form, and the filter matrices result directly decomposed as a convolution of smaller matrices, a major advantage in implementation.
Abstract: This work presents an analytic design procedure for 2D filters with wedge-shaped frequency response. The design starts from a wide-band, maximally-flat zero-phase low-pass prototype filter, to which a frequency mapping is applied, which leads to the 2D filter with the desired shape. The overall frequency response of the wedge filter is determined in a factored form, and the filter matrices result directly decomposed as a convolution of smaller matrices, a major advantage in implementation. The resulted filter is parametric, being adjustable depending on specifications, namely orientation and aperture angles. Several wedge filter design examples are provided, for various specifications.
Proceedings ArticleDOI
28 May 2022
TL;DR: In this paper , a weighted least-squares (WLS) design method was proposed for 2D IIR filters with arbitrary frequency response and stable in the practical bounded-input bounded-output (P-BIBO) sense.
Abstract: Two-dimensional (2-D) infinite-extent impulse response (IIR) filter design is a challenging problem due to the difficulty in verifying stability. optimization methods proposed so far predominantly consider the design of 2-D IIR filters having quadrantally-symmetric frequency responses, where the transfer functions have separable denominators. In this paper, we propose a weighted least-squares (WLS) design method for 2-D IIR filters having arbitrary frequency response and stable in the practical bounded-input bounded-output (P-BIBO) sense. Our design considers transfer functions with nonseparable numerators and denominators having complex-and real-valued coefficients, respectively. We formulate the WLS design as an iterative second-order cone programming problem, which includes constraints to guarantee the P-BIBO stability. Design examples confirm that the proposed WLS method leads to P-BIBO stable 2-D IIR filters.
References
More filters
Book
03 Oct 1988
TL;DR: This chapter discusses two Dimensional Systems and Mathematical Preliminaries and their applications in Image Analysis and Computer Vision, as well as image reconstruction from Projections and image enhancement.
Abstract: Introduction. 1. Two Dimensional Systems and Mathematical Preliminaries. 2. Image Perception. 3. Image Sampling and Quantization. 4. Image Transforms. 5. Image Representation by Stochastic Models. 6. Image Enhancement. 7. Image Filtering and Restoration. 8. Image Analysis and Computer Vision. 9. Image Reconstruction From Projections. 10. Image Data Compression.

8,504 citations

Book
01 Jan 1992
TL;DR: Presents basic theories, techniques, and procedures used to analyze, design, and implement two-dimensional filters; and surveys a number of applications in image and seismic data processing that demonstrate their use in real-world signal processing.
Abstract: Presents basic theories, techniques, and procedures used to analyze, design, and implement two-dimensional filters; and surveys a number of applications in image and seismic data processing that demonstrate their use in real-world signal processing. For graduate students in electrical and computer e

475 citations

Journal ArticleDOI
TL;DR: This implementation yields an infinite impulse response filter that has six MADDs per dimension independent of the value of σ in the Gaussian kernel.

355 citations

Trending Questions (1)
What are the general application of analytical prototype?

The paper does not explicitly mention the general applications of the analytical prototype.