Analytical Design of Elliptically-Shaped 2D Recursive Filters
01 Aug 2018-pp 964-967
TL;DR: An analytic design technique for 2D IIR filters with elliptical symmetry, which have useful applications in image processing, and which have an accurate elliptical shape with low distortions even close to the frequency plane margins.
Abstract: This paper presents an analytic design technique for 2D IIR filters with elliptical symmetry, which have useful applications in image processing. The design is based on efficient elliptic digital filters, regarded as 1D prototypes, to which specific complex frequency transformations are applied; this allows to obtain directly a factored form of the transfer function for the 2D elliptically-shaped filter. The design procedure uses accurate approximations, but no global optimization algorithm. Finally the 2D filter matrices are obtained. The filter is adjustable, its coefficients depending explicitly on the specified orientation and bandwidth. Another advantage is versatility, since the design need not be resumed each time from the start for various specifications. The designed 2D filters have an accurate elliptical shape with low distortions even close to the frequency plane margins, being efficient, of high selectivity and low order.
Citations
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15 Jul 2021
TL;DR: In this article, a two-dimensional (2D) lattice structured digital filter was proposed, which has an absolutely minimal state-space vector and is characterized by lattice structure having alternate delay element orientation.
Abstract: This paper proposes a new two dimensional (2D) lattice structured digital filter, having a minimal number of delay elements. This filter, besides having a minimal number of delay elements, also has an absolutely minimal state-space vector. The new finite impulse response (FIR) digital filter is characterized by lattice structure having alternate delay element orientation. It is worth mentioning that the transfer function coefficients of the proposed 2D filter, are complements of the classic lattice filter. The results of this paper are directly applicable to one-dimensional (1D) lattice digital filters. First and second degree 2D examples are provided to show the features of the circuit and state-space realization structures.
2 citations
01 Sep 2020
TL;DR: An analytical design procedure is described in this paper for a type of 2D recursive filter, with a frequency response elliptical or circular in shape, based on a specially determined frequency mapping, applied to an digital prototype filter.
Abstract: An analytical design procedure is described in this paper for a type of 2D recursive filter, with a frequency response elliptical or circular in shape. The design is based on a specially determined frequency mapping, applied to an digital prototype filter. This analytical design approach yields the transfer function of the desired 2D filter in a factored, closed form. Some efficient, accurate approximations are used, like Chebyshev-Pade method, without resorting to global optimization algorithms. The filter matrices are a convolution of smaller size matrices, an obvious advantage in implementation. Moreover, the obtained filter is tunable, since its coefficients depend on the specified orientation and bandwidth. As proven by given design examples, these 2D filters have a precise shape, with negligible distortions even near the margins of frequency plane, good selectivity and low order.
Cites methods from "Analytical Design of Elliptically-S..."
...Other analytical design methods for directional filters, in particular elliptical, were proposed by the author in [17]-[20]....
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References
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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
Additional excerpts
...INTRODUCTION The field of two-dimensional filters has been attracting the interest of researchers worldwide for a long time and various design methods were proposed [1]....
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TL;DR: A feature-level fusion approach for improving the efficiency of palmprint identification using multiple elliptical Gabor filters with different orientations to extract the phase information on a palmprint image, which is then merged according to a fusion rule to produce a single feature called the Fusion Code.
338 citations
"Analytical Design of Elliptically-S..." refers background in this paper
...Interesting applications of elliptically-shaped filters were found in the biometric field, like pose robust human detection [11], iris recognition [12], palm print identification [13], fingerprint enhancement [14]....
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TL;DR: In this paper, a general stability preserving mapping theorem is presented which allows most recursive filters of a particular type to be mapped into any other type of recursive filter, and a number of practical stability tests are developed including one which requires the testing of several one-dimensional polynomial root distributions with respect to the unit circle.
Abstract: Two-dimensional recursive filters are defined from a different point of view. A general stability preserving mapping theorem is presented which allows most recursive filters of a particular type to be mapped into any other type of recursive filter. In particular, any type of filter can be mapped into a first-quadrant filter. This mapping is used to prove a number of general stability theorems. Among these is a theorem which relates the stability of any digital filter to its two-dimensional phase function. Furthermore, other stability theorems which are valid for any type of recursive filter are presented. Finally, a number of practical stability tests are developed including one which requires the testing of only several one-dimensional polynomial root distributions with respect to the unit circle.
94 citations
"Analytical Design of Elliptically-S..." refers background in this paper
...Stability of 2D filters and stabilization methods are important and rather difficult issues, studied in papers like [19], [20]....
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...Various stability criteria exist [19], and stabilization methods can be applied for some unstable filters [20]....
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TL;DR: This letter introduces a directional filter that retains the ability to handle missing data and is separable, making it computationally efficient, and demonstrates the directional filter on weather radar data where it can be used to smooth along fronts.
Abstract: Anisotropic and directional filters can smooth noisy images while preserving object boundaries. Data from remote sensing instruments often have missing pixels due to geometric or power limitations. In such cases, these nonisotropic filters are very inefficient, because transform methods cannot be used when there is missing data or when logical operations need to be performed. A directional filter is introduced in this letter that retains the ability to handle missing data and is separable, making it computationally efficient. We demonstrate the directional filter on weather radar data where it can be used to smooth along fronts. Since the filter introduced here can be parameterized for scale, orientation, and aspect ratio, this filter can be used in any directional filtering application where transform methods cannot be used, but computational efficiency is desired.
66 citations
"Analytical Design of Elliptically-S..." refers background in this paper
...Anisotropic filters were also studied extensively and used in interesting applications, like remote sensing for directional smoothing applied to weather images, texture segmentation and pattern recognition [5], [6]....
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TL;DR: In this article, a new theory is presented for the design of 2-D IIR filters using the transformation Z = H_1(z_1)H_2 (z_2), where H_ 1(z-1) and H_ 2 (z-2) are stable, digital spectral transformations, originally proposed by Constantinides for a different purpose.
Abstract: In this paper, a new theory is presented for the design of 2-D IIR filters using the transformation Z = H_1(z_1)H_2(z_2) , where H_1(z_1) and H_2(z_2) are stable, digital spectral transformations, originally proposed by Constantinides for a different purpose. This transformation is found to be analogous to McClellan's transformation for designing 2-D FIR filters like the circular, elliptic-support and fan filters. But the design of these filters, using our method, involves only a one-dimensional search procedure and not any optimization. The design procedure is very simple and guarantees stability of the resulting IIR filters at the same time. Design examples are included to illustrate the theory and also its relative simplicity.
59 citations
"Analytical Design of Elliptically-S..." refers methods in this paper
...The existing design methods for 2D filters rely on 1D prototypes, using frequency transformations from s to z plane via bilinear or Euler approximations, aiming to obtain a 2D filter with a desired frequency response [2]....
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