On the Computational Complexity of 2D Filtering by Winograd Method

Lyakhov, Pavel; Abdulsalyamova, Albina S.; Semyonova, Nataliya; Nagornov, Nikolay; Voznesensky, A. S.; Kaplun, Dmitrii I.

doi:10.1109/meco55406.2022.9797092

Cited by 5 publications

(2 citation statements)

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“…where Z is the fragment of the processed image of size z × 1; R is the wavelet filter mask of size r × 1; N is the fragment of the original image of size n × 1, where n = z + r − 1; A T , G, B T are the transformation matrices of sizes z × n, n × r, n × n, respectively; and is the operator of element-wise matrix multiplication. Algorithms for compiling transformation matrices are described in detail in paper [16]. The notation WM F(n, r) contains processed image fragments of size n and the order r of the wavelet used.…”

Section: B Digital Filtering Using the Winograd Methodsmentioning

confidence: 99%

High-Speed Wavelet Image Processing Using the Winograd Method with Downsampling

Lyakhov,

Semyonova,

Nagornov

et al. 2023

Mathematics

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Wavelets are actively used to solve a wide range of image processing problems in various fields of science and technology. Modern image processing systems cannot keep up with the rapid growth in digital visual information. Various approaches are used to reduce the computational complexity and increase computational speeds. The Winograd method (WM) is one of the most promising. However, this method is used to obtain sequential values. Its use for wavelet image processing requires expanding the calculation methodology to cases of downsampling. This paper proposes a new approach to reduce the computational complexity of wavelet image processing based on the WM with decimation. Calculations have been carried out and formulas have been derived that implement digital filtering using the WM with downsampling. The derived formulas can be used for 1D filtering with an arbitrary downsampling stride. Hardware modeling of wavelet image filtering on an FPGA showed that the WM reduces the computational time by up to 66%, with increases in the hardware costs and power consumption of 95% and 344%, respectively, compared to the direct method. A promising direction for further research is the implementation of the developed approach on ASIC and the use of modular computing for more efficient parallelization of calculations and an even greater increase in the device speed.

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Section: B Digital Filtering Using the Winograd Methodsmentioning

confidence: 99%

High-Speed Wavelet Image Processing Using the Winograd Method with Downsampling

Lyakhov,

Semyonova,

Nagornov

et al. 2023

Mathematics

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“…Area-efficient 2D structures for 2D filtering are also approached in [42,43]. A computational complexity evaluation of 2D filtering by the Winograd method is performed in [44]. Novel stability tests for 2D continuous-time systems are established in [45].…”

Section: Introductionmentioning

confidence: 99%

Analytical Design of Gaussian Anisotropic 2D FIR Filters and Their Implementation Using the Block Filtering Approach

Matei,

Chiper

2024

Electronics

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This work proposes an analytical design procedure for a particular class of 2D filters, namely anisotropic Gaussian FIR filters. The design is achieved in the frequency domain and starts from a low-pass Gaussian 1D prototype with imposed specifications, whose frequency response is efficiently approximated by a factored trigonometric polynomial using the Chebyshev series. Then, using specific 1D to 2D frequency mappings applied to the prototype, the frequency response for a 2D anisotropic filter with a specified orientation angle is directly derived in two versions, namely with a straight or elliptical shape in the frequency plane. The resulting filters have an accurate shape with low distortion. Several design examples for specified parameters (angle and selectivity) are provided. Then, simulations of directional filtering on various test images are given, which show their capability of extracting oriented lines or other various oriented objects from synthetic or real-life images. Finally, a computationally efficient implementation at the system level is proposed, based on a polyphase decomposition and block-filtering approach, which yields a 2D filter with a high degree of parallelism and low arithmetic complexity.

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