Winograd Method Research Articles

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

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.

Reducing the Computational Complexity of Image Processing Using Wavelet Transform Based on the Winograd Method

Reducing the Computational Complexity of Image Processing Using Wavelet Transform Based on the Winograd Method

A novel modified Winograd surgical tricks and tips with a “bird flap” for the treatment of ingrown toenails

BackgroundThe Winograd technique is the most commonly used surgical treatment for ingrown toenails. We describe a novel modified approach, more effective and simpler to perform with a better cosmetic outcome. MethodsWe retrospectively included 45 and 39 patients with 67 and 58 ingrown toenails who underwent our modified Winograd technique and the Winograd technique, respectively, from July 2017 to June 2020, and obtained data after 3, 6, and 12 months of follow-up. ResultsNo significant differences in the postoperative time taken to return to regular activities in the modified Winograd and traditional Winograd groups (p = 0.103) and regarding the recurrence in both groups (p = 0.055) were found. The extent of proximal germinal matrix exposure with the modified Winograd technique was significantly more clearly revealed than in the traditional Winograd method contextually (p < 0.05). The postoperative appearance satisfaction rate was significantly higher in the modified Winograd group than in the traditional Winograd group (p = 0.029). ConclusionThe modified Winograd technique is effective in treating ingrown toenails.

Development of digital image processing algorithms based on the Winograd method in general form and analysis of their computational complexity

The fast increase of the amount of quantitative and qualitative characteristics of digital visual data calls for the improvement of the performance of modern image processing devices. This article proposes new algorithms for 2D digital image processing based on the Winograd method in a general form. An analysis of the obtained results showed that the use of the Winograd method reduces the computational complexity of image processing by up to 84% compared to the traditional direct digital filtering method depending on the filter parameters and image fragments, while not affecting the quality of image processing. The resulting Winograd method transformation matrices and the algorithms developed can be used in image processing systems to improve the performance of the modern microelectronic devices that carry out image denoising, compression, and pattern recognition. Research directions that show promise for further research include hardware implementation on a field-programmable gate array and application-specific integrated circuit, development of algorithms for digital image processing based on the Winograd method in a general form for a 1D wavelet filter bank and for stride convolution used in convolutional neural networks.

Digital Filter Architecture Based on Modified Winograd Method F(2× 2, 5× 5) and Residue Number System

Improving the characteristics of digital signal processing devices is an important task in many practical problems. The paper proposes the architecture of a two-dimensional digital filter with a 5×5 mask, in which calculations are performed according to the Winograd method in the Residue Number System (RNS) with moduli of a special type. Theoretical analysis and hardware Field-Programmable Gate Array simulation are presented. The results show that the fragment throughput fr/s (number of fragments per second) of the device is 29.6% – 724.7% higher than state-of-the-art solutions. This is achieved by the combination of the Winograd method, which reduces the number of multiplications, with the RNS arithmetic, which performs addition and multiplication under smaller operands in parallel. However, our experiments showed that the proposed method requires up to 2.54% – 11.01% more Look-Up Tables and 3.58% – 19.83% higher power consumption compared to known analogues.

Batık Tırnak Tedavisinde Winograde Ve Vandenbos Cerrahi Tekniklerinin Heifetz Evresine Göre Karşılaştırılması

Abstract&#x0D; Background: In ingrown toenail, classifications and the treatment approaches according to staging has been clearly reported in the literature. However, there are not enough data about the selection of the appropriate surgical technique according to the stage. In this study, we compared two different surgical techniques in patients with Heifetz stage 2 and 3 in means of surgical results, recovery time, patient comfort and cosmetics.&#x0D; Methods: Between January 2019 and January 21, patients who applied with the complaint of ingrown toenails who were treated with two mentioned surgical techniques in two centers with at least 1 year follow-up were included. The patients were evaluated preoperatively in means of the Heifetz classification. In group 1 (n:54) matrix excising Winograd and in group 2 (n:51) matrix preserving Vandenbos techniques were used. Postoperative recovery time, complication rates, functional and cosmetic patient satisfaction were evaluated in tall cases. &#x0D; Results: 105 cases of ingrown toenails treated surgically were included in the study. 62 (59%) cases were Heifetz stage 2, 43 (41%) cases were Heifetz stage 3. No statistically significant difference was found between Heifetz stage 2 and stage 3, regardless of surgical technique, in complication, recurrence, patient functional/cosmetic satisfaction rates, and recovery time. In overall analysis regardless of Heifetz staging, recovery time was shorter with Winograd method (p:0.0001), complication and recurrence rates were lower with Vandenbos method (p:0.0001), and VAS cosmetic satisfaction was higher in Vandenbos (p:0.002).&#x0D; Conclusion: Winograd and Vandenbos in Heifitz stages 2 and 3 have low complication rates and high patient satisfaction. Earlier healing could be achieved with the Winograd technique, while low complication/recurrence rates and high cosmetic satisfaction could be achieved with the Vandenbos technique. Early recovery/high cosmetic expectation should be considered instead of Heifetz staging in determining the surgical technique.

High-performance digital image filtering architectures in the residue number system based on the Winograd method

Continuous improvement of methods for visual information registration, processing and storage leads to the need of improving technical characteristics of digital image processing systems. The paper proposes new high-performance digital filter architectures for image processing by the Winograd method with calculations performed in a residue number system with special-type moduli. To assess the performance and hardware costs of the proposed architectures, hardware simulation is carried out using a field-programmable gate array in a computer-aided design envi-ronment Xilinx Vivado 2018.3 for the target device Artix-7 xc7a200tffg1156-3. The results of hardware simulation show that the proposed filter architectures have 1.13 – 5.42 times higher performance, but require more hardware costs compared to the known methods. The results of this study can be used in the design of complex systems for image processing and analysis for their performance to be increased.

A tile-fusion method for accelerating Winograd convolutions

Compared with fast convolution methods such as im2col and the fast Fourier transform, Winograd-based convolution, which has been widely applied to accelerate convolutional neural networks (CNNs), can provide high performance with smaller filters. Although there are several reported studies on the algorithmic optimization of CNNs, most of them are targeted at hardware architectures. The existing implementations of the Winograd method perform well below what one would expect, due to the fact that the tile size of Winograd-based convolution is usually empirical and the features of each convolution layer are ignored. This study aims to fill this gap and focuses on the efficient implementation of Winograd-based convolution in the CNN model. Specifically, we discuss the causes of poor performance, calculate the coefficient of computation complexity model and demonstrate a speedup in the inference process using an elaborate tile-fusion method, which derives the optimal tile size for each convolution layer in a CNN model. Compared with the representative existing implementations of CuDNN with a 4 × 4 tile, Arm Compute Library with a 6 × 6 tile, and NNPACK with an 8 × 8 tile, the results show significant performance improvements on of up to 1.89 × , 1.29 × and 1.17 × , respectively.

A Minimally-Invasive, Simple, Rapid, and Effective Surgical Technique for the Treatment of Ingrown Toenails: A Reminder of the Original Winograd Procedure.

(1) Background: Ingrown toenail is a common disorder of the toe that induces severe toe pain and limits daily activities. The Winograd method, the most widely used operative modality for ingrown toenails, has been modified over years to include wedge resection of the nail fold and complete ablation of the germinal matrix. We evaluated the outcomes of original Winograd procedure without wedge resection with electrocautery-aided matrixectomy. (2) Methods: We retrospectively analyzed the outcomes of patients who underwent surgery for ingrown toenails at a university hospital for two years from November 2015 to October 2017. Surgery was performed in 76 feet with a mean operation time of 9.34 min. (3) Results: The minimal interval from surgery to return to regular activities was 13.26 (range 7 to 22) days. Recurrence and postoperative wound infections were found in 3 (3.95%) and 2 (2.63%) patients, respectively. Evaluation of patient satisfaction at one-year follow-up showed that 40 (52.63%) patients were very satisfied, 33 (43.42%) were satisfied, 3 (3.95%) were dissatisfied, and none of them were very dissatisfied. The average follow-up duration was 14.66 (range 12 to 25) months. (4) Conclusions: Therefore, it is believed that this less-invasive and simple procedure could be easily performed by clinicians, with satisfactory patient outcomes.

Digital Filter Architecture With Calculations in the Residue Number System by Winograd Method F (2 × 2, 2 × 2)

Improving the technical characteristics of digital signal processing devices is an important problem in many practical tasks. The paper proposes the architecture of a device for two-dimensional filtering in a residue number system (RNS) with moduli of a special type according to the Winograd method. The work carried out the technical parameters theoretical analysis of the proposed filter architecture for different RNS moduli sets by the “unit-gate”-model. In addition, the proposed architecture is compared with known digital filter implementations. The theoretical analysis results showed that the use of the proposed filter architecture makes it possible to increase the signal processing speed by 1.33 – 6.90 times, in comparison with the known device implementations. Also, in the work, the hardware simulation of the proposed filter architecture was performed on FPGA, which showed that the performance of the proposed device is 1.31 – 4.12 times higher than known digital filter architectures. The research results can be used in digital signal processing systems to increase their performance and reduce hardware costs. In addition, the developed architectures can be applied in the development of hardware accelerators for complex digital signals analysis systems.

АНАЛИЗ БЫСТРОГО АЛГОРИТМА УМНОЖЕНИЯ МАТРИЦ И ВЕКТОРОВ ДЛЯ БАНКА ЦИФРОВЫХ ФИЛЬТРОВ

Algorithms of implementation of vector-matrix multiplication are presented, which are intended for application in banks (sets) of digital filters. These algorithms provide significant savings in computational costs over traditional algorithms. At the same time, reduction of computational complexity of algorithms is achieved without any performance loss of banks (sets) of digital filters. As the basis for the construction of algorithms proposed in the article, the previously known Winograd method of multiplication of real matrices and vectors and two versions of the method of type 3M for multiplication of complex matrices and vectors are used. Methods of combining these known methods of multiplying matrices and vectors for building digital filter banks (sets) are considered. The analysis of computing complexity of such ways which showed a possibility of reduction of computing complexity in comparison with a traditional algorithm of realization of bank (set) of digital filters approximately in 2.66 times – at realization on the processor without hardware multiplier is carried out; and by 1.33 times – at realization on the processor with the hardware multiplier. These indicators are markedly higher than those of known algorithms. Analysis of sensitivity of algorithms proposed in this article to rounding errors arising by digital signal processing was carried out. Based on this analysis, an algorithm is selected that has a computational complexity smaller than that of a traditional algorithm, but its sensitivity to rounding errors is the same as that of a traditional algorithm. Recommendations are given on its practical application in the development of a bank (set) of digital filters.

The Asymptotic Induced Matching Number of Hypergraphs: Balanced Binary Strings

We compute the asymptotic induced matching number of the $k$-partite $k$-uniform hypergraphs whose edges are the $k$-bit strings of Hamming weight $k/2$, for any large enough even number $k$. Our lower bound relies on the higher-order extension of the well-known Coppersmith–Winograd method from algebraic complexity theory, which was proven by Christandl, Vrana and Zuiddam. Our result is motivated by the study of the power of this method as well as of the power of the Strassen support functionals (which provide upper bounds on the asymptotic induced matching number), and the connections to questions in tensor theory, quantum information theory and theoretical computer science.Our proof relies on a new combinatorial inequality that may be of independent interest. This inequality concerns how many pairs of Boolean vectors of fixed Hamming weight can have their sum in a fixed subspace.

DWM: A Decomposable Winograd Method for Convolution Acceleration

Winograd's minimal filtering algorithm has been widely used in Convolutional Neural Networks (CNNs) to reduce the number of multiplications for faster processing. However, it is only effective on convolutions with kernel size as 3x3 and stride as 1, because it suffers from significantly increased FLOPs and numerical accuracy problem for kernel size larger than 3x3 and fails on convolution with stride larger than 1. In this paper, we propose a novel Decomposable Winograd Method (DWM), which breaks through the limitation of original Winograd's minimal filtering algorithm to a wide and general convolutions. DWM decomposes kernels with large size or large stride to several small kernels with stride as 1 for further applying Winograd method, so that DWM can reduce the number of multiplications while keeping the numerical accuracy. It enables the fast exploring of larger kernel size and larger stride value in CNNs for high performance and accuracy and even the potential for new CNNs. Comparing against the original Winograd, the proposed DWM is able to support all kinds of convolutions with a speedup of ∼2, without affecting the numerical accuracy.

Winograd Method Versus Winograd Method With Electrocoagulation in the Treatment of Ingrown Toenails

An important component of the Winograd surgical method for an ingrown toenail is total excision of the associated germinal matrix. However, this might not always be accomplished with the procedure. We hypothesized that the surgical results might be improved by adding electrocoagulation of the germinal matrix to the Winograd method. The objective of the present study was to compare the recurrence, satisfaction, and complication rates of the Winograd method with those of the Winograd method with electrocoagulation. We retrospectively evaluated the records of 102 patients with single Heifetz stage 2 or 3 ingrown toenails who had undergone surgery from January 2013 to October 2014 using 1 of these 2 methods. Of the 102 patients, 50 (49%) underwent the Winograd method and 52 (51%) underwent the Winograd method with electrocoagulation. The mean follow-up period of our patients was 12 (range 6 to 22) months. An ingrown toenail recurred in 3 patients (6%) in the Winograd group and in no patient in the Winograd with electrocoagulation group (p = .04). Among the patients in the Winograd group, 46 (92.0%) were satisfied or very satisfied. Among the patients in the Winograd plus electrocoagulation group, 49 (94.2%) were satisfied or very satisfied (p = .04). No complications developed in either group. In conclusion, the Winograd method for ingrown toenails results in high satisfaction rates, low recurrence rates, and low complication rates. The addition of electrocoagulation of the germinal matrix to the Winograd method could result in even lower recurrence rates, while maintaining high patient satisfaction and without increasing the risk of complications.

Comparison of the Winograd method and chemical cauterization with 10% sodium hydroxide for treating ingrown toenails

Comparison of the Winograd method and chemical cauterization with 10% sodium hydroxide for treating ingrown toenails

An Evaluation of Partial Matrix Excision with Winograd Method for the Surgical Treatment of Ingrown Toenails

Objective: The most frequent nail pathology of the hallux is the ingrown toenail. In our study, we evaluated Winograd’s partial matrix excision method as a treatment for unilateral ingrown hallux toenail. Methods: Winograd’s partial toenail excision was performed on 239 patients (127 males, 112 females; mean age 37.4 years) with an ingrown toenail. Primary patient complaints included a painful hallux toenail, discharge, nail deformation, and difficulty walking. According to the Heifetz staging system, there were 62 patients evaluated as Stage l, 96 as Stage ll, and 81 as Stage lll. A total of 174 (74%) patients had discharge from infection. In infected cases, an antibiotic was administered until inflammatory signs and discharged ceased, at which time surgical treatment was performed. Patients’ duration to return to daily living and work, recurrence ratio, satisfaction, and cosmetic issues were evaluated. The mean follow-up time was 27 months (range: 14-45 months). Results: Patients returned to daily living in 10-15 days (mean 11.3) and to work in 8.7 days (range: 6-13 days). A total of 230 patients (96.3%) were satisfied with the procedure, and 231 patients (96.6%) were satisfied with the cosmetic results. Nine patients were dissatisfied with the surgical outcome, and eight patients who experienced recurrence were dissatisfied with the cosmetic results. None of the patients experienced deep tissue infections or neurovascular complications. Conclusion: Winograd’s partial matrix excision method is a beneficial surgical procedure for ingrown toenail, resulting in low recurrence and high satisfaction rates. (JAREM 2014; 1: 7-11)

Surgery for ingrowing nail is an effective treatment choice in an urban region

Objectives: The aim of this study is to evaluate the risk factors and treatment outcomes of patients with ingrowing nails in an urban region. Methods: This descriptive prospective study was performed in a General Surgery outpatient clinic in an urban region for 6 months. The data about sex, risk factors, age, history of previous medication were obtained. Body mass index, the ratio of second toe to the length of hallux, the ratio of the diameter of hallux to width of hallux nail were calculated. The ingrowing nails with stage II and III were treated by Winograd method. The patients were followed for recurrences and complications for nearly 6 months. Results: Total 61 patients were treated. Female to male ratio was 33/28. The man age was 24.8±11.8. The mean BMI was 28.5±5.3. Tight shoes, improper nail trimming were the leading etiological factors. Total 44 patients had a history of at least one time antibiotic usage history. Symptoms were found to be increased after pregnancy (66.7%). Lateral localization was significantly higher in patients with longer second toe than the hallux. There were 5 postoperative infections (8.2%) and only one (1.6%) recurrence. Conclusion: Ingrowing nail is an important problem because of increased risk factors in urban region. Winograd method which is an easy method with low recurrence and high patient satisfaction can be preferred.

Neutralized Chemical Matricectomy with the Winograd Method in the Management of Ingrowing Toenail

ABSTRACT Background Ingrowing toenail is a common condition provoking pain, inflammation and functional limitation. Many surgical methods have evolved over the years for its treatment. The most important aspect of treatment of this problem is to prevent recurrence. The purpose of this paper was to study the effectiveness of combining the standard Winograd technique with neutralized chemical matricectomy to reduce the chances of recurrence and expedite postoperative recovery. Materials and methods Between 2006 and 2013, 33 patients (18 males, 15 females); with mean age 37.39 years (range 16 to 65 years) with 38 ingrowing toenails were treated with the standard Winograd technique combined with phenol matricectomy. The patients were evaluated in subsequent follow-ups for postoperative relapse, pain score (VAS) and time return to daily activities and ability to wear footwear and overall satisfaction. The mean follow-up period was 3.57 years (range 2 to 7 years). Results A total of 94.73% patients were satisfied with the overall outcome. The average return to normal shoe-wear was 1.54 weeks and the average return to normal activity was 1.18 weeks. Recurrence was seen in two patients (5.26%), 5 and 6 months after surgery. Four patients had delayed healing. None of the patients had any deep infection or neurovascular complications. Conclusion The Winograd technique when combined with neutralized phenol matricectomy is associated with a very low recurrence and infection rate. It allows early postoperative recovery and good cosmetic results with a high level of patient satisfaction. How to cite this article Agarwala S, Sobti AS, Mohrir G. Neutralized Chemical Matricectomy with the Winograd Method in the Management of Ingrowing Toenail. J Foot Ankle Surg (Asia-Pacific) 2014;1(2):55-59.

The Results of the Winograd Method in Surgical Treatment of Ingrown Toenail

The Results of the Winograd Method in Surgical Treatment of Ingrown Toenail

Computation reduction of the maximum likelihood classifier using the Winograd identity

The maximum likelihood classifier is one of the most used image processing routines in remote sensing. However, most implementations have exhibited the so-called “Hughes phenomenon” and the computation cost increases quickly as the dimensionality of the feature set increases. Based on the above reasons, the recursive maximum likelihood classification strategy is more suitable for hyperspectral imaging data than the conventional nonrecursive approach. In this paper we derive some computation aspects of quadratic forms by applying the Winograd's method to three previous approaches. The new, modified approaches are approximately four times faster than the conventional nonrecursive approach and two times faster than the existing recursive algorithms.