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Automatic extraction and discrimination of vocal main melody based on quadratic wave equation

Pubblicato online: 15 Jul 2022
Volume & Edizione: AHEAD OF PRINT
Pagine: -
Ricevuto: 10 Apr 2022
Accettato: 10 Jun 2022
Dettagli della rivista
License
Formato
Rivista
eISSN
2444-8656
Prima pubblicazione
01 Jan 2016
Frequenza di pubblicazione
2 volte all'anno
Lingue
Inglese
Introduction

Due to the rapid development of the Internet, music data is growing explosively. The need for people to retrieve audio data is growing. The traditional retrieval method is to manually annotate the music into text, and then people use the traditional text retrieval method to retrieve the database of the annotated information. This mainly has the following shortcomings. First, the number of songs is increasing day by day, and the cost of manual labeling is huge; second, the information of manual labeling is mostly concentrated in song name, song style, song author and other information, but does not contain song melody information; third, in human natural thinking Songs are mainly identified by melody, and retrieval of songs by text is not in line with the natural habits of human beings [1]. Therefore, it is necessary to propose a new characteristic theme to automatically label songs. There are two explanations for the word main melody. One explanation is that it is the melody line composed of the fundamental frequency that occupies the main position at each moment in the song. Another explanation is that the melody line formed by the fundamental frequency of the vocals in the song is the main melody. Because the melody of the human voice is more widely spread and used in general songs, the main melody in this topic refers to the second interpretation method, that is, the fundamental frequency curve of the human voice in the song. Selecting it as a new feature is mainly based on the following three aspects. First, the main melody is an intuitive description that can be perceived by people without professional musical training, which means that the main melody is a concise and natural description of a song by humans [2]. Second, the main melody plays a significant role in identifying song fragments in popular songs, which can bring good results in many applications and promote the development of various related applications. Third, even in very complex song signals, the main melody can maintain its simple and highly recognizable characteristics, which shows that the main melody description method has better adaptability to different types of songs. Theme extraction has been widely used in many fields [3]. The most common application is to use the extracted main melody as an index to generate a humming search database or an acoustic search database. Humming search is a song retrieval method that is most in line with the natural expression habits of human beings. The searcher hums a tune of the song they are looking for. The retrieval system automatically returns the song information corresponding to the tune, such as song name, author, download link and other information. In addition to humming retrieval, vocal melody extraction can also be applied in a wide range of other fields. For example, music vocal separation, automatic karaoke soundtrack generation, song retrieval, song structure analysis and song classification, etc. [4].

Murray E and others proposed a main melody extraction method based on speech separation. Experiments show that the performance of the main melody extraction algorithm with speech separation is higher than that of the algorithm without [5]. Zhu M X and others used a data-driven approach to train a deep neural network model for each fundamental frequency label with sufficient labeled data. Due to the simple singing melody localization algorithm, the overall accuracy of the algorithm is slightly lower than other algorithms. However, the original pitch accuracy of the algorithm has been improved compared with other algorithms, so as long as a more effective singing melody localization algorithm is added, the overall accuracy will be significantly improved [6]. Combining two saliency function calculation methods, source filter model and harmonic weighting, multiple candidate melody lines are extracted according to the continuity of the melody, and finally singing melody localization and main melody extraction are carried out according to a series of features of the candidate melody lines. Through the above research status, it is found that the research on the pitch saliency function algorithm runs through the entire research process of the automatic main melody extraction algorithm, while the research on the singing melody localization algorithm has only attracted the attention of scholars in recent years, and has not yet reached the upper limit of performance. Experiments show that the introduction of a simple singing melody localization algorithm is helpful to improve the overall accuracy, and further improving the accuracy of the singing melody localization algorithm will help to improve the overall accuracy of the automatic main melody extraction algorithm [7].

Summarizing the advantages and disadvantages of previous studies, this article introduces the patterns of note segmentation and basic frequency differentiation in terms of tone differentiation based on the volume tightening function. Adding note-based time stability to note segmentation based on spectral distance and dividing the sound into paragraphs with a relatively stable frequency spectrum helps to control the melody and determine the melody to be sung. In the localization of the melody, a basic model of frequency differentiation using a neural network based on different timbre and accompaniment of the vocal cords is added, and the probability that the predominant basic frequency trajectory belongs to the singing melody is based on segmented statistics, it can effectively reduce the false alarm speed of tone localization and improve the overall accuracy.

Algorithm principle
The overall framework of the algorithm

The overall framework of the algorithm is shown in Figure 1.

Figure 1

The overall framework of the vocal music theme extraction algorithm

According to the overall framework, the main melody extraction steps of vocal music are as follows: The first step is to preprocess the input music, mainly including signal down sampling, normalization, framing, windowing and time-frequency domain transformation; The second step is to segment notes and detect voiced segments through spectrum analysis; The third step is pitch estimation. The pitch saliency is calculated on each frame of the voiced segment, and three candidate fundamental frequencies are selected according to the fundamental frequency characteristics and pitch saliency function; The fourth step is to track the dominant fundamental frequency, and extract a main melody line by Viterbi algorithm in each voiced segment; The fifth step is to distinguish the main melody of the song. Since the extracted main melody is not dominated by the song, a song discrimination model is used to judge whether the dominant fundamental frequency belongs to the song and connect all the pitch sequences belonging to the song to form the main melody of the vocal music [8].

Signal preprocessing

Singing is a time-varying non-stationary speech signal. In order to better analyze the information it carries, a series of measures are usually taken to preprocess it first, including down sampling and normalization of the input audio signal, framing, windowing and STFT.

Considering that the frequency range of voice signal is concentrated in 300 ~ 3400 Hz, in order to reduce the amount of calculation of subsequent signal processing, the audio signal used is uniformly down sampled to 8 kHz. In addition, the input signal is normalized to ensure the consistency of further processing. The speech signal is almost stable in a short time. Based on this, the speech signal can be processed by frame windowing. In this paper, Hamming window is adopted, and its formula is: w(n)={0.540.46cos[2πnN1]0else0nN w\left(n \right) = \left\{{\matrix{\hfill {0.54 - 0.46\cos} & \hfill {\left[ {{{2\pi n} \over {N - 1}}} \right]} \cr \hfill 0 & \hfill {else} \cr}} \right.\,0 \le n \le N

Where, N is the window length, the frame length is 40 ms, and the frame shift is 20 ms. As required, STFT (short-time Fourier transform) can be used to time-frequency transform the signal after framing.

Note segmentation and voiced segment detection

Music consists of musical notes. Each note has a relatively stable spectral character. By segmenting the music, we can obtain a more reliable and accurate sound frequency based on the calculated note frequency. The notes were segmented using a distance-based audio segmentation algorithm (DIS algorithm). One feature used to segment notes is the short-term amplitude spectrum. Slide the data window along the frame, and calculate the disk measurement distance of the sound function of the two information windows before and after the L frame of the audio as follows. DIS(t)=(μt,1μt,2)T(μt,1μt,2)tr(t,1)+tr(t,2) DIS\left(t \right) = {{{{\left({{\mu _{t,1}} - {\mu _{t,2}}} \right)}^T}\left({{\mu _{t,1}} - {\mu _{t,2}}} \right)} \over {tr\left({\sum\nolimits_{t,1} {}} \right) + tr\left({\sum\nolimits_{t,2} {}} \right)}}

Where, μt,1 and μt,2 represent the mean vector of two adjacent segments of audio features, and tr(t,1) tr\left({\sum\nolimits_{t,1} {}} \right) and tr(t,2) tr\left({\sum\nolimits_{t,1} {}} \right) represent the trace of two adjacent segments of audio feature matrix.

After obtaining the DIS measurement distance curve, find the maximum point of DIS(t) and screen the note segmentation points according to certain screening rules. The screening rule is: compare the standard deviation threshold with the maximum point. If the maximum point is greater than the standard deviation threshold, it is the note segmentation point, otherwise it is rounded off [9].

In addition, there is a non voiced segment in the music signal, and there is no fundamental frequency in the non voiced segment. Therefore, these segments should be excluded before fundamental frequency estimation. In this paper, the spectral variance method is used to judge the voiced and non voiced segments in the sound segment.

Multi pitch estimation

In polyphonic music, there are often multiple fundamental frequencies at the same time. The system uses the pitch significance function to extract the quadratic wave equation. Specifically, the extraction method of fundamental quadratic wave equation based on pitch estimation filter with amplitude compression (PEFAC) is adopted. If the fundamental frequency of a voiced signal is, the signal can be expressed as: Y(f)=k=1kakδ(fkf0) Y\left(f \right) = \sum\limits_{k = 1}^k {{a_k}\delta \left({f - k{f_0}} \right)}

Where ak is the coefficient of k-th harmonic. Take logarithm of f to get: Y(q)=k=1kakδ(qlogklogf0) Y\left(q \right) = \sum\limits_{k = 1}^k {{a_k}\delta \left({q - {{\log}_k} - \log {f_0}} \right)}

Where q = log f0, convolute it with a comb filter, and the convolution junction Y(qh(−q), that is, the significance function of the fundamental frequency, will produce a peak at the position of q0 = log f0. The position in the frequency domain is the fundamental frequency of the voiced segment of the required signal.

The comb filter actually used in this paper is: h(q)=k=1kh(qlogk) h\left(q \right) = \sum\limits_{k = 1}^k {{h^{'}}\left({q - \log k} \right)} h(q)=1γcos(2πexp(q))β {h^{'}}\left(q \right) = {1 \over {\gamma - \cos \left({2\pi \cdot \exp \left(q \right)} \right)}} - \beta

Parameter γ controls the width of the spectral peak of the comb filter, and K represents the number of spectral peaks [10].

The significance function of each frame is defined as: S(q)=Y(q)h(q) S\left(q \right) = Y\left(q \right) \cdot h\left({- q} \right)

For the multi fundamental frequency signal, find the frequency set {ψ1} corresponding to all peak positions of S (q) as the candidate fundamental frequency. In addition, the fundamental frequency range of singing is usually 70 ~ 1000 Hz, and calculating S(q) according to formula (7) at each frequency point requires a large amount of computation. In order to reduce the computational complexity, according to the characteristics of singing spectrum, only some frequency points with large signal spectrum amplitude are selected to calculate the significance value, which can greatly reduce the amount of calculation.

The improved pitch saliency calculation is realized as follows: set a threshold T and judge whether the amplitude of the logarithmic amplitude spectrum of the signal is greater than t for the frequency point of 70 ~ 1000 Hz. If it is greater than t, calculate the significance value according to formula (8); Otherwise, set the significance value corresponding to the frequency point directly to 0 [11]. S(q)={q=q0Y(q)h(qq0)Y(q)T0Y(q)<T S\left(q \right) = \left\{{\matrix{{\sum\limits_{q = {q_0}} {Y\left(q \right) \cdot h\left({q - {q_0}} \right)}} & {Y\left(q \right) \ge T} \cr 0 & {Y\left(q \right) < T} \cr}} \right.

Where q is the frequency point in log domain, Y (q) is the spectrum in log domain, and h (q) is the comb filter function in log domain; S (q) is the pitch saliency function.

Since only the significance values of a limited number of frequency points with large energy of 70 ~ 1000 Hz are calculated, the computational complexity is significantly reduced. Finally, from all frequency points, find the largest three frequencies that do not become double or half frequency to each other as the final candidate fundamental frequency. Where, fn represents the frequency position of the n-th candidate fundamental frequency, and sn represents the significance value of the n-th candidate fundamental frequency.

Dominant fundamental frequency trajectory tracking

A similar method is used to track the dominant fundamental frequency trajectory. According to the peak value of pitch saliency function, multiple candidate fundamental frequencies are extracted, and then Viterbi algorithm is used to track the dominant fundamental frequency in the voiced segment (in each note).

For each voiced segment, Viterbi algorithm based on pitch likelihood and pitch transition probability is used to extract the optimal pitch sequence of the segment, that is, the dominant pitch trajectory, so that it meets the formula: F=argmax(f1,f2,,fT){αt=1T1lgp(ft|Xt)+βt=2T1lgp(Δft)} F = \mathop {\arg\max}\limits_{\left({{f_1},{f_2}, \ldots,{f_T}} \right)} \left\{{\alpha \sum\limits_{t = 1}^{{T_1}} {\lg \,p} \left({{f_t}|{X_t}} \right) + \beta \sum\limits_{t = 2}^{{T_1}} {\lg} \,p\left({\Delta {f_t}} \right)} \right\}

Where, T1 represents the segment length of voiced segment, p(ft|Xt) and pft) represent pitch likelihood and transition probability respectively, and α and β are their corresponding weights [12].

Main melody discrimination

The main melody of vocal music refers to the melody of the song sung by people, and the dominant fundamental frequency track of each note segment extracted by the main melody extraction method may belong to the song or the accompaniment instrument. Therefore, it is necessary to introduce the fundamental frequency discrimination model to judge whether the dominant fundamental frequency track of each audio belongs to the song melody.

The original algorithm uses the shallow BP neural network as the fundamental frequency discrimination model. At present, the deep neural network shows better performance in the classification task and has been widely used in the field of speech signal processing. Therefore, sparse self coding neural network (SAENN) and softmax classifier will be used to establish the discrimination model of training fundamental frequency, so as to achieve better recognition effect of vocal fundamental frequency.

Sparse self coding (SAE) neural network adds sparse constraint on the basis of self coding (AE) neural network. An unsupervised feature learning algorithm is adopted. The algorithm limits the sparsity to the neurons in the middle hidden layer. The trained sparse noise reduction self coding neural network is equivalent to a nonlinear filter. A small number of hidden layer activation units are used to characterize the original signal and automatically screen the signal significance atoms, which is of great significance to improve the recognition rate of vocal fundamental frequency.

The front end of the fundamental frequency discrimination model is a sparse self coding neural network, and its structure is 12-200-50-16, that is, the input is a 12 dimensional MFCC feature that can reflect the envelope characteristics of the sound spectrum. The hidden layer neurons used in the middle are 200, 50 and 16 respectively. The back end of the last hidden layer neuron is connected to the softmax classifier, which contains two outputs. They represent the fundamental frequency of singing and instrumental music respectively [13].

In addition, the super parameters are set as follows: the weight penalty parameter λ is set to 0.0001; The expected sparse parameter p is 0.05; The weight value β of sparse penalty term is 3; The maximum number of iterations of pre training and softmax classifier is 500; The maximum number of fine-tuning iterations that saenn (sparse self coding neural network) can withstand is 2000.

During the training, a square wave equation algorithm is used to optimize the weight. The algorithm stores only the last m iteration curve information and uses it to construct a matrix close to the Hessian matrix. The cost of each iteration is low, and each iteration can provide positive clarity of the matrix. Based on the above basic frequency discrimination model. Determine if the dominant frequency of each sound segment is the main melody of the song. The specific steps are as follows.

Firstly, a comb filter with rectangular wave b(f) as the basic waveform is constructed. The filter frequency range is 0 ~ 4000Hz, and the formula is h(f)=k=1kδ(fkF0)b(f) h\left(f \right) = \sum\limits_{k = 1}^k {\delta \left({f - k{F_0}} \right) \cdot b\left(f \right)} Where k represents the number of waveforms within the frequency range.

Find the harmonic spectrum corresponding to the fundamental frequency F0: filter the amplitude spectrum of the signal with the comb filter constructed in the above step, and extract the Mel cepstrum parameter MFCC of the harmonic spectrum (the product of the combination of sound generation mechanism and human auditory perception characteristics, which is one of the important characteristic parameters of audio signal analysis).

The MFCC parameters are sent into the trained fundamental frequency discrimination model for recognition, and the judgment result of whether F0 is the fundamental frequency of singing is obtained.

If the number of frames judged as the fundamental frequency of the song in each voiced segment is less than 1 / 2 of the total number of frames in a segment, the track of F0 is not the main melody of the song, on the contrary, it is the main melody of the song.

Experimental results and analysis
Experimental data

The music data sets used in the experiment are all taken from the mir-1k data set provided by Hsu. It is composed of 110 Chinese karaoke songs. The singing part is 1000 music clips recorded by amateur song lovers with a sampling rate of 16 kHz. The background music and song are input into the left and right channels respectively, including the song fundamental frequency tag with a time interval of 10 ms. 500 pieces of music are randomly selected to train the neural network of the dominant fundamental frequency discrimination model, and the other 500 pieces of music are used as the main melody extraction test set.

Fundamental frequency discriminant model training and testing

In order to compare with the fundamental frequency discriminant model of the original algorithm. The same experimental conditions are used to train and test the SAE-based fundamental frequency discriminant model. The data used is shown in Table 1.

Test data of model training data

Number of dominant fundamental frequency frames Style dominant fundamental frame number Total frames
Training data 13789 14576 28365
test data 12475 17543 30018

Use the above training data. The quadratic wave equation algorithm is used to train the fundamental frequency discrimination model based on sparse self coding neural network. After completing the model training, the performance test is carried out by using the test set data. Firstly, extract the MFCC parameters of each frame of the test data signal and its corresponding label, then send the MFCC parameters of each frame of the signal into the fundamental frequency discrimination model, obtain the judgment result of whether it is the fundamental frequency of human voice, compare it with the label result, and finally count the recognition accuracy β: β=N1N \beta = {{{N_1}} \over N}

Where β is the recognition rate, N1 is the number of frames judged to be correct in the test data set, and N is the number of frames of the total test data.

Experiments show that the recognition accuracy of the model is 85.1%, and the performance index is about 5% higher than that of the original algorithm, which is better than the fundamental frequency discrimination model of the original algorithm. Subsequent experiments show that the application of this model can reduce the false alarm rate of melody location and improve the overall accuracy of the algorithm [14].

Music theme extraction experiment

There are two main tasks in extracting the main melody of a song: one is to judge whether the melody really exists, and the other is to accurately calculate the melody of the main melody (there should be no difference between the calculated sound level and the reference value. More than half a tone). Around the main task, the algorithm's performance is also assessed using five performance criteria: melody call speed (VR), pitch false alarm level (false signal level, VFAR), and original sound level (raw frequency accuracy, RPA), raw chromium accuracy (raw chromium accuracy, RCA), general accuracy (total accuracy, 0A). Based on the first five commonly used evaluation indices, the “average extraction time” of the sixth evaluation index is added to compare the calculated size of the improved algorithm and the original algorithm.

The experimental data used were 500 randomly selected music. The following experiments were performed under SIR 0 dB and SIR 5 dB. The specific results are shown in Figure 2 and Figure 3.

Figure 2

Experimental results when the SIR is 5dB

Figure 3

Experimental results when SIR is 0dB

As shown in Figure 2, Figure 3, all performance parameters of the enhanced algorithm are higher than the original algorithm, tone localization speed (VRR), initial sound frequency accuracy (RPA), initial chroma accuracy level (RCA), and the General Accuracy Level (OA) of the Four Parameters The false alarm level (VFAR) of the tone localization is reduced by about 2% if the signal and interference ratios are improved under different conditions, indicating that the improved algorithm is able to more accurately identify the accessory. and singing melody., because the accuracy of recognizing the basic frequency differential model in an enhanced algorithm is higher than in the original algorithm. In addition, the AET of the improved algorithm is reduced by approximately 0.12 seconds compared to the original algorithm, which ensures that the process calculation and complexity of the frequency function function of the improved algorithm is lower than that of the original algorithm melody of music [15].

Conclusion

This paper proposes an algorithm for extracting the quadratic wave equation and extracting the sound theme based on the basic frequency differentiation of the singing. Compared to traditional methods, this paper introduces a segmentation algorithm based on the stability properties of notes and a basic model for distinguishing frequencies based on the timbre characteristics of singing instruments. The note segmentation algorithm helps to control the predominant base frequency trajectory and the localization of the melody. Experiments have shown that the basic tone differentiation algorithm in this article can effectively reduce octave error when the signal interference is 5 dB and 0 dB, and when the false signal level of tone localization is much lower than other algorithms. The overall level of accuracy is higher than other algorithms, which can effectively produce the basic melody of the song.

Figure 1

The overall framework of the vocal music theme extraction algorithm
The overall framework of the vocal music theme extraction algorithm

Figure 2

Experimental results when the SIR is 5dB
Experimental results when the SIR is 5dB

Figure 3

Experimental results when SIR is 0dB
Experimental results when SIR is 0dB

Test data of model training data

Number of dominant fundamental frequency frames Style dominant fundamental frame number Total frames
Training data 13789 14576 28365
test data 12475 17543 30018

English D, Hickson D, Callander D, et al. Racial Discrimination, Sexual Partner Race/Ethnicity, and Depressive Symptoms Among Black Sexual Minority Men[J]. Archives of Sexual Behavior, 2020, 49(5):1799–1809. EnglishD HicksonD CallanderD Racial Discrimination, Sexual Partner Race/Ethnicity, and Depressive Symptoms Among Black Sexual Minority Men[J] Archives of Sexual Behavior 2020 49 5 1799 1809 10.1007/s10508-020-01647-5734034032222852 Search in Google Scholar

Tong C, Xu J, Fu Q, et al. Rapid extraction, discrimination and quantification of thermally unstable isomeric acteoside and isoacteoside in natural products by online extraction-quadrupole time-of-flight tandem mass spectrometry[J]. Analytical Methods, 2019, 11(16):2148–2154. TongC XuJ FuQ Rapid extraction, discrimination and quantification of thermally unstable isomeric acteoside and isoacteoside in natural products by online extraction-quadrupole time-of-flight tandem mass spectrometry[J] Analytical Methods 2019 11 16 2148 2154 10.1039/C8AY02584C Search in Google Scholar

Kim J, Oh J E, Lee J, et al. Rectal cancer: Toward fully automatic discrimination of T2 and T3 rectal cancers using deep convolutional neural network[J]. International Journal of Imaging Systems and Technology, 2019, 29(3):247–259. KimJ OhJ E LeeJ Rectal cancer: Toward fully automatic discrimination of T2 and T3 rectal cancers using deep convolutional neural network[J] International Journal of Imaging Systems and Technology 2019 29 3 247 259 10.1002/ima.22311 Search in Google Scholar

Cao Y, J Chen, Zhang G, et al. Characterization and discrimination of human colorectal cancer cells using terahertz spectroscopy[J]. Spectrochimica Acta Part A Molecular and Biomolecular Spectroscopy, 2021, 256(1):119713. CaoY ChenJ ZhangG Characterization and discrimination of human colorectal cancer cells using terahertz spectroscopy[J] Spectrochimica Acta Part A Molecular and Biomolecular Spectroscopy 2021 256 1 119713 10.1016/j.saa.2021.11971333823401 Search in Google Scholar

Murray E, Stepp C E. Relationships between vocal pitch perception and production: a developmental perspective[J]. Scientific Reports, 2020, 10(1):3912. MurrayE SteppC E Relationships between vocal pitch perception and production: a developmental perspective[J] Scientific Reports 2020 10 1 3912 10.1038/s41598-020-60756-2705431532127585 Search in Google Scholar

Zhu M X, Wang Y B, Chang D G, et al. Discrimination of three or more partial discharge sources by multi-step clustering of cumulative energy features[J]. IET Science, Measurement & Technology, 2019, 13(2):149–159. ZhuM X WangY B ChangD G Discrimination of three or more partial discharge sources by multi-step clustering of cumulative energy features[J] IET Science, Measurement & Technology 2019 13 2 149 159 10.1049/iet-smt.2018.5240 Search in Google Scholar

Shang R, Meng Y, Zhang W, et al. Graph Convolutional Neural Networks with Geometric and Discrimination information[J]. Engineering Applications of Artificial Intelligence, 2021, 104(1):104364. ShangR MengY ZhangW Graph Convolutional Neural Networks with Geometric and Discrimination information[J] Engineering Applications of Artificial Intelligence 2021 104 1 104364 10.1016/j.engappai.2021.104364 Search in Google Scholar

Lu L, Huang H. Component-based feature extraction and representation schemes for vehicle make and model recognition[J]. Neurocomputing, 2020, 372(Jan.8):92–99. LuL HuangH Component-based feature extraction and representation schemes for vehicle make and model recognition[J] Neurocomputing 2020 372 Jan. 8 92 99 10.1016/j.neucom.2019.09.049 Search in Google Scholar

Aminu M, Ahmad N A. Complex Chemical Data Classification and Discrimination Using Locality Preserving Partial Least Squares Discriminant Analysis[J]. ACS Omega, 2020, 5(41):26601–26610. AminuM AhmadN A Complex Chemical Data Classification and Discrimination Using Locality Preserving Partial Least Squares Discriminant Analysis[J] ACS Omega 2020 5 41 26601 26610 10.1021/acsomega.0c03362758126733110988 Search in Google Scholar

Boudraa S, Melouah A, Merouani H F. Improving mass discrimination in mammogram-CAD system using texture information and super-resolution reconstruction[J]. Evolving Systems, 2020, 11(4):697–706. BoudraaS MelouahA MerouaniH F Improving mass discrimination in mammogram-CAD system using texture information and super-resolution reconstruction[J] Evolving Systems 2020 11 4 697 706 10.1007/s12530-019-09322-4 Search in Google Scholar

Shi J, Jiang J, Chang W, et al. Multi-class discrimination of lymphadenopathy by using dual-modal ultrasound radiomics with elastography and B-mode ultrasound[J]. Sheng wu yi xue gong cheng xue za zhi = Journal of biomedical engineering = Shengwu yixue gongchengxue zazhi, 2019, 36(6):957–963. ShiJ JiangJ ChangW Multi-class discrimination of lymphadenopathy by using dual-modal ultrasound radiomics with elastography and B-mode ultrasound[J] Sheng wu yi xue gong cheng xue za zhi = Journal of biomedical engineering = Shengwu yixue gongchengxue zazhi 2019 36 6 957 963 Search in Google Scholar

Peng C W, Yang Z. Image Feature Extraction and Object Recognition Based on Vision Neural Mechanism[J]. International Journal of Pattern Recognition and Artificial Intelligence, 2020, 34(06):3340–3342. PengC W YangZ Image Feature Extraction and Object Recognition Based on Vision Neural Mechanism[J] International Journal of Pattern Recognition and Artificial Intelligence 2020 34 06 3340 3342 Search in Google Scholar

Toma E. Analysis of motor fan radiated sound and vibration waveform by automatic pattern recognition technique using “Mahalanobis distance”[J]. Journal of Industrial Engineering International, 2019, 15(1):81–92. TomaE Analysis of motor fan radiated sound and vibration waveform by automatic pattern recognition technique using “Mahalanobis distance”[J] Journal of Industrial Engineering International 2019 15 1 81 92 10.1007/s40092-018-0274-6 Search in Google Scholar

Mohit Arya and Amit Ujlayan. A Modified Iterative Method for Solving Nonlinear Functional Equation[J]. Applied Mathematics and Nonlinear Sciences, 2020, 6(2) : 347–360. AryaMohit UjlayanAmit A Modified Iterative Method for Solving Nonlinear Functional Equation[J] Applied Mathematics and Nonlinear Sciences 2020 6 2 347 360 Search in Google Scholar

Fatma Bulut Korkmaz and Mehmet Bektaandş. Second Binormal Motions of Inextensible Curves in 4-dimensional Galilean Space[J]. Applied Mathematics and Nonlinear Sciences, 2020, 5(1) : 249–254. KorkmazFatma Bulut BektaandşMehmet Second Binormal Motions of Inextensible Curves in 4-dimensional Galilean Space[J] Applied Mathematics and Nonlinear Sciences 2020 5 1 249 254 10.2478/amns.2020.1.00022 Search in Google Scholar

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