Discrete Wavelet Analysis: A Mighty Approach for Image Segmentation





Discrete Wavelet Analysis, image segmentation, image processing, Fourier Transform


This paper explores the application of Discrete Wavelet Analysis, a mathematical and signal processing technique, in the context of image segmentation, which provide a pixel-level or region-level decomposition of the image, enabling the extraction of relevant information for subsequent analysis and interpretation. Introducing the basic image segmentation techniques and the DWA, this paper discovers that DWA has found widespread application in fields such as signal processing, image analysis, and data compression. Compared with Fourier Transform, DWA is more suitable for image segmentation, having unique advantages and characteristics. Among the procedures of image segmentation, the most important point is feature selection, which determine the criteria for distinguishing different regions within the image. Despite DWA has many advantages, this technology also owns many challenges and limitations, which may be solved by lasting academic research to refine and extend Discrete Wavelet Analysis methodologies for image segmentation. In short, this research highlights the promise of Discrete Wavelet Analysis, emphasizing the use of high- quality image processing.  


L. T. Thuong, T. T. Nha, and V. Giang, "GRAPH-BASED SIGNAL PROCESSING TO CONVOLUTIONAL NEURAL NETWORKS FOR MEDICAL IMAGE SEGMENTATION," SEATUC journal of science and engineering, vol. 3, no. 1, pp. 9-15, 2022.

S. S. L. Kumar et al., "Fully-automated, semantic segmentation of whole-body 18F-FDG PET/CT images based on data-centric artificial intelligence," Journal of nuclear medicine: official publication, Society of Nuclear Medicine, vol. 63, no. 12, 2022, doi: 10.2967/JNUMED.122.264063.

S.-H. Wang, "Polarimetric synthetic aperture radar image segmentation by convolutional neural network using graphical processing units," Journal of Real-Time Image Processing, vol. 15, no. 3, pp. 631-642, 2018, doi: 10.1007/s11554-017-0717-0.

M. Bernardo, F. Carlos, S. Samuel, S. Andreia, D. Paulo, and S. B. Sousa, "Are the Instructions Clear? Evaluating the Visual Characteristics of Augmented Reality Content for Remote Guidance," Multimodal Technologies and Interaction, vol. 6, no. 10, pp. 92-92, 2022.

M. Ricardo and R. Eduardo, "Removing non-nuclei information from histopathological images: A preprocessing step towards improving nuclei segmentation methods," Journal of Pathology Informatics, vol. 14, pp. 100315-100315, 2023.

L. Dan, M. Carol, Z. Cecilia, Z. Fei, and X. Qian, "Wound tissue segmentation by computerised image analysis of clinical pressure injury photographs: a pilot study," Journal of Wound Care, vol. 31, no. 8, pp. 710-719, 2022.

Y. Yao, W. Wang, Q. Wu, D. Liu, and J. Zheng, "Guest Editorial: Learning from limited annotations for computer vision tasks," IET Computer Vision, vol. 17, no. 5, pp. 509-512, 2023.

J. Chow, T. Palmeri, and I. Gauthier, "Haptic object recognition abilities correlate across feature types and with visual object recognition ability," Journal of Vision, vol. 22, no. 14, pp. 3260-3260, 2022.

Y. Liu and C. Hubo, "Cost-Efficient Image Semantic Segmentation for Indoor Scene Understanding Using Weakly Supervised Learning and BIM," Journal of Computing in Civil Engineering, vol. 37, no. 2, 2023, doi: 10.1061/JCCEE5.CPENG-5065.

T. Amy, "Automated Size Measurements of Halyomorpha halys (Stål) (Heteroptera: Pentatomidae) with Simple Image-Based Methodology," Florida Entomologist, vol. 105, no. 3, pp. 262-264, 2022.

J. Sun, "DSGA-Net: Deeply separable gated transformer and attention strategy for medical image segmentation network," Journal of King Saud University - Computer and Information Sciences, vol. 35, no. 5, p. 101553, 2023/05/01/ 2023, doi: https://doi.org/10.1016/j.jksuci.2023.04.006.

A. Tahir, Z. Junping, U. Inam, G. Y. Yasin, A. Osama, and G. Amr, "Multiscale Feature-Learning with a Unified Model for Hyperspectral Image Classification," Sensors (Basel, Switzerland), vol. 23, no. 17, 2023, doi: 0.1016/J.ISWA.2023.200274.

F. Yuncong, L. Yunfei, L. Zhicheng, L. Wanru, Y. Qingan, and Z. Xiaoli, "A Novel Interval Iterative Multi-Thresholding Algorithm Based on Hybrid Spatial Filter and Region Growing for Medical Brain MR Images," Applied Sciences, vol. 13, no. 2, pp. 1087-1087, 2023.

F. Chengcai, L. Fengli, and Z. Guoying, "Gradient- enhanced waterpixels clustering for coal gangue image segmentation," International Journal of Coal Preparation and Utilization, vol. 43, no. 4, pp. 677-690, 2023.

Y. Zhang, H. Guo, F. Chen, and H. Yang, "Weighted kernel mapping model with spring simulation based watershed transformation for level set image segmentation," Neurocomputing, vol. 249, pp. 1-18, 2017.

Y. Zepa, C. Insung, C. Juwhan, J. Jongha, R. Minyeong, and Y. H. Seok, "Deep learning-based pectoralis muscle volume segmentation method from chest computed tomography image using sagittal range detection and axial slice-based segmentation," PloS one, vol. 18, no. 9, pp. 10273-10292, 2023.

C. S. Woon, B. N. Rae, and P. K. Ryoung, "Deep Learning-based Multi-stage segmentation method using ultrasound images for breast cancer diagnosis," Journal of King Saud University - Computer and Information Sciences, vol. 34, no. 10PB, pp. 1946-1958, 2022.

Z. Yawu, W. Shudong, Z. Yulin, Q. Sibo, and Z. Mufei, "WRANet: wavelet integrated residual attention U-Net network for medical image segmentation," Complex & intelligent systems, pp. 11-13, 2023.

T. Javid, M. Faris, A. Aziz, and P. Akhtar, "Integrated representation for discrete Fourier and wavelet transforms using vector notation," Mehran University Research Journal of Engineering and Technolo gy, vol. 41, no. 3, pp. 175-184, 2022.

H. K. Kelele, M. B. Kahsay, and T. K. Nielsen, "Dynamic Response Analysis of Wind Turbine Structure to Turbulent Wind Load: Comparative Assessment in Time and Frequency Domains," Applied Mechanics, vol. 4, no. 3, pp. 841-855, 2023.

Z. Yu, J. Chen, B. Zhang, D. Wang, and H. Jiang, "Selection Method of Optimal Wavelet Basis Function for Aeromagnetic Anomaly Signal Processing," Journal of Coastal Research, vol. 115, no. sp1, pp. 530-534, 2020.

F. Sajjad, "High-resolution diffusion-weighted imaging at 7 Tesla: single-shot readout trajectories and their impact on signal-to-noise ratio, spatial resolution and accuracy," NeuroImage, vol. 274, pp. 120159-120159, 2023.

C. Jagrati, P. A. Kumar, H. Angel, S. P. Dev, P. Chetan, and K. Rakesh, "99m-Tc TRODAT Single-Photon Emission Computerized Tomography Scan Image Compression using Singular Value Decomposition," Indian journal of nuclear medicine: IJNM: the official journal of the Society of Nuclear Medicine, India, vol. 38, no. 2, pp. 103-109, 2023.

S. Shen and I. Toshio, "IMPROVING OBJECT FEATURE DETECTION USING POINTCLOUD AND IMAGE FUSION," SEATUC journal of science and engineering, vol. 2, no. 1, pp. 28-33, 2021.

Y. Guangji, "Some invariant and inverse invariant characters of information systems under homomorphisms based on data compression," International Journal of General Systems, vol. 49, no. 3, pp. 302-333, 2020.

X. Li and X. Ruan, "Discrete Fourier transform based frequency characteristics of iterative learning control for linear discretetime systems," Advances in Difference Equations, vol. 2019, no. 1, pp. 1-22, 2019.

O. Agboje, O. Idowu-Bismark, and A. Ibhaze, "Comparative Analysis of Fast Fourier Transform and Discrete Wavelet Transform Based MIMO-OFDM," International Journal on Communications Antenna and Propagation IRECAP, vol. 7, no. 2, pp. 168-175, 2017.

V. Srivardhan, "Stratigraphic correlation of wells using discrete wavelet transform with fourier transform and multi-scale analysis," Geomechanics and Geophysics for Geo-Energy and Geo-Resources, vol. 2, no. 3, pp. 137-150, 2016.

Y. Zhang, "Magnetic resonance brain image classification based on weighted-type fractional Fourier transform and nonparallel support vector machine," International Journal of Imaging Systems and Technology, vol. 25, no. 4, pp. 317-327, 2015, doi: 10.1002/ima.22144.

S. Wang, "Pathological Brain Detection by a Novel Image Feature—Fractional Fourier Entropy," Entropy, vol. 17, no. 12, pp. 8278-8296, 2015.

L. Lian, R. Wei-Xin, and W. Shi-Dong, "Fractional Fourier transform: Time-frequency representation and structural instantaneous frequency identification," Mechanical Systems and Signal Processing, vol. 178, 2022, doi: 10.1016/J.YMSSP.2022.109305.

K. Pritiranjan and R. K. Chandra, "An Efficient DCT-II Based Harmonic Wavelet Transform for Time-Frequency Analysis," Journal of Signal Processing Systems, vol. 94, no. 12, pp. 1381-1394, 2022.

Y.-D. Zhang, "Computer-aided diagnosis of abnormal breasts in mammogram images by weighted-type fractional Fourier transform," (in English), Advances in Mechanical Engineering, Article vol. 8, no. 2, Feb 2016, Art no. 11, doi: 10.1177/1687814016634243.

G. Saifallah and M. Hatem, "Time-frequency concentration and localization operators associated with the directional short-time fourier transform," Journal of Pseudo-Differential Operators and Applications, vol. 13, no. 3, 2022, doi: 10.1007/S11868-022-00465-8.

G. S. P. et al., "Tracking IMF Fluctuations Nearby Sun Using Wavelet Analysis: Parker Solar Probe First Encounter Data," Geomagnetism and Aeronomy, vol. 62, no. 1-2, pp. 138-150, 2022.

W. Haiming, Y. Shaopu, L. Yongqiang, and L. Qiang, "Compressive sensing reconstruction for rolling bearing vibration signal based on improved iterative soft thresholding algorithm," Measurement, vol. 210, pp. 168-175, 2023.

W. Jing, W. Li, S. Miao, L. Y. ni, and H. Y. hua, "Application of Boundary Local Feature Scale Adaptive Matching Extension EMD Endpoint Effect Suppression Method in Blasting Seismic Wave Signal Processing," Shock and Vibration, vol. 2021, 2021, doi: 10.1155/2021/2804539.

K. Evert, S. Shahrokh, and C. D. Y. C, "Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform," The Journal of the Acoustical Society of America, vol. 142, no. 2, p. 697, 2017.

S. Wang, "Detection of Left-Sided and Right-Sided Hearing Loss via Fractional Fourier Transform," Entropy, vol. 18, no. 5, 2016, Art no. 194, doi: 10.3390/e18050194.

Y. Zhang, "Tea Category Identification Using a Novel Fractional Fourier Entropy and Jaya Algorithm," Entropy, vol. 18, no. 3, p. 77, 2016.

Y. Zhang, "A Multilayer Perceptron Based Smart Pathological Brain Detection System by Fractional Fourier Entropy," Journal of Medical Systems, vol. 40, no. 7, p. 173, 2016/06/02 2016, doi: 10.1007/s10916-016-0525-2.

H. Guosheng, W. Jinjun, and R. Akira, "Orthogonal wavelet multiresolution analysis of the turbulent boundary layer measured with two-dimensional time-resolved particle image velocimetry," Physical review. E, vol. 99, no. 5-1, p. 053105, 2019.

L. N. Wu, "Improved image filter based on SPCNN," (in English), Science In China Series F-Information Sciences, Article vol. 51, no. 12, pp. 2115-2125, Dec 2008, doi: 10.1007/s11432-008-0124-z.

L. N. Wu, "Pattern Recognition via PCNN and Tsallis Entropy," (in English), Sensors, Article vol. 8, no. 11, pp. 7518-7529, Nov 2008, doi: 10.3390/s8117518.

B. Natarajan and P. Krishnan, "Contrast Enhancement Based Image Detection Using Edge Preserved Key Pixel Point Filtering," COMPUTER SYSTEMS SCIENCE AND ENGINEERING, vol. 42, no. 2, pp. 423-438, 2022.

T. T. A. Azevedo, F. A. Dias, d. F. P. Rogério, N. L. Alves, M. A. Santana, and d. N. M. Zanchetta, "A stain color normalization with robust dictionary learning for breast cancer histological images processing," Biomedical Signal Processing and Control, vol. 85, 2023, doi: 10.1016/J.BSPC.2023.104978.

D. Gyanesh, P. Rutuparna, S. Leena, and A. Sanjay, "A Novel Segmentation Error Minimization-Based Method for Multilevel Optimal Threshold Selection Using Opposition Equilibrium Optimizer," International Journal of Image and Graphics, vol. 23, no. 02, 2023, doi: 10.1142/S0219467823500213.

M. Khaled, L. HengChao, A. Zaid, R. Ali, and M. Asad, "Weakly supervised building semantic segmentation via superpixel‐CRF with initial deep seeds guiding," IET Image Processing, vol. 16, no. 12, pp. 3258-3267, 2022.

K. B. Pavan, K. Arvind, and P. Rajoo, "A generic post-processing framework for image dehazing," Signal, Image and Video Processing, vol. 17, no. 6, pp. 3183-3191, 2023.

T. Hongjun et al., "Enhancing PV panel segmentation in remote sensing images with constraint refinement modules," Applied Energy, vol. 350, 2023, doi: 10.1016/J.APENERGY.2023.121757.

B. Manoel et al., "An automated method to analyze root filling voids and gaps using confocal microscopy images," Odontology, 2023, doi: 10.1007/S10266-023-00859-0.

Z. Junhua, G. Minghao, C. Pengzhi, L. Yang, C. Jun, and L. Huanxi, "Weld Defect Segmentation in X-ray Image with Boundary Label Smoothing," Applied Sciences, vol. 12, no. 24, pp. 12818-12818, 2022.

S. Pohchoo et al., "Evaluation of Compressed SENSE on Image Quality and Reduction of MRI Acquisition Time: A Clinical Validation Study," Academic radiology, 2023, doi: 10.1016/J.ACRA.2023.07.013.

J. Man, X. Jingmei, Y. Ruoxi, L. Zongan, Z. Ling, and W. Ye, "Three filters for the enhancement of the images acquired from fluorescence microscope and weak-light-sources and the image compression," Heliyon, vol. 9, no. 9, pp. A4063-A4083, 2023.

B. Sebastián et al., "Easy One-Step Amplification and Labeling Procedure for Copy Number Variation Detection," Clinical chemistry, vol. 66, no. 3, pp. 463-473, 2020.

E. Mohammad, T. Solale, and A. Malek, "A unique color-coded visualization system with multimodal information fusion and deep learning in a longitudinal study of Alzheimer's disease," Artificial Intelligence In Medicine, vol. 140, pp. 102543-102543, 2023.

J. Jeong, Y. H. Yoon, and J. H. Park, "Reliable Road Scene Interpretation Based on ITOM with the Integrated Fusion of Vehicle and Lane Tracker in Dense Traffic Situation," Sensors, vol. 20, no. 9, p. 2457, 2020.

Y. Jinsoo, L. Seongjin, L. Wontaek, and S. Myoungho, "Human-like Decision-Making System for Overtaking Stationary Vehicles Based on Traffic Scene Interpretation," Sensors, vol. 21, no. 20, pp. 6768-6768, 2021.

L. Chun, Y. Jian, Z. Jiangbin, and N. Xuan, "An Unsupervised Port Detection Method in Polarimetric SAR Images Based on Three-Component Decomposition and Multi-Scale Thresholding Segmentation," Remote Sensing, vol. 14, no. 1, pp. 205-205, 2022.

N. V. Glukhova, "Method for Determining the Measurement Uncertainty of the Detailing Coefficients of the Wavelet Transform of Image Brightness Profiles," Measurement Techniques, vol. 63, no. 3, pp. 177-183, 2020.

S. C. Kosaraju, J. Hao, H. M. Koh, and M. Kang, "Deep-Hipo: Multi-scale receptive field deep learning for histopathological image analysis," Methods, vol. 179, no. prepublish, pp. 3-13, 2020.

Q. Zhe et al., "A reconstruction and convolution operations enabled variant vision transformer with gastroscopic images for automatic locating of polyps in Internet of Medical Things," Information Fusion, vol. 101, 2024, doi: 10.1016/J.INFFUS.2023.102007.

B. Piyalee and D. Arighna, "Design Space Exploration of Matrix–Matrix Convolution Operation," Journal of Circuits, Systems and Computers, vol. 30, no. 16, 2021, doi: 10.1142/S0218126621502881.

Z. Peijia and H. Jiwu, "Discrete wavelet transform and data expansion reduction in homomorphic encrypted domain," IEEE transactions on image processing: a publication of the IEEE Signal Processing Society, vol. 22, no. 6, pp. 2455-68, 2013.

S. Debabrata, B. Sayan, and M. P. Madan, "An efficient interpolating wavelet collocation scheme for quasi‐exactly solvable Sturm–Liouville problems in ℝ+," Mathematical Methods in the Applied Sciences, vol. 45, no. 7, pp. 4002-4023, 2022.

F. Jiahui, Q. Jingze, L. Yuanning, D. Liyan, and L. Zhen, "A task processing efficiency improvement scheme based on Cloud-Edge architecture in computationally intensive scenarios," Journal of Parallel and Distributed Computing, vol. 181, 2023, doi: 10.1016/J.JPDC.2023.104742.

Z. Zhang, "The Improvement of the Discrete Wavelet Transform," Mathematics, vol. 11, no. 8, 2023, doi: 10.3390/MATH11081770.




How to Cite

Meng Wu and Y. Hou, “Discrete Wavelet Analysis: A Mighty Approach for Image Segmentation”, EAI Endorsed Trans e-Learn, vol. 9, Dec. 2023.