Fourier Descriptors Research Articles

Feature Extraction and Identification of Rheumatoid Nodules Using Advanced Image Processing Techniques

Background/Objectives: Accurate detection and classification of nodules in medical images, particularly rheumatoid nodules, are critical due to the varying nature of these nodules, where their specific type is often unknown before analysis. This study addresses the challenges of multi-class prediction in nodule detection, with a specific focus on rheumatoid nodules, by employing a comprehensive approach to feature extraction and classification. We utilized a diverse dataset of nodules, including rheumatoid nodules sourced from the DermNet dataset and local rheumatologists. Method: This study integrates 62 features, combining traditional image characteristics with advanced graph-based features derived from a superpixel graph constructed through Delaunay triangulation. The key steps include image preprocessing with anisotropic diffusion and Retinex enhancement, superpixel segmentation using SLIC, and graph-based feature extraction. Texture analysis was performed using Gray-Level Co-occurrence Matrix (GLCM) metrics, while shape analysis was conducted with Fourier descriptors. Vascular pattern recognition, crucial for identifying rheumatoid nodules, was enhanced using the Frangi filter. A Hybrid CNN–Transformer model was employed for feature fusion, and feature selection and hyperparameter tuning were optimized using Gray Wolf Optimization (GWO) and Particle Swarm Optimization (PSO). Feature importance was assessed using SHAP values. Results: The proposed methodology achieved an accuracy of 85%, with a precision of 0.85, a recall of 0.89, and an F1 measure of 0.87, demonstrating the effectiveness of the approach in detecting and classifying rheumatoid nodules in both binary and multi-class classification scenarios. Conclusions: This study presents a robust tool for the detection and classification of nodules, particularly rheumatoid nodules, in medical imaging, offering significant potential for improving diagnostic accuracy and aiding in the early identification of rheumatoid conditions.

A New Method for Determining the Safety Distance Between Irregular Karst Cave and Circumferential Shield Tunnel

ABSTRACTWhen a shield tunnel passes through a karst area, the water‐filled cave can easily make the surrounding rock metamorphic, resulting in water inrush, ground collapse, and shield machine failure and other engineering hazards. Natural cavities have a significant degree of geometric irregularity due to groundwater alteration and soluble rock erosion. Considering the difficulties in describing the shape of a natural irregular cavity, circular, rectangular, and elliptical geometries have been simplified in most related studies. Based on the upper bound theorem of limit analysis, we established a three‐dimensional failure model including the karst caves located directly above and below the circumferential side of the tunnel. Then, we deduced the corresponding analytical solution of the critical safety distance (CSD). Furthermore, the effects of rock mass parameters, cave parameters, and geometric parameters on the CSD were analyzed. Then we designed the numerical simulation considering the irregular geometry shape at the circumferential side of tunnel using the Fourier descriptors. In addition, we estimated the CSDs for two failure models using the revised dichotomy and failure criterion. The findings demonstrated a quantifiable association between CSD and Fourier descriptors of irregular cave shape, resulting in the development of a CSD prediction model. These test results can provide a theoretical foundation and direction for predicting water inrush caused by the constrained irregular cave.

The issue of continuous characters in the copulatory bulb of Neodiplothele spiders: a morpho-geometric approach

ABSTRACT The definition of species boundaries in mygalomorph spiders is historically based on morphological characters, which can be problematic due to the homogeneous morphology and continuous variation across species. The male copulatory bulb of Neodiplothele, as of many mygalomorphs, is phenotypically diverse and the differences are displayed mostly by subtle shape variations. The purpose of this research was to evaluate the traditional morphology-based delimitation of species informal groups and assess the significance of morphological characters in the systematics of the highly variable and widespread mygalomorph spiders of the barychelid genus Neodiplothele. We conducted a geometric morphometric analysis on the bulb of specimens of Neodiplothele using Fourier descriptors. The results show that the bulb is rather difficult to apply as a discrete character in a taxonomic context and show the proximity of a group of undescribed species of Neodiplothele to both groups proposed in a previous revision, indicating a continuous variation. As a taxonomic character, the use of the copulatory bulb shape as a discrete character may be uninformative in the case of species that present one or more intermediate states, when the incorrect treatment of the character can result in a misrepresentation of shape diversity and equivocate inference of evolutionary relationships.https://zoobank.org/urn:lsid:zoobank.org:author:471C6BE5-D24C-4805-B2DE-EB89B6D1D8FA https://zoobank.org/urn:lsid:zoobank.org:author:D4955FF5-FE7F-4E68-AB2F-4A89593F9850

Sports Player Action Recognition based on Deep Learning

A sports auxiliary evaluation system suitable for China’s national conditions was established using big data and sports identification technology. First of all, this paper extends the data of normative behavior and constructs a normative library of scores and comparisons. The acquisition of 3D data is emphasized. The method based on Fourier descriptors is used to locate the motion accurately. In this way, better gait recognition results can be obtained. The Fourier characteristics before and after wavelet transform are compared with the actual object characteristics, and the results show that the proposed algorithm can extract the features with high precision. This scheme can obtain a more accurate identification effect. The system proposed in this paper provides a powerful means for judges to score.

Fourier Features and Machine Learning for Contour Profile Inspection in CNC Milling Parts: A Novel Intelligent Inspection Method (NIIM)

Form deviation generated during the milling profile process challenges the precision and functionality of industrial fixtures and product manufacturing across various sectors. Inspecting contour profile quality relies on commonly employed contact methods for measuring form deviation. However, the methods employed frequently face limitations that can impact the reliability and overall accuracy of the inspection process. This paper introduces a novel approach, the novel intelligent inspection method (NIIM), developed to accurately inspect and categorize contour profiles in machined parts manufactured through the milling process by computer numerical control (CNC) machines. The NIIM integrates a calibration piece, a vision system (RAM-StarliteTM), and machine learning techniques to analyze the line profile and classify the quality of contour profile deformation generated during CNC milling. The calibration piece is specifically designed to identify form deviations in the contour profile during the milling process. The RAM-StarliteTM vision system captures contour profile images corresponding to curves, lines, and slopes. An algorithm generates a profile signature, extracting Fourier descriptor features from the contour profile to analyze form deviations compared to an image reference. A feed-forward neural network is employed to classify contour profiles based on quality properties. Experimental evaluations involving 60 machined calibration pieces, resulting in 356 images for training and testing, demonstrate the accuracy and computational efficiency of the proposed NIIM for profile line tolerance inspection. The results demonstrate that the NIIM offers 96.99% accuracy, low computational requirements, 100% inspection capability, and valuable information to improve machining parameters, as well as quality classification.

Segmentation of beach plastic fragments’ contours based on self-organizing map and multi-shape descriptors: A rapid indication of fragmentation and wearing types

Environmental plastic fragments have been verified as byproducts of large plastic and its secondary pollutants including micro and nanoplastics. There are few quantitative studies available, but their contours have values for the weathering mechanisms. We used geometric descriptors, fractal dimensions, and Fourier descriptors to characterize field and artificial polyethylene and polypropylene samples as a means of investigating the contour characteristics. It provides a methodological framework for contour classification. Unsupervised classification was performed using self-organizing neural networks with size-invariance parameters. We revealed the isometric phenomenon of plastic fragments during fragmentation, i.e., that the degree of contour rounding and complexity increase and decrease, respectively, with decreasing fragment size. With an average error rate of 8.9 %, we can distinguish artificial samples from field samples. It was also validated by the difference in Carbonyl Index between groups. We propose a two-stage process for plastic fragmentation and give three types of contour features which were key in the description of fragmented contours, i.e., size, complexity, and rounding. Our work will improve the accuracy of characterizations regarding the weathering and fragmentation processes of certain kinds of plastic fragments. The contour parameters also have the potential to be applied in more realistic scenarios and varied polymers.

Shell shape variation of the symbiotic gastropod Phenacovolva rosea in Vietnam

This study investigates the shell variability of Phenacovolva rosea, a symbiotic gastropod inhabiting octocorals, in relation to geographical location and host coral species. We analyzed shells from 53 adult specimens collected at three locations in the north of Vietnam and one in the vicinities of Nha Trang City (southern Vietnam). To describe the shells' outlines, elliptical Fourier descriptors were applied. Based on the shell outline data, principal component analysis was performed. Additionally, height and width of P. rosea shells were measured. Only the first two principal components were effective, with the first principal component accounting for 92.8% of the variation. It closely correlated with width-to-height ratio of shells. According to dispersion analysis (ANOVA), shells in Nha Trang were significantly slimmer with longer terminal processes compared to those from the three northern locations. The coral host species also impacted shell shape when considering the entire dataset. However, this difference may have stemmed from shell variations between locations, as coral composition is not independent of location. When regional samples were analyzed separately, no significant impact of the host was detected. The factors that differed between northern locations and Nha Trang were then discussed, along with the mechanisms underlying their influence. We suggest that predation risk, influenced by water turbidity, is greater in the clearer waters of Nha Trang. This increased predator pressure may explain the presence of long terminals on P. rosea shells found in Nha Trang, potentially providing protection against some fish predators. Furthermore, the shorter and wider shells found in northern locations may be advantageous in waters with higher current speeds, whereas the long-teminal shells with narrow apertures observed in Nha Trang may be better suited for slower currents. The climate disparity, encompassing temperature and salinity mediated through precipitation, could also potentially influence shell morphology. However, the underlying mechanism remains unclear due to the complex nature of these interactions and the scarcity of literature data. Isolating host-specific shell shape traits from other factors proved challenging, given the close association between host species composition and location. Laboratory experiments modeling each factor independently may provide a solution to this issue.

Otolith Shape Analysis of Five Sillaginidae Species from the Persian Gulf and the Oman Sea

The discrimination power of sagittal otolith shape analysis is evaluated for five closely related sillaginid species from the Persian Gulf and the Oman Sea; (Sillago arabica, Sillago attenuata, Sillago indica, Sillago sihama and Sillaginopodys chondropus) besides the description of morphological characters using scanning electron microscopy (SEM). The identification of sillaginids is difficult due to the limited reliable diagnostic morphological characters. The otolith shape was described by six shape indices (Roundness, Rectangularity, Circularity, Ellipticity, Form factor and Aspect ratio) and Elliptic Fourier Descriptors (EFD). For all shape indices, there was at least an overlap between the two species and no one was significantly different among the five species. Based on EFD analysis all five species were discriminated (91.7%) evidencing the high taxonomic value of sagittal otolith for the studied taxa. SEM images revealed sulcus acusticus as homosulcoid with an inframedian position in all five species. S. arabica and S. sihama are characterized by having a pseudo-ostiocaudal, while S. indica, S. attenuate and Sillaginopodys chondropus have ostial mode of opening. The ostium was tubular and slightly curved in all studied species, which was more strongly curved in S. arabica. These findings suggest that the sagittal otolith shape is a reliable tool to recognize inter-specific diagnosis for sillginid species in the Persian Gulf and Oman Sea.

Otolith shape reveals the population structure of 'Malabar Labeo’, Labeo dussumieri (Valenciennes, 1842), in the four west-flowing rivers of India

Otolith shape variation in Labeo dussumieri from the four west-flowing rivers of India was analyzed using Wavelet coefficients and elliptic Fourier descriptors in the ShapeR package. The mean otolith shape of L. dussumieri varied significantly among sampling locations, with the posterior margin of the otolith showing the maximum variation. Otolith shape analysis also revealed variations between regions of different latitudes, with the northern (Narmada and Kundalika River) and southern populations (Achankovil and Chalakudy River) forming two distinct clusters. This variability in otolith shape might be attributed to the variation in environmental conditions prevailing in the sampling locations. The linear discriminant analysis based on elliptic Fourier descriptors and Wavelet coefficients showed an overall classification success of 89.03 % and 89.20 %, respectively. The present study validated that the lapillar otoliths are ideal for investigating the population structure of cyprinid fishes like L. dussumieri. The present study provided the first comprehensive information on the otolith shape analysis of L. dussumieri from the four west-flowing rivers of India.

New Parametric 2D Curves for Modeling Prostate Shape in Magnetic Resonance Images

Geometric shape models often help to extract specific contours in digital images (the segmentation process) with major precision. Motivated by this idea, we introduce two models for the representation of prostate shape in the axial plane of magnetic resonance images. In more detail, the models are two parametric closed curves of the plane. The analytic study of the models includes the geometric role of the parameters describing the curves, symmetries, invariants, special cases, elliptic Fourier descriptors, conditions for simple curves and area of the enclosed surfaces. The models were validated for prostate shapes by fitting the curves to prostate contours delineated by a radiologist and measuring the errors with the mean distance, the Hausdorff distance and the Dice similarity coefficient. Validation was also conducted by comparing our models with the deformed superellipse model used in literature. Our models are equivalent in fitting metrics to the deformed superellipse model; however, they have the advantage of a more straightforward formulation and they depend on fewer parameters, implying a reduced computational time for the fitting process. Due to the validation, our models may be applied for developing innovative and performing segmentation methods or improving existing ones.

Identification of Key Genes of Fruit Shape Variation in Jujube with Integrating Elliptic Fourier Descriptors and Transcriptome.

Jujube (Ziziphus jujuba) exhibits a rich diversity in fruit shape, with natural occurrences of gourd-like, flattened, and other special shapes. Despite the ongoing research into fruit shape, studies integrating elliptical Fourier descriptors (EFDs) with both Short Time-series Expression Miner (STEM) and weighted gene co-expression network analysis (WGCNA) for gene discovery remain scarce. In this study, six cultivars of jujube fruits with distinct shapes were selected, and samples were collected from the fruit set period to the white mature stage across five time points for shape analysis and transcriptome studies. By combining EFDs with WGCNA and STEM, the study aimed to identify the critical periods and key genes involved in the formation of jujube fruit shape. The findings indicated that the D25 (25 days after flowering) is crucial for the development of jujube fruit shape. Moreover, ZjAGL80, ZjABI3, and eight other genes have been implicated to regulate the shape development of jujubes at different periods of fruit development, through seed development and fruit development pathway. In this research, EFDs were employed to precisely delineate the shape of jujube fruits. This approach, in conjunction with transcriptome, enhanced the precision of gene identification, and offered an innovative methodology for fruit shape analysis. This integration facilitates the advancement of research into the morphological characteristics of plant fruits, underpinning the development of a refined framework for the genetic underpinnings of fruit shape variation.

Path synthesis of planar four-bar linkages for closed and open curves using elliptical Fourier descriptors

Path synthesis of planar four-bar linkages for closed and open curves using elliptical Fourier descriptors

Digital dual test syphilis/HIV detection based on Fourier Descriptors of Cyclic Voltammetry curves

Background:Effective and timely detection is vital for mitigating the severe impacts of Sexually Transmitted Infections (STI), including syphilis and HIV. Cyclic Voltammetry (CV) sensors have shown promise as diagnostic tools for these STI, offering a pathway towards cost-effective solutions in primary health care settings. Objective:This study aims to pioneer the use of Fourier Descriptors (FDs) in analyzing CV curves as 2D closed contours, targeting the simultaneous detection of syphilis and HIV. Methods:Raw CV signals are filtered, resampled, and transformed into 2D closed contours for FD extraction. Essential shape characteristics are captured through selected coefficients. A complementary geometrical analysis further extracts features like curve areas and principal axes lengths from CV curves. A Mahalanobis Distance Classifier is employed for differentiation between patient and control groups. Results:The evaluation of the proposed method revealed promising results with classification performance metrics such as Accuracy and F1-Score consistently achieving values rounded to 0.95 for syphilis and 0.90 for HIV. These results underscore the potential efficacy of the proposed approach in differentiating between patient and control samples for STI detection. Conclusion:By integrating principles from biosensors, signal processing, image processing, machine learning, and medical diagnostics, this study presents a comprehensive approach to enhance the detection of both syphilis and HIV. This setts the stage for advanced and accessible STI diagnostic solutions.

Microstructure reconstruction of 2D/3D random materials via diffusion-based deep generative models

Microstructure reconstruction serves as a crucial foundation for establishing process–structure–property (PSP) relationship in material design. Confronting the limitations of variational autoencoder and generative adversarial network within generative models, this study adopted the denoising diffusion probabilistic model (DDPM) to learn the probability distribution of high-dimensional raw data and successfully reconstructed the microstructures of various composite materials, such as inclusion materials, spinodal decomposition materials, chessboard materials, fractal noise materials, and so on. The quality of generated microstructure was evaluated using quantitative measures like spatial correlation functions and Fourier descriptor. On this basis, this study also achieved the regulation of microstructure randomness and the generation of gradient materials through continuous interpolation in latent space using denoising diffusion implicit model (DDIM). Furthermore, the two-dimensional microstructure reconstruction was extended to three-dimensional framework and integrated permeability as a feature encoding embedding. This enables the conditional generation of three-dimensional microstructures for random porous materials within a defined permeability range. The permeabilities of these generated microstructures were further validated through the application of the lattice Boltzmann method. The above methods provide new ideas and references for material reverse design.

Real-Time Cucumber Target Recognition in Greenhouse Environments Using Color Segmentation and Shape Matching

Accurate identification of fruits in greenhouse environments is an essential need for the precise functioning of agricultural robots. This study presents a solution to the problem of distinguishing cucumber fruits from their stems and leaves, which often have similar colors in their natural environment. The proposed algorithm for cucumber fruit identification relies on color segmentation and form matching. First, we get the boundary details from the acquired image of the cucumber sample. The edge information is described and reconstructed by utilizing a shape descriptor known as the Fourier descriptor in order to acquire a matching template image. Subsequently, we generate a multi-scale template by amalgamating computational and real-world data. The target image is subjected to color conditioning in order to enhance the segmenacktation of the target region inside the HSV color space. Then, the segmented target region is compared to the multi-scale template based on its shape. The method of color segmentation decreases the presence of unwanted information in the target image, hence improving the effectiveness of shape matching. An analysis was performed on a set of 200 cucumber photos that were obtained from the field. The findings indicate that the method presented in this study surpasses conventional recognition algorithms in terms of accuracy and efficiency, with a recognition rate of up to 86%. Moreover, the system has exceptional proficiency in identifying cucumber targets within greenhouses. This attribute renders it a great resource for offering technical assistance to agricultural robots that operate with accuracy.

Analysis of the properties and geometric characteristics of machined parts using computer vision

In milling contour profiles, tools create minute surface variations known as roughness. An algorithm is proposed to analyze the profile dimensional variation in milled parts by an artificial vision and Fourier descriptors as a measurement technique. The proposed method is based on the Fourier spectrum to analyze three profile signatures extracted from an image of a milled part with the aim of measuring the variation in three materials. It is found that when performing the profile machining process, the combination of the parameters: spindle speed, feed rate, cutting depth, and coolant fluid influence the dimensional variation of the part. The proposed approach concludes that this inspection method is faster and more efficient to guarantee the quality of parts manufactured by machining.

Frequency and Spatial Domain-Based Approaches for Recognition of Indian Sign Language Gestures

Objectives: The objective of this paper is to introduce and demonstrate an innovative approach for the recognition of Indian sign language gestures, with a focus on bridging communication gap between the deaf and hearing communities. The goal is to contribute to the development of effective tools and technologies that facilitate seamless communication between individuals using sign language and the people with no knowledge about sign language. Methods: The methodology consists of three key steps. First, data pre-processing involves resizing and contours extraction. Next, feature extraction employs Fourier descriptors for frequency domain analysis and gray-level-co-occurrence matrix for spatial domain analysis. Finally, various machine learning models including SVM, Random Forest, Logistic Regression, K-Nearest Neighbor and Naive Bayes are trained on a standard dataset. Findings: In our controlled experimental setup, we applied a diverse set of machine learning classifiers to evaluate the proposed approach for gesture recognition. Among the classifiers tested, K-Nearest Neighbors demonstrated the highest accuracy, achieving 99.82%. To validate the robustness of our approach, we employed k-fold cross-validation with 5 folds. Novelty: This study presents an innovative method for sign language recognition by employing a dual-domain fusion strategy that prominently emphasizes the frequency domain. Through the integration of Fourier descriptors, the research conducts a detailed frequency domain analysis to characterize the contour shapes of sign language gestures. The synergy with gray-level co-occurrence matrix texture features in the spatial domain analysis, contributes to the creation of a comprehensive feature vector. The proposed approach ensures a thorough exploration of gesture features, there by advancing the precision and efficacy of sign language recognition. Keywords: Indian Sign Language (ISL), Sign Language Recognition (SLR), Frequency domain, Spatial domain, Fourier descriptors, Gray level co­occurrence matrix (GLCM), K­ Fold

Morphometric Analysis of the Tibial Attachment Shape of the Anterior Cruciate Ligament and Its Relationship With the Location of the Anterior Horn of the Lateral Meniscus

Background: The success of anterior cruciate ligament (ACL) reconstruction relies on the accurate replication of the native ACL anatomy, including attachment shapes. The tibial attachment of the ACL exhibits significant shape variations with elliptical, C, and triangular shapes, highlighting the need for objective classification methods and additional information to identify individual anatomic variations. Hypothesis: The location of the attachment of the anterior horn of the lateral meniscus (AHLM) may determine the shape of the ACL attachment. Study Design: Cross-sectional study; Level of evidence, 3. Methods: The study used 25 knees from 17 Japanese cadavers for macroscopic anatomic examination and quantitative analysis. The shape of the ACL attachment was quantified using principal component analysis with elliptical Fourier descriptors, whereas the AHLM location was quantified by measuring its mediolateral and anteroposterior positions on the superior surface of the tibia. Reliability was assessed statistically. Results: The shape of the tibial attachment of the ACL varied among individuals and was classified as elliptical, C-shaped, or triangular. Scatterplots of the principal components of the ACL attachment shape showed overlapping regions of elliptical, C-shaped, and triangular ACL attachments, indicating that a C-shaped attachment is intermediate between elliptical and triangular attachments. The location of the AHLM attachment also varied, with areas in the anterolateral, anteromedial, or posteromedial region. The ACL shape and AHLM location were related, with elliptical, C-shaped, and triangular ACL attachments corresponding to anterolateral, anteromedial, and posteromedial AHLM attachments, respectively. Conclusion: The AHLM attachment location influences the shape of the ACL attachment. Information on the location of the AHLM attachment can aid in predicting the shape of the ACL attachment during ACL reconstruction, potentially improving footprint coverage.

Quantitative 2D fruit shape analysis of a wide range of pear genetic resources toward shape design breeding

The shape of a fruit is one of the main characteristics of fruit morphology, and its quantitative description is crucial to improve fruit quality. However, the shape of a pear fruit is relatively complex, and difficult to describe comprehensively. This study aimed to quantitatively analyze the morphological diversity of 2D fruit shapes of 276 cultivars, covering 6 groups including Pyrus pyrifolia, Pyrus bretschneideri, Pyrus ussuriensis, Pyrus sinkiangensis, Pyrus communis and interspecific hybridization, and discover shape traits with high heritability. Through an automated image processing method, the fruit contour was first accurately extracted, and then geometrical parameters and Fourier descriptors of the pear fruit shape were obtained. Furthermore, principal components (PCs) of the Fourier descriptors were analyzed, and the broad-sense heritability (H2) of the PCs and standardized width (WSD) were estimated. After that, the pear shape stability was calculated, and cultivars were clustered by their shape characteristics. This paper mainly discusses the longitudinal section, as the cross-section variation among cultivars is small. For the longitudinal section, the results showed more than 95 % of the two-dimensional shape variation can be explained by only six principal components; WSD20, WSD30 and PC1 have high H2; the shape stability of western pear was the lowest; a new class of shape was found by clustering the shape traits. The results indicated that the proposed pipeline can provide an objective and comprehensive quantitative description of pear fruit shape for a wide range of cultivars, which is necessary to discover the key genes determining pear shape. This approach is also beneficial for research on pear breeding and germplasm resource management.

Robust video hashing based on deep feature and quaternion generic Fourier descriptor for copy detection

Robust video hashing based on deep feature and quaternion generic Fourier descriptor for copy detection