Fourier Descriptors Research Articles

Morphometric approaches to promote the use of exotic germplasm for improved food security and resilience to climate change: a kura clover example

Adaptation of agriculture to climate change and its associated ecological pressures will require new crops, novel trait combinations, and previously unknown phenotypic attributes to deploy in climate resilient cropping systems. Genebanks, a primary source of exotic germplasm for novel crops and breeding materials, need comprehensive methods to detect novel and unknown phenotypes without a priori information about the species or trait under consideration. We demonstrate how persistent homology (PH) and elliptical Fourier descriptors (EFD), two morphometric techniques easily applied to image-based data, can serve this purpose by cataloging leaf morphology in the USDA NPGS kura clover collection and demarcating a leaf morphospace for the species. Additionally, we identify a set of representative accessions spanning the leaf morphospace and propose they serve as a kura clover core collection. The core collection will be a framework for monitoring the effects of climate change on kura clover in situ diversity and determining the role of ex situ accessions in modern agriculture.

Population structure of Chelidonichthys lucerna in Portugal mainland using otolith shape and elemental signatures

ABSTRACTThe tub gurnard, Chelidonichthys lucerna, is considered the most important commercial fish species of the family Triglidae captured by the Portuguese traditional fisheries. However, the data available about its population structure, movement patterns and habitat connectivity is, at present, scarce. In this study, otolith chemistry and shape analyses of 90 individuals captured, between March and June 2016, in the three main fishing grounds of the Portuguese mainland coast (Matosinhos, Aveiro and Peniche) were investigated. Otolith morphological (shape indices and elliptic Fourier descriptors) and elemental (Ba:Ca, Fe:Ca, Mg:Ca, Mn:Ca, Sr:Ca and Zn:Ca) signatures of individuals with similar length range were assessed through uni and multivariate statistical tests. The overall combination of otolith elemental chemistry and morphology techniques revealed the highest re-classification success (74%) of samples to their original location and the existence of significant differences among sampling regions. However, linear discrimination function analyses and canonical analyses of principal coordinates did not fully discriminate C. lucerna individuals from the three sampling regions of Portugal. Moreover, the hereby data revealed a partial overlap among individuals from the different sampling regions. The obtained shape and chemical signatures suggest that C. lucerna is apparently a unique, although not necessarily homogenous, single population-unit in Portugal mainland, and that these fish populations should not be managed separately for fisheries purposes.

SAR village targets extraction and heterogonous image registration

Since the signal-to-noise ratio of synthetic aperture radar (SAR) image is low, it is difficult to match SAR images with optical images accurately. A new method of SAR village targets extraction and heterogonous image registration is proposed in this study. Median filter and partial differential method are first used to remove speckle noise; next, the grey level co-occurrence matrix algorithm is used by calculating four typical texture parameters of it to obtain preliminary regions of interest (ROI) of village targets and false alarm areas are cleared by proposed local-grey-level congruency method; then proper numbers of Fourier descriptors and morphological algorithms are used to describe ROI again to maintain the boundary features of targets better. Finally, HU moment invariants, which is combined with Euclidean distance and cosine similarity measurements, are utilised to achieve heterogonous image registration. The experimental results show that the root-mean-square-error of the registration image is small and the heterogonous registration image is accurate, demonstrating that the authors’ method is stable and accurate, and owns certain research value and broad application prospect as well.

Factual Extraction with Choicest Retrieval in CBIR Using Angular Robust Techniques

Content-Based Image Retrieval (CBIR) plays a vital role in various digital image processing fields such as image retrieval, classification, feature extraction, clustering, and indexing. In some cases, the high computational time as well the poor performance of similarity score makes the process of image retrieval an unsuitable one for CBIR having larger datasets. To overcome this trauma, the article presents a combined scheme to perform image retrieval and feature extraction using an eminent utilization of angular patterned wavelet Fourier descriptor with Randomized Robust Learning. With this prominent technique, both the local and the global feature descriptors are extracted to attain a maximum retrieval accuracy. Furthermore, the learning process is made prominent, owing to the unique extracted features. It makes the process of indexing similar images faster and the retrieval of relevant images with less computational time in an organized manner. Our proposed methodology is executed in MATLAB and is compared with the existing methodologies regarding retrieval accuracy and surfing time by fast indexed output.

Region-based image registration for remote sensing imagery

We propose an automatic region-based registration method for remote sensing imagery. In this method, we aim to register two images by matching region properties to address possible errors caused by local feature estimators. We apply automated image segmentation to identify the regions and calculate regional Fourier descriptors and standardized regional intensity descriptors for each region. We define a joint matching cost, as a linear combination of Euclidean distances, to establish and extract correspondences between regions. The segmentation technique utilizes kernel density estimators for edge localization, followed by morphological reconstruction and the watershed transform. We evaluated the registration performance of our method on synthetic and real datasets. We measured the registration accuracy by calculating the root-mean-squared error (RMSE) between the estimated transformation and the ground truth transformation. The results obtained using the joint intensity-Fourier descriptor were compared to the results obtained using Harris, Minimum eigenvalue, Features accelerated segment test (FAST), speeded-up robust features (SURF), binary robust invariant scalable keypoints (BRISK) and KAZE keypoint descriptors. The joint intensity-Fourier descriptor yielded average RMSE of 0.446±0.359 pixels and 1.152±0.488 pixels on two satellite imagery datasets consisting of 35 image pairs in total. These results indicate the capacity of the proposed technique for high accuracy. Our method also produces a lower registration error than the compared feature-based methods.

Application of otolith morphometry for the study of ontogenetic variations of Odontesthes argentinensis

The study of otolith morphometry is a tool widely used in numerous studies of fish populations (fish stocks, taxonomic, ecological, ontogeny, among others). The aim of this study was to detect ontogenetic variations in the otolith of Odontesthes argentinensis through the application of traditional and geometric morphometry and the association of these variations with ecological and trophic habits of the species. Fish (52 to 360 mm TL) were collected seasonally between years 2013–2016 in the southwest coast of the Atlantic Ocean (36°39’30.96”S - 56°40’40.09”W). Otolith shape indices (circularity, rectangularity, aspect ratio and surface occupied by sulcus) and Fourier descriptors were measured and compared through ontogenetic stages (I, II and III). The three stages analysed in the present study were differentiated by both traditional and geometric morphometry. The four analysed indices showed significant differences between stages (ANOVA Kruskal Wallis test, P < 0.001) and a simultaneous analysis of the morphometric variables also showed significant differences (Hotelling’s T2 < 0.001). The quadratic discriminant analysis performed on the Fourier descriptors showed a clear separation for each defined group. Therefore, the use of both methodologies simultaneously could be considered robust to evaluate the ontogenetic variations in this species. The observed changes could be associated to changes in the habitat throughout its development, to the sexual maturity of fish and to dietary shifting of these organisms.

Two new methodological approaches for assessing skeletal maturity in archeological human remains based on the femoral distal epiphysis

This study presents two new methodological approaches for estimating skeletal age from maturational changes in the femoral distal epiphysis. In the first approach, five maturity stages were coded based on morphological changes in the epiphysis that encompass the overall developmental process. Data were presented as age ranges for the different maturity stages in the reference sample. As this approach has a number of shortcomings for age assessment, a probabilistic approach was also used. Cross-validation was then used to compare the accuracy of the age estimation from the maturity stages with that from Pyle and Hoerr’s atlas. This study’s findings showed that Pyle and Hoerr’s atlas is more precise than our qualitative method in the oldest age categories. Nonetheless, results from the test of agreement between methods showed that skeletal age estimates from both methods are interchangeable. In the second approach, the overall shape of the femoral distal epiphyses was first analyzed based on elliptical Fourier descriptors (EFDs). Since the number of EFDs is excessively large, a principal component analysis (PCA) of these EFDs was carried out. PC1 scores were used to model the relationship between age and overall shape in a sample of 110 cases of the femoral distal epiphysis. Inverse and classical regression methods of calibration were used to explore the relationship. Based on our results, we recommend the use of a classical calibration model for those cases in which we suspect that the growth and development of the target individual is advanced or delayed relative to those of the Portuguese sample. Otherwise, the inverse calibration model is preferable. Both, quantitative and qualitative methods presented herein notably improve our abilities to estimate skeletal age using incomplete femora from skeletal samples.

Target Recognition in SAR Image by Joint Classification of Target Region and Shadow

Background: A synthetic aperture radar (SAR) automatic target recognition (ATR) method is proposed in this paper via the joint classification of the target region and shadow. Methods: The elliptical Fourier descriptors (EFDs) are used to describe the target region and shadow extracted from the original SAR image. In addition, the relative positions between the target region and shadow are represented by a constructed feature vector. The three feature vectors complement each other to provide more comprehensive descriptions of the target’s physical properties, e.g., sizes and shape. In the classification stage, the three feature vectors are jointly classified based on the joint sparse representation (JSR). JSR is a multi-task learning algorithm, which can not only represent each component properly but also exploit the inner correlations of different components. Finally, the target type is determined to the class with the minimum reconstruction error. Results: Experiments have been conducted on the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset. The proposed method achieves a high recognition accuracy of 96.86% for 10-class recognition problem under the standard operating condition (SOC). Moreover, robustness of the proposed method is also superior over the reference methods under the extended operating conditions (EOCs) like configuration variance, depression angle variance, and noise corruption. Conclusion: Therefore, the effectiveness and robustness of the proposed method can be quantitatively demonstrated by the experimental results.

Quantifying Dynamic Shapes in Soft Morphologies.

Soft materials are driving the development of a new generation of robots that are intelligent, versatile, and adept at overcoming uncertainties in their everyday operation. The resulting soft robots are compliant and deform readily to change shape. In contrast to rigid-bodied robots, the shape of soft robots cannot be described easily. A numerical description is needed to enable the understanding of key features of shape and how they change as the soft body deforms. It can also quantify similarity between shapes. In this article, we use a method based on elliptic Fourier descriptors to describe soft deformable morphologies. We perform eigenshape analysis on the descriptors to extract key features that change during the motion of soft robots, showing the first analysis of this type on dynamic systems. We apply the method to both biological and soft robotic systems, which include the movement of a passive tentacle, the crawling movement of two species of caterpillar (Manduca sexta and Sphacelodes sp.), the motion of body segments in the M. sexta, and a comparison of the motion of a soft robot with that of a microorganism (euglenoid, Eutreptiella sp.). In the case of the tentacle, we show that the method captures differences in movement in varied media. In the caterpillars, the method illuminates a prominent feature of crawling, the extension of the terminal proleg. In the comparison between the robot and euglenoids, our method quantifies the similarity in shape to ∼85%. Furthermore, we present a possible method of extending the analysis to three-dimensional shapes.

Evolution of Lineage-Specific Gene Networks Underlying the Considerable Fruit Shape Diversity in Persimmon.

The shapes of plant organs reflect the evolution of each lineage and have been diversified according to lineage-specific adaptations to environment. Research on the molecular pathways responsible for organ shapes has traditionally been focused mainly on leaves or flowers. Thus, little is known about the pathways controlling fruit shapes, despite their diversity in some plant species. In this study, we analyzed oriental persimmon (Diospyros kaki), which exhibits considerable diversity in fruit shapes among cultivars, to elucidate the underlying molecular mechanism using transcriptomic data and quantitative evaluation. First, to filter the candidate genes associated with persimmon fruit shapes, the whole gene expression patterns obtained using mRNA-Seq analysis from 100 individuals, including a segregated population and various cultivars, were assessed to detect correlations with principal component scores for fruit shapes characterized with elliptic Fourier descriptors. Next, a gene co-expression network analysis with weighted gene co-expression network analysis (WGCNA) package revealed that class 1 KNOX family genes and SEEDSTICK function as integrators along with some phytohormone-related genes, to regulate the fruit shape diversity. On the other hand, the OVATE family genes also contribute to fruit shape diversity, of which pathway would be potentially shared with other plant species. Evolutionary aspects suggest that acquisition of a high lineage-specific and variable expression of class 1 KNOX gene, knotted-like homeobox of Arabidopsis thaliana 1 (KNAT1), in young fruit is important for establishing the persimmon-specific mechanism that determines fruit shape diversity.

Evaluation of machine learning methods with Fourier Transform features for classifying ovarian tumors based on ultrasound images.

IntroductionOvarian tumors are the most common diagnostic challenge for gynecologists and ultrasound examination has become the main technique for assessment of ovarian pathology and for preoperative distinction between malignant and benign ovarian tumors. However, ultrasonography is highly examiner-dependent and there may be an important variability between two different specialists when examining the same case. The objective of this work is the evaluation of different well-known Machine Learning (ML) systems to perform the automatic categorization of ovarian tumors from ultrasound images.MethodsWe have used a real patient database whose input features have been extracted from 348 images, from the IOTA tumor images database, holding together with the class labels of the images. For each patient case and ultrasound image, its input features have been previously extracted using Fourier descriptors computed on the Region Of Interest (ROI). Then, four ML techniques are considered for performing the classification stage: K-Nearest Neighbors (KNN), Linear Discriminant (LD), Support Vector Machine (SVM) and Extreme Learning Machine (ELM).ResultsAccording to our obtained results, the KNN classifier provides inaccurate predictions (less than 60% of accuracy) independently of the size of the local approximation, whereas the classifiers based on LD, SVM and ELM are robust in this biomedical classification (more than 85% of accuracy).ConclusionsML methods can be efficiently used for developing the classification stage in computer-aided diagnosis systems of ovarian tumor from ultrasound images. These approaches are able to provide automatic classification with a high rate of accuracy. Future work should aim at enhancing the classifier design using ensemble techniques. Another ongoing work is to exploit different kind of features extracted from ultrasound images.

Design of a tomato classifier based on machine vision.

This paper attempts to design an automated, efficient and intelligent tomato grading method that facilitates the graded selling of the fruit. Based on machine vision, the color images of tomatoes with different morphologies were studied, and the color, shape and size were selected as the key features. On this basis, an automated grading classifier was created based on the surface features of tomatoes, and a grading platform was set up to verify the effect of the classifier. Specifically, the Hue value distributions of tomatoes with different maturities were investigated, and the Hue value ranges were determined for mature, semi-mature and immature tomatoes, producing the color classifier. Next, the first-order Fourier descriptor (1D- FD) was adopted to describe the radius sequence of tomato contour, and an equation was established to compute the irregularity of tomato contour, creating the shape classifier. After that, a linear regression equation was constructed to reflect the relationship between the transverse diameters of actual tomatoes and tomato images, and a classifier between large, medium and small tomatoes was produced based on the transverse diameter. Finally, a comprehensive tomato classifier was built based on the color, shape and size diameters. The experimental results show that the mean grading accuracy of the proposed method was 90.7%. This means our method can achieve automated real-time grading of tomatoes.

Detecting Brain Tumor using Machines Learning Techniques Based on Different Features Extracting Strategies.

Brain tumor is the leading cause of death worldwide. It is obvious that the chances of survival can be increased if the tumor is identified and properly classified at an initial stage. MRI (Magnetic Resonance Imaging) is one source of brain tumors detection tool and is extensively used in the diagnosis of brain to detect blood clots. In the past, many researchers developed Computer-Aided Diagnosis (CAD) systems that help the radiologist to detect the abnormalities in an efficient manner. The aim of this research is to improve the brain tumor detection performance by proposing a multimodal feature extracting strategy and employing machine learning techniques. In this study, we extracted multimodal features such as texture, morphological, entropybased, Scale Invariant Feature Transform (SIFT), and Elliptic Fourier Descriptors (EFDs) from brain tumor imaging database. The tumor was detected using robust machine learning techniques such as Support Vector Machine (SVM) with kernels: polynomial, Radial Base Function (RBF), Gaussian; Decision Tree (DT), and Naïve Bayes. Most commonly used Jack-knife 10-fold Cross- Validation (CV) was used for testing and validation of dataset. The performance was evaluated in terms of specificity, sensitivity, Positive Predictive Value (PPV), Negative Predictive Value (NPV), False Positive Rate (FPR), Total Accuracy (TA), Area under the receiver operating Curve (AUC), and P-value. The highest performance of 100% in terms of Specificity, Sensitivity, PPV, NPV, TA, AUC using Naïve Bayes classifiers based on entropy, morphological, SIFT and texture features followed by Decision Tree classifier with texture features (TA=97.81%, AUC=1.0) and SVM polynomial kernel with texture features (TA=94.63%). The highest significant p-value was obtained using SVM polynomial with texture features (P-value 2.65e-104) followed by SVM RB with texture features (P-value 1.96e-98). The results reveal that Naïve Bayes followed by Decision Tree gives highest detection accuracy based on entropy, morphological, SIFT and texture features.

Supervised dictionary learning supported classifier with feature fusion scheme to noninvasively detect TRISO-particle defects

This paper presents a novel method to support analyzing TRISO-particle failure rate by exploiting X-ray phase contrast imaging (PCI) modality to nondestructively visualize inter-defects and supervised dictionary learning to automatically distinguish cracked particles. Histogram of oriented gradient (HOG) operator was combined with local binary pattern histogram Fourier (LBP-HF) descriptor by canonical correlation analysis (CCA) method in order to extract crack features more significantly. Label consistent K-singular value decomposition (LC K-SVD) dictionary learning followed to encode features with more discriminability and learn a dictionary capable of excluding noise and intra-class variability to enforce recognition, with comparatively high recognition accuracy.

Automatic detection of intracranial aneurysm using LBP and Fourier descriptor in angiographic images.

Intracranial aneurysms (IA) are abnormal dilatation of the arteries at the circle of Willis whose rupture can lead to catastrophic complications such as hemorrhagic stroke. The purpose of this work is to detect IA in 2D-DSA images. The proposed detection framework uses local binary patterns for the determination of initial aneurysm candidates and generic Fourier descriptor (GFD) for false positive removal. Here, the designed framework takes DSA images including IA as input and produces images where the IA is clearly identified and localized. The multi-step approach is defined as the following: The first phase presents the determination of initial aneurysm candidates using the uniform local binary patterns (LBPs). The LBPs are calculated from these images in order to identify texture contents of both aneurysm and no-aneurysm classes. The second phase presents the false positives removal using a shape descriptor based on contours: the GFD. We demonstrated that the proposed detection method successfully recognized morphological features of intracranial aneurysm. The results demonstrated excellent agreement between manual and automated detections. With the computerized IA detection framework, all aneurysms were correctly detected with zero false negative and low FP rates. This study shows the potential of LBP and GFD as a feature descriptors and paves the way for a whole image analysis tool to predict intracranial aneurysm risk of rupture.

A Weighted Fourier and Wavelet-Like Shape Descriptor Based on IDSC for Object Recognition

This article presents an effective shape descriptor with a property of fast matching. This descriptor, called IDSC-wFW (a weighted Fourier and wavelet-like descriptor based on inner distance shape context), first rewrites shape histograms of IDSC descriptors, changing the histogram belonging to a point to the histogram belonging to a field, and sets the histogram of a field as a one-dimensional signal, then transforms this one-dimensional signal by using a Fourier transform and a transform similar to Haar wavelet. Finally, the two transform results are linearly combined to form a new descriptor. This new descriptor requires only a distance-based measure method during the matching stage. Experimental results on three well-known databases show that this new descriptor not only obtains accurate retrieval results but also runs fast.

METHOD FOR ASSESSING THE SYMMETRY OF OBJECTS ON DIGITAL BINARY IMAGES BASED ON FOURIER DESCRIPTOR

Abstract. In this paper we solve the problem of finding the symmetry axis of the object in a digital binary image. A new axial symmetry criterion is formulated for a connected discrete object. The problem of determining the symmetry measure and finding the symmetry axes arises in a variety of applications. In discrete images, exact symmetry is possible only in special cases. The disadvantage of the existing methods solving this problem is the high computational complexity. To improve computational efficiency, it is proposed to use the so-called Fourier descriptor. A new method for estimating the asymmetry of a discrete silhouette is proposed. The described algorithm for calculating the measure of asymmetry and determining the axis of symmetry is quadratic by the number of contour points. Methods for reducing the volume of calculations using a convex hull and taking into account the values of the modules of Fourier coefficients are proposed. Computational experiments are conducted with silhouettes of aircraft extracted from earth remote sensing images. The reliability of the described solution is established.

Diatom identification including life cycle stages through morphological and texture descriptors.

Diatoms are unicellular algae present almost wherever there is water. Diatom identification has many applications in different fields of study, such as ecology, forensic science, etc. In environmental studies, algae can be used as a natural water quality indicator. The diatom life cycle consists of the set of stages that pass through the successive generations of each species from the initial to the senescent cells. Life cycle modeling is a complex process since in general the distribution of the parameter vectors that represent the variations that occur in this process is non-linear and of high dimensionality. In this paper, we propose to characterize the diatom life cycle by the main features that change during the algae life cycle, mainly the contour shape and the texture. Elliptical Fourier Descriptors (EFD) are used to describe the diatom contour while phase congruency and Gabor filters describe the inner ornamentation of the algae. The proposed method has been tested with a small algae dataset (eight different classes and more than 50 samples per type) using supervised and non-supervised classification techniques obtaining accuracy results up to 99% and 98% respectively.

Radon–Fourier descriptor for invariant pattern recognition

Radon transform is not only robust to noise, but also independent on the calculation of pattern centroid. In this paper, Radon–Mellin transform (RMT), which is a combination of Radon transform and Mellin transform, is proposed to extract invariant features. RMT converts any object into a closed curve. Radon–Fourier descriptor (RFD) is derived by applying Fourier descriptor to the obtained closed curve. The obtained RFD is invariant to scaling and rotation. (Generic) R-transform and some other Radon-based methods can be viewed as special cases of the proposed method. Experiments are conducted on some binary images and gray images.

Real-time stereo matching on CUDA using Fourier descriptors and dynamic programming

Computation of stereoscopic depth and disparity map extraction are dynamic research topics. A large variety of algorithms has been developed, among which we cite feature matching, moment extraction, and image representation using descriptors to determine a disparity map. This paper proposes a new method for stereo matching based on Fourier descriptors. The robustness of these descriptors under photometric and geometric transformations provides a better representation of a template or a local region in the image. In our work, we specifically use generalized Fourier descriptors to compute a robust cost function. Then, a box filter is applied for cost aggregation to enforce a smoothness constraint between neighboring pixels. Optimization and disparity calculation are done using dynamic programming, with a cost based on similarity between generalized Fourier descriptors using Euclidean distance. This local cost function is used to optimize correspondences. Our stereo matching algorithm is evaluated using the Middlebury stereo benchmark; our approach has been implemented on parallel high-performance graphics hardware using CUDA to accelerate our algorithm, giving a real-time implementation.