Decomposing Strain Maps Using Fourier-Zernike Shape Descriptors

Selective Laser Melting (SLM) is a powder-bed additive manufacturing technique whose part quality depends critically on feedstock morphology. However, conventional powder characterization methods are low-throughput and qualitative, failing to capture the heterogeneity of industrial-scale batches. We present an automated, machine learning framework that couples high-throughput imaging with shape extraction and clustering to profile metallic powder morphology at scale. We evaluate three complementary approaches. The first uses an orientation-invariant variational autoencoder (VAE) to learn shape features that are insensitive to particle rotation, after which the resulting latent representations are grouped using clustering methods. The second applies classic shape descriptors – centroid distance functions, Fourier descriptors, and Zernike moments – followed by k-means or Gaussian mixture clustering to group particles with similar outlines. The third treats each particle’s radial profile as a continuous function and clusters these functional representations using the GPmix algorithm, allowing subtle differences in lobing and eccentricity to be captured. Across a dataset of approximately 126,000 powder images (0.5 – 102 μ m diameter), internal validity metrics identify the Fourier-descriptor + k-means pipeline as the most effective, achieving the lowest Davies–Bouldin index and highest Calinski–Harabasz score while maintaining sub-millisecond runtime per particle on a standard desktop workstation. The VAE provides orientation-invariant representations but at significantly higher computational cost, whereas the functional-data approach captures finer shape variations but requires a more complex configuration. Although the present work focuses on establishing the morphological-clustering framework, the resulting shape groups form a basis for future studies examining their relationship to flowability, packing density, and SLM part quality. Overall, this unsupervised learning framework enables rapid, automated assessment of powder morphology and supports tracking of shape evolution across reuse cycles, offering a path toward real-time feedstock monitoring in SLM workflows. • Automated machine learning framework for large-scale Selective Laser Melting (SLM) powder morphology profiling. • Evaluated three unsupervised pipelines: using variational autoencoder, shape descriptors, and functional clustering. • Fourier-descriptor + K-means achieved best accuracy, speed, and efficiency. • Framework distinguishes spherical, lobed, elongated, and defective particles. • Enables real-time monitoring of powder quality across reuse cycles in SLM.

Shape descriptors and mapping methods for full-field comparison of experimental to simulation data

This study aimed to demonstrate feasibility of statistical shape analysis techniques to identify distinguishing features of right ventricle (RV) shape as related to hemodynamic variables and outcome data in pulmonary hypertension (PH). Cardiovascular magnetic resonance images were acquired from 50 patients (33 PH, 17 non-PH). Contemporaneous right heart catheterization data were collected for all individuals. Outcome was defined by all-cause mortality and hospitalization for heart failure. RV endocardial borders were manually segmented, and three-dimensional surfaces reconstructed at end diastole and end systole. Registration and harmonic mapping were then used to create a quantitative correspondence between all RV surfaces. Proper orthogonal decomposition was performed to generate modes describing RV shape features. The first 15 modes captured over 98% of the total modal energy. Two shape modes, 8 (free wall expansion) and 13 (septal flattening), stood out as relating to PH state (mode 13: r = 0.424, p = 0.002; mode 8: r = 0.429, p = 0.002). Mode 13 was significantly correlated with outcome (r = 0.438, p = 0.001), more so than any hemodynamic variable. Shape analysis techniques can derive unique RV shape descriptors corresponding to specific, anatomically meaningful features. The modes quantify shape features that had been previously only qualitatively related to PH progression. Modes describing relevant RV features are shown to correlate with clinical measures of RV status, as well as outcomes. These new shape descriptors lay the groundwork for a noninvasive strategy for identification of failing RVs, beyond what is currently available to clinicians.

Traffic obstacle identification has been widely studied as part of the broader obstacle detection area for Autonomous Vehicles (AV). Existing in-vehicle perceptual systems are concentrated on obstacle detection for pedestrian or vehicle, and limited work has been conducted on obstacle comprehensive identification. In general, the feature selection is particularly critical in the process of obstacle identification. As a set of features to describe a given shape or contour, shape descriptor have attracted much attention in recent years and play an important roles in target recognition. This paper proposed a shape descriptor based obstacle comprehensive identification method where the traffic obstacles be classified into four classes: vehicle, lateral moving pedestrian, longitudinal moving pedestrian, and unknown (such as trees, road lamp etc.). Here first a variety of shape descriptors be extracted from the contour curve, such as Hu moment, Zernike moments, Krawtchouk moments, Shape Context, and Axis of Least Inertia. Then, these shape descriptors be used to identification obstacles respectively. Finally, the identification results are contrastive analyzed. Though a single shape descriptor does not achieve ideal identification results for traffic obstacle, but this will provide a new idea for obstacle comprehensive identification using shape descriptor in video for AV.

A methodology to characterize large-scale shape of macromolecular conformations is generalized and applied to a simple model of branched polymers. The standard global analysis of polymer configurations uses geometric shape descriptors, such as the mean radius of gyration. However, geometric descriptors alone do not depict well the intrincate folding features found in many macromolecules. For a more complete characterization, we employ here a new class of shape descriptors which convey the degree and complexity of the “entanglements” in a branched chain. Recently, the methodology has been applied to study statistical properties of linear polymer chains. In the present work, we extend the technique to branched polymers and analyze the configurational and long-chain behavior of their entanglement descriptors. A family of “stars” (polymers with a single branchpoint) with excluded volume interaction is studied, and the results are contrasted with those for linear chains. The relation between changes in geometric and shape descriptors within the polymer conformational space is presented. The complexity of entanglements for large chains and large stars are compared. The results suggest a similar scaling behavior of the entanglement descriptors for the two polymer architectures. © 1994 John Wiley & Sons, Inc.

Shape descriptors have demonstrated encouraging potential in retrieving images based on image content. A number of shape descriptors have been reported in the literature. Nevertheless, most of the reported descriptors still face accuracy and computational challenges. Fourier descriptors are considered to be promising descriptors as they are based on sound theoretical foundation, and possess computational efficiency and attractive invariance properties. In this paper, we propose a novel Fourier descriptor based on contour curvature. The proposed descriptor takes an unconventional view of the curvature-scale-space representation of a shape contour as it treats it as a 2-D binary image (hence referred to as Curvature-Scale Image, or CSI). The invariant descriptor is derived from the 2-D Fourier transform of the Curvature-Scale Image. This allows the descriptor to capture detailed dynamics of the shape curvature and enhance the efficiency of the shape matching process. Experiments using images from the MPEG-7 database have been conducted to compare the performance of the proposed descriptor with the Curvature- Scale-Space Descriptor (CSSD), the Generic Fourier Descriptor (GFD), and the 1-D Fourier Descriptor (1-FD). The proposed descriptor demonstrated superior performance.

The paper proposes a new spatio-temporal gait representation, called cycles gait Zernike moments (CGZM), to characterize human walking properties for individual recognition. Firstly, Zernike moments as shape descriptors are used to characterize gait silhouette shape. Secondly, we generate CGZM from Zernike moments of silhouette sequences. Finally, the phase and magnitude coefficientsof CGZM are utilized to perform classification by the modified Hausdorff distance (MHD) classifier. Experimental results show that the proposed approach have an encouraging recognition performance.

The Fourier descriptors (FDs) is a classical but still popular method for contour matching. The key idea is to apply the Fourier transform to a periodic representation of the contour, which results in a shape descriptor in the frequency domain. FDs are most commonly used to compare object silhouettes and object contours; the authors instead use this well-established machinery to describe local regions to be used in an object-recognition framework. Many approaches to matching FDs are based on the magnitude of each FD component, thus ignoring the information contained in the phase. Keeping the phase information requires us to take into account the global rotation of the contour and shifting of the contour samples. The authors show that the sum-of-squared differences of FDs can be computed without explicitly de-rotating the contours. The authors compare correlation-based matching against affine-invariant Fourier descriptors (AFDs) and WARP-matched FDs and demonstrate that correlation-based approach outperforms AFDs and WARP on real data. As a practical application the authors demonstrate the proposed correlation-based matching on a road sign recognition task.

Fourier descriptors (FDs) is a classical but still popular method for contour matching. The key idea is to apply the Fourier transform to a periodic representation of the contour, which results in a shape descriptor in the frequency domain. Fourier descriptors have mostly been used to compare object silhouettes and object contours; we instead use this well established machinery to describe local regions to be used in an object recognition framework. We extract local regions using the Maximally Stable Extremal Regions (MSER) detector and represent the external contour by FDs. Many approaches to matching FDs are based on the magnitude of each FD component, thus ignoring the information contained in the phase. Keeping the phase information requires us to take into account the global rotation of the contour and shifting of the contour samples. We show that the sum-of-squared differences of FDs can be computed without explicitly de-rotating the contours. We compare our correlation based matching against affine-invariant Fourier descriptors (AFDs) and demonstrate that our correlation based approach outperforms AFDs on real world data.

OpenCorr is an open source C++ library made for research and development of digital image correlation (DIC) technology. It provides full-function modules of 2D and stereo DIC, as well as digital volume correlation (DVC). In contrast with most of current open source DIC software which is application-oriented, the sophisticated design of OpenCorr makes it developer-friendly and facilitates the method study. Users can create DIC software quickly for specific applications by assembling the modules in this library and realize new algorithms readily by modifying the modules or incorporating additional modules. Three examples are given as the showcases for the capability of OpenCorr. The first one is an image feature guided DIC method, which can accurately measure large strain over 35%. The second is a stereo DIC method combining image feature guided DIC with an epipolar constraint aided algorithm to achieve enhanced robustness. The third is a novel self-adaptive DIC method, which dynamically optimize the size and shape of subset at each point of interest (POI) according to the nearby image features. The computation speed of DIC and DVC modules is evaluated through a few tests, which demonstrate superior running efficiency of the library. OpenCorr has attracted rapidly growing interest from both academic and industrial communities. It is expected to stimulate the advance and spread of DIC technology.

Plants play a crucial role in foodstuff, medicine, industry, and environmental protection. The skill of recognising plants is very important in some applications, including conservation of endangered species and rehabilitation of lands after mining activities. However, it is a difficult task to identify plant species because it requires specialized knowledge. Developing an automated classification system for plant species is necessary and valuable since it can help specialists as well as the public in identifying plant species easily. Shape descriptors were applied on the myDAUN dataset that contains 45 tropical shrub species collected from the University of Malaya (UM), Malaysia. Based on literature review, this is the first study in the development of tropical shrub species image dataset and classification using a hybrid of leaf shape and machine learning approach. Four types of shape descriptors were used in this study namely morphological shape descriptors (MSD), Histogram of Oriented Gradients (HOG), Hu invariant moments (Hu) and Zernike moments (ZM). Single descriptor, as well as the combination of hybrid descriptors were tested and compared. The tropical shrub species are classified using six different classifiers, which are artificial neural network (ANN), random forest (RF), support vector machine (SVM), k-nearest neighbour (k-NN), linear discriminant analysis (LDA) and directed acyclic graph multiclass least squares twin support vector machine (DAG MLSTSVM). In addition, three types of feature selection methods were tested in the myDAUN dataset, Relief, Correlation-based feature selection (CFS) and Pearson’s coefficient correlation (PCC). The well-known Flavia dataset and Swedish Leaf dataset were used as the validation dataset on the proposed methods. The results showed that the hybrid of all descriptors of ANN outperformed the other classifiers with an average classification accuracy of 98.23% for the myDAUN dataset, 95.25% for the Flavia dataset and 99.89% for the Swedish Leaf dataset. In addition, the Relief feature selection method achieved the highest classification accuracy of 98.13% after 80 (or 60%) of the original features were reduced, from 133 to 53 descriptors in the myDAUN dataset with the reduction in computational time. Subsequently, the hybridisation of four descriptors gave the best results compared to others. It is proven that the combination MSD and HOG were good enough for tropical shrubs species classification. Hu and ZM descriptors also improved the accuracy in tropical shrubs species classification in terms of invariant to translation, rotation and scale. ANN outperformed the others for tropical shrub species classification in this study. Feature selection methods can be used in the classification of tropical shrub species, as the comparable results could be obtained with the reduced descriptors and reduced in computational time and cost.

: Problem Statement: Pecan weevil is one of the most destructive pests of Oklahoma. The scope of this study is to develop a recognition system that can serve in a wireless imaging network for monitoring pecan weevils. Approach: The recognition methods used in this study are based on template matching. Five recognition methods were implemented: Normalized cross-correlation, Fourier descriptors, Zernike moments, String matching and Regional properties. The training set consisted of 205 pecan weevils and the testing set included 30 randomly selected pecan weevils and 74 other insects which typically exist in pecan habitat. Results: It was found that Region-based methods were better in representing and recognizing biological objects such as insects. Different recognition rates were obtained at different order of Zernike moments. The optimum result among the tested orders of Zernike moments was found to be at the order 3. The results also showed that using different number of Fourier descriptors may not significantly increase the recognition rate of this method. Conclusion: The most robust and reliable recognition rate was achieved when the Zernike moments and Region properties recognition methods were used in a combination. A positive match from either of these two independent tests would yield reliable results. Therefore, 100% recognition could be achieved by adopting the proposed algorithm. The processing time for such recognition is 0.44 sec.

Automated determination of poplar chip size distribution based on combined image and multivariate analyses

A novel sparse model based forensic writer identification

With the increasing number of available digital images, there is an urgent need of image content description to facilitate content based image retrieval (CBIR). Besides colour and texture, shape is an important low level feature in describing image content. An object can be photographed from different distances and angles. However, we often want to classify the images of the same object into one class, despite the change of perspective. So, it is desired to extract shape features that are invariant to the change of perspective. The shape of an object from one viewpoint to another can be linked through an affine transformation, if it is viewed from a much larger distance than its size along the line of sight. Those invariant shape features are known as affine invariant shape representations. Because of the change of perspective, it is more difficult to develop affine invariant shape representations than normal ones. The goal of this work is to develop affine invariant shape descriptors. Through shape retrieval experiments, we find that the performance of the existing affine invariant shape representations are not satisfactory. Especially, when the shape boundary is corrupted by noise, their performance degrades quickly. In this work, two new affine invariant contour-based shape descriptors, the ICA Fourier shape descriptor (ICAFSD) and the whitening Fourier shape descriptor (WFSD) have been developed. They perform better than most of the existing affine invariant shape representations, while having compact feature size and low computational time requirement. Four region-based affine-invariant shape descriptors, the ICA Zernike moment shape descriptor (ICAZMSD), the whitening Zernike moment shape descriptor (WZMSD), the ICA orthogonal Fourier Mellin moment shape descriptor (ICAOFMMSD), and the whitening orthogonal Fourier Mellin moment shape descriptor (WOFMMSD), are also proposed, in this work. They can be applied to both simple and complex shapes, and have close to perfect performance in retrieval experiments. The advantage of those newly proposed shape descriptors is even more apparent in experiments on shapes with added boundary noise: Their performance does not deteriorate as much as the existing ones.