Quantitative Shape Analysis Research Articles

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.

Variational Autoencoders for Generating Synthetic Tractography-Based Bundle Templates in a Low-Data Setting.

White matter tracts generated from whole brain tractography are often processed using automatic segmentation methods with standard atlases. Atlases are generated from hundreds of subjects, which becomes time-consuming to create and difficult to apply to all populations. In this study, we extended our prior work on using a deep generative model - a Convolutional Variational Autoencoder - to map complex and data-intensive streamlines to a low-dimensional latent space given a limited sample size of 50 subjects from the ADNI3 dataset, to generate synthetic population-specific bundle templates using Kernel Density Estimation (KDE) on streamline embeddings. We conducted a quantitative shape analysis by calculating bundle shape metrics, and found that our bundle templates better capture the shape distribution of the bundles than the atlas data used in the original segmentation derived from young healthy adults. We further demonstrated the use of our framework for direct bundle segmentation from whole-brain tractograms.

Brain pericytes in culture display diverse morphological and functional phenotypes

Pericytes play several important functions in the neurovascular unit including contractile control of capillaries, maintenance of the BBB, regulation of angiogenesis, and neuroinflammation. There exists a continuum of pericyte subtypes along the vascular tree which exhibit both morphological and transcriptomic differences. While different functions have been associated with the pericyte subtypes in vivo, numerous recent publications have used a primary human brain vascular pericytes (HBVP) cell line where this pericyte heterogeneity has not been considered. Here, we used primary HBVP cultures, high-definition imaging, cell motility tracking, and immunocytochemistry to characterise morphology, protein expression, and contractile behaviour to determine whether heterogeneity of pericytes also exists in cultures. We identified five distinct morphological subtypes that were defined using both qualitative criteria and quantitative shape analysis. The proportion of each subtype present within the culture changed as passage number increased, but pericytes did not change morphological subtype over short time periods. The rate and extent of cellular and membrane motility differed across the subtypes. Immunocytochemistry revealed differential expression of alpha-smooth muscle actin (αSMA) across subtypes. αSMA is essential for cell contractility, and consequently, only subtypes with high αSMA expression contracted in response to physiological vasoconstrictors endothelin-1 (ET1) and noradrenaline (NA). We conclude that there are distinct morphological subtypes in HBVP culture, which display different behaviours. This has significance for the use of HBVP when modelling pericyte physiology in vitro where relevance to in vivo pericyte subtypes along the vascular tree must be considered.Graphical abstract

Sharpening the mesowear tool: geometric morphometric analysis of cusp shape and diet in ruminants

Mesowear is a dietary proxy that relates attritive wear and abrasive wear to the shape of worn tooth cusps of ungulates. Traditional mesowear methods categorize cusps according to relief and sharpness. A geometric morphometric approach has the potential to measure shape with higher precision and to discover unrecognized aspects of cusp shape, possibly improving the efficacy of mesowear. We quantified mesowear in extant Ruminantia, using a 2-D semilandmark outline technique on upper second molar metacones generated from photographs. Among the 91 species sampled, 65 were preassigned to dietary categories, browser, grazer, mixed feeder, and frugivore based on substantiated documentation of diet in the wildlife literature. Metacone cusp shape and metacone mesowear score were found to be independent of size. Principal component and discriminant function analyses of Procrustes transformed semilandmark coordinates revealed two diet-related components of cusp shape. The primary component is related to the traditional mesowear variables of cusp height and side steepness. The secondary shape component reveals variation in the mesiodistal symmetry of the metacone and may relate to a proal vector during the power stroke phase or the relative orientation of the cusps with respect to the chewing stroke vector. Discriminant function analysis of semilandmark data accurately classified the diets of species more frequently (67.2%) than the traditional mesowear method (56.1%). The semilandmark data successfully recognized the diets of grazing and browsing species with correct classification rates ranging from 69% to 95%. The diets of frugivorous and mixed feeding species were less frequently correctly recognized (33%–53%). Mixed feeding diets may be more difficult to recognize due to more heterogeneous diets when compared to browsers and grazers. Frugivores are more difficult to recognize because their rounded cusp apices resemble those of mixed feeders and grazers. We conclude that quantitative shape analysis improves the potential of mesowear. When used as a dietary proxy, we anticipate that mesowear analysis will correctly categorize the diets of most species. When misclassifications are made, they may most often be misclassifications of generalist mixed feeders and frugivores as either browsers or grazers.

Shape analysis and morphometric evaluation of the obturator foramen in dry human bones

Purpose: This study aims to analyze the shape and morphometric features of the obturator foramen (OF) in dry human bones.
 Methods: Forty-six (Right:15, Left:31) dry human coxal bones were evaluated. Photographs of samples for morphometric measurements were taken using a transparent osteometric box (TOB) designed for this study. Horizontal and vertical diameters of OF were measured according to two different principles. Measurements were taken to determine the localization of OF on the coxal bone (hip bone) relative to the acetabulum, pubis, and ischium. Shape analysis (visual typing) of OF was performed with the conventional method. In order to examine the shape variations of the OF in more detail, quantitative shape analysis based on Elliptic Fourier Analysis was performed with the SHAPE software.
 Results: A significant difference was observed between the diameter measurements obtained by the two methods (p

Large-scale analysis and computer modeling reveal hidden regularities behind variability of cell division patterns in Arabidopsis thaliana embryogenesis.

Noise plays a major role in cellular processes and in the development of tissues and organs. Several studies have examined the origin, the integration or the accommodation of noise in gene expression, cell growth and elaboration of organ shape. By contrast, much less is known about variability in cell division plane positioning, its origin and links with cell geometry, and its impact on tissue organization. Taking advantage of the first-stereotyped-then-variable division patterns in the embryo of the model plant Arabidopsis thaliana, we combined 3D imaging and quantitative cell shape and cell lineage analysis together with mathematical and computer modeling to perform a large-scale, systematic analysis of variability in division plane orientation. Our results reveal that, paradoxically, variability in cell division patterns of Arabidopsis embryos is accompanied by a progressive reduction of heterogeneity in cell shape topology. The paradox is solved by showing that variability operates within a reduced repertoire of possible division plane orientations that is related to cell geometry. We show that in several domains of the embryo, a recently proposed geometrical division rule recapitulates observed variable patterns, suggesting that variable patterns emerge from deterministic principles operating in a variable geometrical context. Our work highlights the importance of emerging patterns in the plant embryo under iterated division principles, but also reveal domains where deviations between rule predictions and experimental observations point to additional regulatory mechanisms.

Morphological growth dynamics, mechanical stability, and active microtubule mechanics underlying spindle self-organization

The spindle is a dynamic intracellular structure self-organized from microtubules and microtubule-associated proteins. The spindle's bipolar morphology is essential for the faithful segregation of chromosomes during cell division, and it is robustly maintained by multifaceted mechanisms. However, abnormally shaped spindles, such as multipolar spindles, can stochastically arise in a cell population and cause chromosome segregation errors. The physical basis of how microtubules fail in bipolarization and occasionally favor nonbipolar assembly is poorly understood. Here, using live fluorescence imaging and quantitative shape analysis in Xenopus egg extracts, we find that spindles of varied shape morphologies emerge through nonrandom, bistable self-organization paths, one leading to a bipolar and the other leading to a multipolar phenotype. The bistability defines the spindle's unique morphological growth dynamics linked to each shape phenotype and can be promoted by a locally distorted microtubule flow that arises within premature structures. We also find that bipolar and multipolar spindles are stable at the steady-state in bulk but can infrequently switch between the two phenotypes. Our microneedle-based physical manipulation further demonstrates that a transient force perturbation applied near the assembled pole can trigger the phenotypic switching, revealing the mechanical plasticity of the spindle. Together with molecular perturbation of kinesin-5 and augmin, our data propose the physical and molecular bases underlying the emergence of spindle-shape variation, which influences chromosome segregation fidelity during cell division.

Prenatal Diagnosis of Craniosynostosis Using Ultrasound.

Craniosynostosis is typically diagnosed postnatally. Prenatal diagnosis would allow for improved parental counseling and facilitate timely intervention. Our purpose was to determine whether prenatal ultrasound can be used to diagnose nonsyndromic craniosynostosis. The authors reviewed 22 prenatal ultrasounds of infants known to have nonsyndromic craniosynostosis and 22 age-matched controls. Cross-sectional images at the plane used to measure biparietal diameter were selected and cranial shape of each participant was parameterized and used to discriminate affected patients from controls. The results from quantitative shape analysis were compared with results from a blinded visual inspection alone. Among the 22 patients, the most common diagnosis was sagittal synostosis ( n = 11), followed by metopic synostosis ( n = 6). The average gestational age at time of ultrasound of controls and synostotic patients was 26 weeks and 6.8 days at the junction of the second and third trimesters. The controls and synostotic cases segregated into statistically different populations by their shape profiles ( p < 0.001). An automatic shape classifier using leave-one-out cross-validation correctly classified the 44 images as normal versus synostotic 85 percent of the time (sensitivity, 82 percent; specificity, 87 percent). Cephalic index was a poor indicator of sagittal synostosis (45 percent sensitivity). Visual inspection alone demonstrated only a fair level of accuracy (40 to 50 percent agreement) in identifying cases of synostosis (kappa, 0.09 to 0.23). Craniosynostosis can be identified on prenatal ultrasound with good sensitivity using formal shape analysis. Cephalic index and visual inspection alone performed poorly. Diagnostic, II.

MR quantitative 3D shape analysis helps to distinguish mucinous cystic neoplasm from serous oligocystic adenoma.

PURPOSE We aimed to assess the performance of quantitative 3D shape analysis in the differential diagno- sis of pancreatic serous oligocystic adenoma (SOA) and mucinous cystic neoplasm (MCN). METHODS Four hundred thirty-two patients diagnosed with serous cystic neoplasms (SCNs) or MCNs were retrospectively reviewed from August 2014 to July 2019 and finally 87 patients with MCNs (n = 45) and SOAs (n = 42) were included. Clinical data and magnetic resonance morphologic fea- tures with 3D shape analysis of lesions (shape sphericity, compacity, and volume) were recorded and compared between MCNs and SOAs according to the pathology. Univariable and multivari- able regression analyses were used to identify independent impact factors for differentiating MCN from SOA. RESULTS The age of MCN patients was younger than SOAs (43.02 ± 10.83 years vs. 52.78 ± 12.31 years; OR = 0.275; 95% CI: 0.098-0.768; P = .014). MCN has a higher female/male ratio than SOA (43/2 vs. 27/15; OR = 40.418; 95% CI: 2.704-604.171; P = .007) and was more often located in the distal of pancreas (OR = 31.403; 95% CI: 2.985-330.342; P = .004). Shape_Sphericity derived from 3D shape analysis was a significant independent factor in the multivariable analysis and the value of MCN was closer to 1 than SOA (OR = 35.153; 95% CI: 5.301-237.585; P < .001). Area under the receiver operating characteristic curve (AUC) of Shape_Sphericity was 0.923 (optimal cutoff value was 0.964876). CONCLUSION Shape_Sphericity in combination with age, sex, and location could help to distinguish MCN from SOA.

Shape Matters in Magnetic-Field-Assisted Assembly of Prolate Colloids.

An anisotropic colloidal shape in combination with an externally tunable interaction potential results in a plethora of self-assembled structures with potential applications toward the fabrication of smart materials. Here we present our investigation on the influence of an external magnetic field on the self-assembly of hematite-silica core–shell prolate colloids for two aspect ratios ρ = 2.9 and 3.69. Our study shows a rather counterintuitive but interesting phenomenon, where prolate colloids self-assemble into oblate liquid crystalline (LC) phases. With increasing concentration, particles with smaller ρ reveal a sequence of LC phases involving para-nematic, nematic, smectic, and oriented glass phases. The occurrence of a smectic phase for colloidal ellipsoids has been neither predicted nor reported before. Quantitative shape analysis of the particles together with extensive computer simulations indicate that in addition to ρ, a subtle deviation from the ideal ellipsoidal shape dictates the formation of this unusual sequence of field-induced structures. Particles with ρ = 2.9 exhibit a hybrid shape containing features from both spherocylinders and ellipsoids, which make their self-assembly behavior richer than that observed for either of the “pure” shapes. The shape of the particles with higher ρ matches closely with the ideal ellipsoids, as a result their phase behavior follows the one expected for a “pure” ellipsoidal shape. Using anisotropic building blocks and external fields, our study demonstrates the ramifications of the subtle changes in the particle shape on the field-directed self-assembled structures with externally tunable properties.

A Nanoscale Shape-Discovery Framework Supporting Systematic Investigations of Shape-Dependent Biological Effects and Immunomodulation.

Since it is now possible to make, in a controlled fashion, an almost unlimited variety of nanostructure shapes, it is of increasing interest to understand the forms of biological control that nanoscale shape allows. However, a priori rational investigation of such a vast universe of shapes appears to present intractable fundamental and practical challenges. This has limited the useful systematic investigation of their biological interactions and the development of innovative nanoscale shape-dependent therapies. Here, we introduce a concept of biologically relevant inductive nanoscale shape discovery and evaluation that is ideally suited to, and will ultimately become, a vehicle for machine learning discovery. Combining the reproducibility and tunability of microfluidic flow nanochemistry syntheses, quantitative computational shape analysis, and iterative feedback from biological responses in vitro and in vivo, we show that these challenges can be mastered, allowing shape biology to be explored within accepted scientific and biomedical research paradigms. Early applications identify significant forms of shape-induced biological and adjuvant-like immunological control.

Distinct roles of nonmuscle myosin II isoforms for establishing tension and elasticity during cell morphodynamics.

Nonmuscle myosin II (NM II) is an integral part of essential cellular processes, including adhesion and migration. Mammalian cells express up to three isoforms termed NM IIA, B, and C. We used U2OS cells to create CRISPR/Cas9-based knockouts of all three isoforms and analyzed the phenotypes on homogenously coated surfaces, in collagen gels, and on micropatterned substrates. In contrast to homogenously coated surfaces, a structured environment supports a cellular phenotype with invaginated actin arcs even in the absence of NM IIA-induced contractility. A quantitative shape analysis of cells on micropatterns combined with a scale-bridging mathematical model reveals that NM IIA is essential to build up cellular tension during initial stages of force generation, while NM IIB is necessary to elastically stabilize NM IIA-generated tension. A dynamic cell stretch/release experiment in a three-dimensional scaffold confirms these conclusions and in addition reveals a novel role for NM IIC, namely the ability to establish tensional homeostasis.

3D MRI of the Knee.

Three-dimensional (3D) magnetic resonance imaging (MRI) of the knee is widely used in musculoskeletal (MSK) imaging. Currently, 3D sequences are most commonly used for morphological imaging. Isotropic 3D MRI provides higher out-of-plane resolution than standard two-dimensional (2D) MRI, leading to reduced partial volume averaging artifacts and allowing for multiplanar reconstructions in any plane with any thickness from a single high-resolution isotropic acquisition. Specifically, isotropic 3D fast spin-echo imaging, with options for tissue weighting similar to those used in multiplanar 2D FSE imaging, is of particular interest to MSK radiologists. New applications for 3D spatially encoded sequences are also increasingly available for clinical use. These applications offer advantages over standard 2D techniques for metal artifact reduction, quantitative cartilage imaging, nerve imaging, and bone shape analysis. Emerging fast imaging techniques can be used to overcome the long acquisition times that have limited the adoption of 3D imaging in clinical protocols.

A novel approach for computerized quantitative image analysis of proximal femur bone shape deformities based on the hip joint symmetry

As a result of most of the bone disorders seen in hip joints, shape deformities occur in the structural form of the hip joint components. Image-based quantitative analysis and assessment of these deformities in bone shapes are very important for the evaluation, treatment, and prognosis of the various hip joint bone disorders. In this article, a novel approach for the image-based computerized quantitative analysis of proximal femur shape deformities is presented. In the proposed approach, shape deformities of the pathological proximal femurs were quantified over the contralateral healthy proximal femur shape structure of the same patient in 2D by taking the hip joint symmetry property of human anatomy into consideration. It is based on the idea that if the right and left proximal femurs in bilateral hip joints are highly symmetrical and also if one of the proximal femurs is healthy and the contralateral one is pathological, the non-overlapping bone shape regions can represent the deformities in pathological proximal femurs when both proximal femurs are registered to overlap each other. In the methodological process of the proposed study, a set of image preprocessing operations was primarily performed on the raw magnetic resonance imaging (MRI) data. Then, the segmented proximal femurs in bilateral hip joint images were automatically aligned with the Iterative Closest Point (ICP) rigid registration method. Following the registration, a set of image postprocessing operations was performed on the images of proximal femurs aligned. In the quantification phase, the bone shape deformities in pathological proximal femurs were quantified simply in terms of the mismatching area in 2D by measuring a shape variation index representing the total bone shape deformity ratio. To evaluate the proposed quantitative shape analysis approach, bilateral hip joints in a total of 13 coronal MRI sections of 13 patients with Legg-Calve-Perthes disease (LCPD) were used. Experimental studies have shown that the proposed approach has quite promising results in the quantitative representation of the pathological proximal femur shape deformities. Furthermore, consistent results have been observed for the Waldenström classification stages of the disease. The shape deformity ratios in pathological proximal femurs were quantified as 9.44% (±1.40), 18.38% (±6.30), 24.73% (±12.42), and 27.66% (±10.41), respectively for the Initial, Fragmentation, Reossification, and Remodelling stages of LCPD with the quantification error rates of 0.29% (±0.16), 0.58% (±0.71), 1.12% (±0.82), and 0.80% (±0.98). Additionally, a mean error rate of 0.65% (±0.68) was observed for the quantified shape deformity ratios of all samples.

ASO Author Reflections: Quantitative Shape Analysis of Thyroid Nodules: A Small But Important Step Towards Software-Based Preoperative Evaluation of Thyroid Nodules.

ASO Author Reflections: Quantitative Shape Analysis of Thyroid Nodules: A Small But Important Step Towards Software-Based Preoperative Evaluation of Thyroid Nodules.

Tectonic evolution of the Karakoram metamorphic complex (NW Himalayas) reflected in the 3D structures of spiral garnets: Insights from X-ray computed micro-tomography

Spiral garnet porphyroblasts are known to record lengthy periods of deformation and metamorphism by preserving single or multiple FIAs (Foliation Intersection Axis) formed normal to tectonic shortening directions. Thanks to technological advances in X-ray computed micro-tomography (XCMT), FIAs can now be readily determined in relatively large samples in contrast to previous methods that require the preparation of a set of radial vertical and horizontal thin sections of samples. XCMT scanning not only alleviates tedious thin section based procedures but also illuminates the complete internal architecture of a rock sample allowing three-dimensional (3D) quantitative shape analysis of an individual porphyroblast as well as precise measurement of FIAs. We applied the technique to a sample from the Hunza Valley in the Karakoram metamorphic complex (KMC), NW Himalayas, containing numerous garnet porphyroblasts with spiral-shaped inclusion trails. The XCMT imaging reveals an E–W trending FIA within the sample, which is consistent with orthogonal N–S collision of the India-Kohistan Island Arc with Asia. Garnet long axes (XGT) have variable plunges that define a broad sub-vertical maximum and a small sub-horizontal maximum. The XGT principle maxima lie at N-090 and N-120. Smaller maxima lie at N-020 and N-340. Geometric relationships between XGT axes and FIA orientation in the sample suggest that porphyroblast shapes are controlled by the geometry of the lens-shaped microlithons in which they tend to nucleate and grow. The orientation of inclusion trails and matrix foliations in the sample are correlated with three discrete tectono-metamorphic events that respectively produced andalusite, sillimanite and kyanite in the KMC. Late staurolite growth in the sample reveals how the rocks extruded to the surface via a significant role of roll-on tectonics, which can be correlated with the Central Himalayas.

DendroScan: an open source tool to conduct comparative statistical tests and dendrogrammatic analyses on particle morphometry

Quantitative shape analysis of juvenile pyroclasts is applied in volcanology to reconstruct the dynamics and styles of eruptions, and to explore the details of tephra transport, dispersal, and emplacement. Morphometric analyses often include comparison of multiple data sets with a set of dimensionless shape parameters. Here we present “DendroScan”, an open source Matlab program that provides the user with all the multivariate statistical methods needed to produce such morphometric comparisons. Serving as a statistical “toolbox”, DendroScan conducts Levene-, t-, and equivalence tests, presenting the results in ad hoc interpretable graphs. Furthermore, it is designed to conduct dendrogrammatic analyses of particle morphometry, a recently developed approach for the inter-comparison of multiple morphometric data sets. DendroScan produces tree diagrams, in which the analysed samples are sorted according to their morphometric dissimilarity, allowing the user to identify, e.g., samples that are statistically equivalent. To demonstrate DendroScan’s potential, ten experimental samples are compared with volcanic ash samples generated by the Havre 2012 deep-sea eruption in the Kermadec arc (New Zealand). We show how, using DendroScan-based results, information on the eruptive mechanism can be inferred, and how the cooling history of the experimental melt is reflected in the dissimilarity of thermally granulated fragments.

Articulatory tongue shape analysis of Mandarin alveolar-retroflex contrast.

As existing descriptions are likely too narrow to reflect a broader range of articulatory variability in Mandarin production, this study is undertaken to explore qualitative and quantitative tongue shape analysis in Mandarin sibilants. Tongue movement data are collected from 18 adult Mandarin speakers producing six sibilants in three vowel contexts. Acoustic information is also analyzed to establish the articulatory-acoustic correspondence. In addition to the common retroflex and bunched shapes, the results discovered a humped shape (e.g., a single, posterior lingual constriction) in most of Mandarin retroflex tokens. This shape is one variant of North American English /r/, but yet identified in Mandarin production. The humped shape adds to the literature and expands existing descriptions of Mandarin retroflex tongue configurations. Despite the shape differences, the general many-to-one articulatory-acoustic mappings also holds true for Mandarin retroflexes. However, while curvature analyses based on Cartesian coordinates significantly differentiated contrastive shapes in retroflex production, these analyses were not equally reliable in separating the alveolar-retroflex distinction, likely due to individual differences. The tongue contour changes in the place contrast were instead quantified by calculations with polar coordinates. The preliminary findings on Mandarin retroflexes are discussed in terms of vocal tract morphology, with possible lip protrusion.

Shape difference of mud clasts depending on depositional facies: application of newly modified elliptic Fourier analysis to hybrid event beds

ABSTRACT Hybrid event beds are the deposits from sediment gravity flows that change their rheological behavior through their passage, entraining muddy sediments and damping turbulence. Muddy facies of hybrid event beds are often associated with abundant mud clasts which show a wide variety of size and shape. The variation of clast occurrence in hybrid event beds is expected to preserve the information of entrainment and transport processes of muddy sediments in submarine density currents. However, previous analyses of hybrid event beds have focused on describing the overall clast occurrence rather than the statistical size and shape analyses because traditional shape parameters are incapable of characterizing the complex shape of mud clasts. Here, a new quantitative grain-shape analysis of mud clasts is conducted and allows visualization of the spatial variation of clast size and shape, which suggests the wide variety of origin and transport systems of entrained mud clasts. This new method revises the traditional elliptic Fourier analysis, substituting Fourier power spectra (FPS) for traditional elliptic Fourier descriptors to overcome the mirror-wise shape problem. Further, principal-component analysis is shown to capture significant shape attributes more effectively than traditional shape parameters. The proposed method is applied to mud clasts in sediment-gravity-flow deposits in the lower Pleistocene Otadai Formation, central Japan. Results imply that there are distinctive shape and size differences of mud clasts that are strongly associated with depositional facies rather than the distance from the source. The clasts have a higher angularity than other facies in the debrite intervals in hybrid event beds. It is also shown that clasts in sandy, structureless facies have different characteristics in shapes based on elongation and convexity compared to laminated facies. Comparison between different shape-analysis methods demonstrates that none of the traditional methods are able to visualize these trends as effectively as the method presented herein. These results highlight the importance of the quantitative shape analysis of sediment grains and the effectiveness of FPS-based elliptic Fourier analysis.

Fourier Shape Analysis, FSA: Freeware for quantitative study of particle morphology

Shape analysis is of paramount importance in sedimentology. Particle morphology is a very useful texture parameter that provides information about particle history and is used to characterize and classify sedimentary material. Particle shape description has been both an important and a controversial subject. The most convincing description of shape defines particle shape by three hierarchical parameters: form, roundness, and surface texture (Barrett, 1980). Many different methods have been proposed to measure these parameters. Among them, Fourier shape analysis is particularly notable. Fourier analysis separates the three parameters into frequency ranges. The low frequency range is related to form, the middle frequency range to roundness and the high frequency to surface texture. However, determining where the boundaries lie between the different morphological classes is not an easy task and has been an unsolvable problem since the FSA method was first proposed. The same is true for the signal-to-noise limit. To date, this information has been obtained empirically and with great uncertainty. One of the most important contributions of this work has been to quantitatively constrain the harmonic ranges corresponding to the morphological ranges proposed by Barrett, and to determine the best possible approximation for the upper limit of the signal and the onset of noise. To estimate these ranges, we propose here two original methodologies based on analysis of the cumulative amplitude spectrum (CAS), and on simulating the effect of artificial noise acting on a well-known geometric figure. The CAS of 3664 volcaniclastic particles and of 106 artificially silhouette charts have been quadrisected into form, roundness, roughness and noise using an optimization process. The analysis indicates overall that the limits are well constrained into a narrow range of harmonics with a small variance. The results obtained are reliable and allow the range of harmonics that contains a useful signal to be extended up to harmonic 256. The method has been successfully applied to the standard figures of Krumbein (1941a) and of Powers (1953), efficiently separating the different classes of roundness. As an example, the methodology has been applied to a real-life case where there was doubt about the pristine nature of the materials from some outcrops related to the block-and-ash flow deposit of the July 17, 1999 eruption of the Colima volcano. The results obtained applying the method show promising results, indicating the potential of FSA information to solve this ambiguity. The powerful, user-friendly FSA software that we distribute freely (open code) can be very useful for characterizing volcano-sedimentary and sedimentary deposits. To date, there is no other software for FSA studies. Moreover, FSA can be useful in other fields of science and engineering where quantitative particle shape analysis is needed.