Three-dimensional Shape Analysis Research Articles

Three-dimensional analysis of particulates in mineral processing systems by cone beam X-ray microtomography

In general X-ray-computed tomographic (CT) techniques are capable of providing three-dimensional images of the internal structure of opaque materials in a nondestructive manner. The unique cone beam geometry allows acquisition of all two-dimensional projections with only one rotation of the sample, thus providing for fast data acquisition and better X-ray utilization, as a complete two-dimensional detector array receives the cone-shaped flux of rays. Thus, an isotropic three-dimensional volume can be reconstructed without the mechanical translation and the stacking of sequential slices, as is the case for more conventional CT scanners. In this regard, a state-of-the-art, custom designed X-ray microtomography facility to provide very detailed three-dimensional spatial analysis of packed beds of multiphase particles was installed and is in operation at the University of Utah. The reconstructed three-dimensional tomographic volume allows for spatial resolution as small as 5 μm for sample dimensions of up to 40 mm in diameter. Utilization of this custom-designed cone-beam X-ray microtomography facility for the analysis of particulate systems in three dimensions is discussed. Applications described include coal washability analysis for the design and operation of coal-preparation plants, liberation analysis for the evaluation of grinding practice and separation efficiency, mineral exposure analysis for the prediction of the ultimate recovery from heap-leaching operations, three-dimensional particle shape analysis to classify particle populations and, finally, analysis of the pore-structure network of packed particle beds for simulation of flow through such porous structures as encountered infiltration and heap leaching. The initial results from these studies demonstrate the potential utility of detailed three-dimensional microCT information for improved design and operation of mineral processing methods.

Three-dimensional morphology of the palate in subjects with unilateral complete cleft lip and palate at the stage of permanent dentition.

Three-dimensional analysis of palate size and shape in patients with complete unilateral cleft lip and palate (UCLP) at the stage of permanent dentition. Thirty randomly selected dental casts of boys approximately 15 years old with complete UCLP and 28 dental casts of normal boys of the same age. All patients underwent lip repair according to Tennison with primary periosteoplasty (mean age 8.5 months) and palate repair by pushback and pharyngeal flap surgery (mean age 4.9 years). Data on the palate height in 210 defined locations. The palate in patients with UCLP was narrower throughout its whole extent, more anteriorly than posteriorly. From the canines posteriorly, it was also lower, and the difference as compared with controls increased in a posterior direction up to the level of second premolars (up to 30%) and then slightly diminished (to 21% between the first molars). The reduction of area of transverse sections reached 45% between premolars and 39% between first molars. The palate in the anterior portion was highest on the cleft side and in a posterior direction the maximum height of the palate shifted toward the midline and even beyond that line toward the noncleft side. Palatal height did not depend on dentoalveolar arch width. The smaller width and height of the palate confirm the substantially reduced space for the tongue in patients with UCLP. The reduction is only slightly larger than in previously examined patients with isolated cleft palate. Palatal vault is asymmetrical, highest anteriorly on the cleft side and posteriorly on the noncleft side.

INVESTIGATING HUMAN COLOR PREFERENCES IN THE PERCEPTION OF COMPLEX THREE-DIMENSIONAL STRUCTURES

This article describes preliminary results of a investigation that addresses the problem of human color perception in the visual analysis of complex three-dimensional shapes. We built 3D visualization models of synthetic neural cells, and designed two experiments to identify user preferences for color when observing and executing tasks on these 3D models. Though preliminary, the results obtained from these experiments are consistent and indicate that some trends exist that deserve further investigation.

Geodesic morphometry with applications to 3-D morpho-functional anatomy

The quantitative analysis of three-dimensional (3-D) shapes in terms of morphology and functionality is one of the most challenging problems in medical image analysis. This paper proposes a general methodology that aims at solving part of this problem. It introduces a nonparametric hierarchical partitioning approach that operates on any arbitrary 3-D shape described as a triangle mesh. It first extends the concept of basin districts to the case of curved spaces through a partitioning process on a valuation representing the main curvatures over a polyhedral support. A hierarchical construction of basin districts is obtained from a watershed transform. The speed of the front propagation on the polyhedral surface is controlled by the local characteristics of the surface geometry. As a prerequisite, a set of co-processing tools has been developed that operates directly on a triangulated domain. This includes classical signal processing tasks (e.g., re-sampling, filtering) on a polyhedral support performing a trade-off between accuracy and efficiency. The ability to provide an intrinsic shape partition from any triangular mesh is useful in a wide range of applications from accurate geometric modeling, and hierarchical shape dissection to robust mesh compression. Examples are presented in the paper to illustrate the principles and methodology.

Three-dimensional analysis of the geometry of individual multiple sclerosis lesions: detection of shape changes over time using spherical harmonics.

To suggest a quantitative method for assessing the temporal changes in the geometry of individual multiple sclerosis (MS) lesions in follow-up studies of MS patients. Computer simulated and in vivo magnetic resonance (MR) imaged MS lesions were studied. Ten in vivo MS lesions were identified from sets of axial MR images acquired from a patient scanned consecutively for 24 times during a one-year period. Each of the lesions was segmented and its three-dimensional surface approximated using spherical harmonics (SH). From the obtained SH polynomial coefficients, indices of shape were defined, and analysis of the temporal changes in each lesion's geometry throughout the year was performed by determining the mean discrete total variation of the shape indices. The results demonstrate that most of the studied lesions undergo notable geometrical changes with time. These changes are not necessarily associated with similar changes in size/volume. Furthermore, it was found that indices corresponding to changes in lesion shape could be 1.4 to 8.0 times higher than those corresponding to changes in the lesion size/volume. Quantitative three-dimensional shape analysis can serve as a new tool for monitoring MS lesion activity and study patterns of MS lesion evolution over time.

Three-dimensional mathematical analysis of particle shape using X-ray tomography and spherical harmonics: Application to aggregates used in concrete

The properties of composites made by placing inclusions in a matrix are often controlled by the shape and size of the particles used. Mathematically, characterizing the shape of particles in three dimensions is not a particularly easy task, especially when the particle, for whatever reason, cannot be readily visualized. But, even when particles can be visualized, as in the case of aggregates used in concrete, three-dimensional (3-D) randomness of the particles can make mathematical characterization difficult. This paper describes a mathematical procedure using spherical harmonic functions that can completely characterize concrete aggregate particles and other particles of the same nature. The original 3-D particle images are acquired via X-ray tomography. Three main consequences of the availability of this procedure are mathematical classification of the shape of aggregates from different sources, comparison of composite performance properties to precise morphological aspects of particles, and incorporation of random particles into many-particle computational models.

Selective bilateral hippocampal volume loss in chronic schizophrenia

Background: The hippocampus is implicated in the pathophysiology of schizophrenia; however, volumetric changes are subtle and have limited diagnostic specificity. It is possible that the shape of the hippocampus may be more characteristic of schizophrenia. Methods: Forty-five patients with chronic schizophrenia and 139 healthy control subjects were scanned using magnetic resonance imaging. Hippocampi were traced manually, and two-dimensional shape information was analyzed. Results: Two shape factors were found to be adequate to represent variance in the shape of the hippocampus. One of these factors, representing volume loss behind the head of the hippocampus, provided a degree of discrimination between patients with chronic schizophrenia and healthy control subjects; however, overall hippocampal volume following appropriate adjustment for brain volume showed a similar level of discrimination. Patients with chronic schizophrenia were best characterized using these two measures together, but diagnostic specificity was only moderate. Conclusions: This study identified that less of the hippocampus was distributed in its posterior two-thirds in patients with chronic schizophrenia, and specifically in the region just posterior to the hippocampal head. Group discrimination on the basis of hippocampal volume and shape measures was moderately good. A full three-dimensional analysis of hippocampal shape, based on large samples, would be a useful extension of the study.

Three-dimensional shape analysis of miarolitic cavities and enclaves in the Kakkonda granite by X-ray computed tomography

Three-dimensional shape analysis of miarolitic cavities and enclaves from the Kakkonda granite, NE Japan, was performed by X-ray computed tomography (CT) and image analysis. The three-dimensional shape of the miarolitic cavities and enclaves was reconstructed by stacked two-dimensional CT slice images with an in-plane resolution of 0.3 mm and an inter-slice spacing of 1 mm. An ellipsoid was fitted to each reconstructed object by the image processing programs. The shortest, intermediate, and longest axes of the ellipsoids fitted to miarolitic cavities had E–W, N–S, and vertical directions, respectively. The shortest axes of the ellipsoids fitted to enclaves were sub-vertical to vertical. Three-dimensional strains calculated from miarolitic cavities and enclaves have E–W and vertical shortening, respectively. The shape characteristics of miarolitic cavities probably reflect regional stress during the late magmatic stage, and those of enclaves reflect shortening by later-intruded magma or body rotation during the early magmatic stage. The miarolitic cavities may not be strained homogeneously with the surrounding granite, because the competence of minerals is different from that of the fluid-filled cavities. Although the strain markers require sufficient contrast between their CT numbers and those of the surrounding minerals, this method has several advantages over conventional methods, including the fact that it is non-destructive, expedient, and allows direct three-dimensional observation of each object.

Three-dimensional analysis of heat flow, segregation, and interface shape of gradient-freeze crystal growth in a centrifuge

Three-dimensional (3D) heat flow, dopant segregation, and interface shape during crystal growth by a gradient freeze technique in a centrifuge are analyzed by a finite volume method. The basic flow patterns for a fixed geometry (with a concave interface) at different configurations agree well with the previous report (Friedrich et al., J. Crystal Growth 167 (1996) 45). However, the self-consistent analysis allows us for the first time to further investigate the role of the Coriolis force and centrifugal acceleration on the heat and mass transfer and the interface, simultaneously. Furthermore, the rotation speed found for the weakest convection, where the Coriolis force balances the gravitational and centrifugal forces, turns out to have larger radial segregation, despite having a larger effective segregation coefficient. Rotation about the growth axis is also investigated. For this configuration, it is found that both axial and radial segregation could be reduced under certain conditions.

A parametric study on forming length in roll forming

A simulation program has been developed in order to examine the roll forming process. The program is based on the three-dimensional finite element analysis of shape and roll forming under kinematically steady-state condition. In this study, the forming length of the strip in the roll forming process was estimated in consideration of some factors such as material properties, strip thickness, roll diameter, roll velocity, and the deformation of the material that influence the forming length decisively. The sensitivity of the forming length to these factors was considered, and the interaction between factors that affect the forming length was considered also. To verify the reliability of the simulation program, the simulated results for longitudinal strain were compared with experimental results available in the literature. It was concluded that the work-hardening exponent plays a major role in the forming length of the pre-deformed strip.

Assessment of left ventricular cardiac shape by the use of volumetric curvature analysis from 3D echocardiography

A method for three-dimensional shape analysis of left ventricle (LV) is presented in this article. The method uses three-dimensional transesophageal echocardiography (TEE) as the source to derive the 3D wire-frame model and the related shape descriptors. The shape descriptors developed in this article include regional surface changing (RSC), global surface curvature (GSC), surface distance (SD), normalized surface distance (ND), and effective radius (ER) of the endocardial surface. Based on these shape descriptors, the shape of LV could be sketched in both static and dynamic manner. The results show that the new approach provides a robust but easy method to quantify regional and global LV shape from 2D and 3D echocardiograms.

Analysis of three-dimensional molecular shape using surface area and molecular volume scaling descriptors

Analysis of three-dimensional molecular shape using surface area and molecular volume scaling descriptors

Shape from shading. I: Surface curvature and orientation.

The human visual system makes effective use of shading alone in recovering the shape of objects. Pictures of sculptures are readily interpreted--a situation where shading provides virtually the sole cue to shape. However, shading has been considered a poor cue to depth in comparison with retinal disparity and kinetic cues. Curvature discrimination thresholds were measured with the use of a surface-alignment task for a range of surface curvatures from 0.16 cm-1 to 1.06 cm-1. Weber fractions were around 0.1, demonstrating considerable precision in this task. Weber fractions did not vary substantially as a function of surface curvature. Rotation of the light source around the line of sight had no effect on curvature discrimination but rotation towards the viewer increased discrimination thresholds. In contrast, slant discrimination declined with rotation of the light-source vector towards the viewpoint. When a band-limited random grey-level texture was mapped onto the sphere, curvature discrimination thresholds increased gradually as a function of texture contrast, even though texture and shading provided consistent cues to depth. Adding texture also increased slant discrimination thresholds, demonstrating that texture can act as a source of noise in shape-from-shading tasks. The psychophysical findings have been used to evaluate whether current algorithms for shape from shading in computer vision could serve as models of human three-dimensional shape analysis and to highlight low-level intramodular interactions between depth cues. It is demonstrated that, in the case of surfaces defined by shading, curvature descriptions are primary and do not depend upon the prior encoding of surface orientation, and Koenderink's local-shape index is suggested as an alternative intermediate representation of surface shape in the human visual system.

3D geometrical features of anatomic structures: the example of the ulna and radius bones

This paper addresses two important issues of three-dimensional (3D) natural shape analysis. The first concerns the segmentation of these shapes into 3D primitives and the second deals with their geometric characterisation by means of intrinsic features. Restricting ourselves to 3D objects formed from two-dimensional (2D) cross-sectional adjacent slices (i.e., long bones), we present a method of contextual classification and results concerning the ulnar bone. With respect to the second issue, a curvature-torsion analysis of the medullar axis is introduced and the results are represented by means of torsion images. A first application to ulnar structures is given. It is shown that radius bones have zero torsion and that their curvatures can be studied in 2D. A preliminary statistical study of the 2D curvature of the radius is also presented.

自動米形状分析装置を用いた原料米の形状解析

自動米形状分析装置を用いた原料米の形状解析

Three-dimensional face shape analysis of French adults, and its application to the design of protective equipment

The study's aim was to identify female and male face shape variability in order to establish typical profiles for the design of masks. A specific data acquisition photogrammetric station was used for this purpose. A preliminary survey using anthropometric techniques was conducted on 301 females and 208 males, randomly selected from the French military population, in order to constitute two samples of 30 males and 30 females for the stereometric survey. For each subject, the stereorestitution of face photos was made on three sets of data: (1) 37 anatomical landmarks previously identified by a black point marked on the face; (2) 7 anatomical arcs, also drawn with a black pencil; and (3) 1500-2000 points distributed on horizontal cross-sections at different vertical levels. The analysis only concerned the global face shape, and excluded the central area (eyes, nose and mouth). A common origin and reference axis system was defined. All the three-dimensional (3D) produced data was processed using computer-aided design software, after some adaptations. Subjects were selected iteratively for five levels of cross-section and three anatomical arcs so as to characterize least variation amplitudes, subject by subject. Five groups were identified. All cross-sections were verified to check the validity of the preceding step. By this method, each group was defined by a mean profile form and by the amplitude of this form for each point of the profile. Males and females were present in each group, and for each group, a greater variability was noted at the lower part of the face. This variability can be explained as the result of morphological and functional phenomena. These results can be applied to the design of new protective equipment for the fore-face indeed they were used for the design of a new mask for the French military.

Three-dimensional shape analysis by use of a projected grating image

A grating pattern projected onto an object deforms in accordance with the three-dimensional shape of the surface. This deformed image can be analyzed by detecting the shifted phase of the original grating pattern with the aid of Fourier transformation. The profile of the object is expressed in moire contours as well as in a wire-frame model for the intuitive understanding of the shape. In this procedure, multiplication and visibility enhancement of moir&#233 fringes are performed with an improved result.

Three-dimensional shape analysis using moments and Fourier descriptors

A procedure for using moment-based feature vectors to identify a three-dimensional object from a two-dimensional image recorded at an arbitrary viewing angle and range is presented. A moment form called standard moments, rather than the usual moment invariants, is considered. A standard six-airplane experiment was used to compare different techniques. Fourier descriptors and moment invariants were both compared to the present scheme for normalized moments. Various experiments were conducted using mixtures of silhouette and boundary moments and different normalization techniques. Standard moments gave slightly better results than Fourier descriptors for this experiment; both of these techniques were much better than moment invariants. >

Metric analyses of the teeth and faces of South Australian twins.

Procedures are described for the acquisition and analysis of data in a study of the dental and facial characteristics of South Australian twins. Comparisons of the mesiodistal diameters of maxillary incisors in MZ and DZ twins revealed heterogeneity of total variances and evidence of inequality of mean values for some dimensions between MZ and DZ twins. Previous estimates of heritabilities for tooth size, relying on classical assumptions in twin research, may be exaggerated. A preliminary analysis of facial shape was undertaken using a procedure for shape matching based on a least squares fit of homologous coordinates. There was evidence of mirror-imaging in some MZ twin pairs and differences in facial asymmetry between male and female DZ twins. Future extensions of the study using methods for three-dimensional shape analysis are described.

Study of the fixed and concentrated type reverse flat plate solar collector. 1st report Analysis on the shape of fixed reflector.

The reverse flat plate solar collector proposed in this study consists of a fixed reflector and an absorber plate installed upside down. It has a higher collective performance than the ordinary flat plate collector for high temperature applications, due to the possible reduction of natural convection heat losses from the absorber plate. In the present paper, three-dimensional geometrical analysis of the optimum shape of the fixed reflector has been conducted on parabolic and partially circular cross-sections of the reflectors. The average concentrated energy flux has been calculated aided by the evaluated solar radiation distribution from the sky, and the geometrical collective performance is discussed.