Extrapolating and interpolating surfaces in depth

Random -dot stereograms were generated with a blank area placed in part of the right-hand image so making a patchwork of monocular and binocular areas. The perceived depth and shape of the monocular region, where depth was not explicitly marked, depended in p art on the depth and surface orientation of adjacent binocular areas. Thus a monocular rectangle flanked by two binocular rectangles which were placed in different fronto-parallel planes was seen as a sloping surface spanning the depth between the binocular regions, and, under some conditions, the gradient of a sloping binocular plane extended into a neighbouring monocular area. Division of the monocular region into two by textural discontinuities or discontinuities of motion sometimes altered the shape of the extrapolated surface. Often, though, the shape was unchanged by such discontinuities implying that both two- and three-dimensional features are used to segment a scene into separate surfaces. Pictorial cues also contribute to the shape and apparent depth of the monocular surface. For instance, when subjects viewed a display consisting of portions of a cube of which two ends were shown stereoscopically and one side monocularly, the monocular side was seen in three dimensions filling the gap between the ends. When stereo cues were pitted against pictorial cues, sometimes pictorial cues and sometimes stereo cues dominated, and sometimes the surface contained sharp discontinuities enabling both to be accommodated.

2020 ◽  
Author(s):  
Gui Chen ◽  
Mona Al Awadi ◽  
David William Chambers ◽  
Manuel O Lagravère-Vich ◽  
Tianmin Xu ◽  
...  

Abstract Background: With the aid of implants, Björk identified the two-dimensional mandibular stable structures in cephalogram during facial growth. However, we don't know the three-dimensional stable structures exactly. The purpose of this study was to identify the most stable mandibular landmarks in growing patients using three-dimensional images.Methods: The sample was comprised of two cone-beam computed tomography (CBCT) scans taken about 4.6 years apart in 20 growing patients between the ages of 12.5 (T1) to 17.1 years (T2). After head orientation, landmarks were located on the chin (Pog), internal symphysis (Points C, D and E), and mandibular canals, which included the mental foramina (MF and MFA) and mandibular foramina (MdF). The linear distance change between Point C and these landmarks was measured on each CBCT to test stability through time. The reliability of the suggested stable landmarks was also evaluated. Results: The total distance changes between Point C and points D, E, Pog, MF, and MFA were all less than 1.0 mm from T1 to T2. The reliability measures of these landmarks, which were measured by the Cronbach alpha, were above 0.94 in all three dimensions for each landmark. From T1 to T2, distance changes from Point C to the right and left mandibular foramina were respectively 3.39±3.29 mm and 3.03±2.83 mm. Conclusions: During a growth period that averaged 4.6-years, ranging from 11.2 to 19.8 years, the structures that appeared relatively stable and could be used in mandibular regional superimposition included Pog, landmarks on the inferior part of the internal symphysis, and the mental foramen. The centers of the mandibular foramina, the starting points of the mandibular canal, underwent significant changes in the transverse and sagittal dimensions.


Author(s):  
Niv Allon

This chapter shifts to three-dimensional art and studies scribal statues. It traces back the history of this statuary motif through time, studying changes in the texts inscribed on the statue and the gesture of the right hand. Analyzing these elements, the chapter investigates the relationships between statue, patron, and text. A close inspection of this statuary motif reveals a growing emphasis on the act of writing and a reinterpretation of the literacy act. Focusing on the Eighteenth Dynasty patrons who commissioned such statues once again suggests that men of military background like Haremhab play a significant role in disseminating images of literacy through their self-representation.


1995 ◽  
Vol 11 (3) ◽  
pp. 245-256 ◽  
Author(s):  
Glenn M. Street ◽  
Edward C. Frederick

This paper describes a system that was developed to measure ski pole and roller-ski reaction forces in three dimensions during roller-ski skating. Uni-axial force transducers mounted in the right and left ski poles measure axial loading of the poles. Six transducers in one roller-ski measure biaxial loads beneath the foot. A remote computer stores the amplified transducer signals transmitted from the skier through 100 m cables. Three-dimensional video-graphy determines the orientations of the poles and roller-ski in order to resolve the resultant poling and skating forces into three components. Calibration data suggest that the resolution of the force measurement system is ±3 to 9% of the actual poling and skating forces, respectively. Sample data are presented from a VI skating trial during roller-skiing. These data provide the first glimpse at the major functions of the upper and lower body during roller-ski skating and show how the tool could be used to examine the size and effectiveness of skier-generated forces.


1978 ◽  
Vol 56 (2) ◽  
pp. 162-165 ◽  
Author(s):  
P. Fewster ◽  
L. Orlóci

When vegetation data are summarized on the basis of some method of ordination, a search for distinct groups or trends is greatly facilitated if the cloud of sample points is viewed under a lens stereoscope in three dimensions. The present paper describes a simple method to construct stereograms and illustrates their application in a classification problem.A stereogram is composed of two images of a three-dimensional object. The left image and the right correspond respectively to sightings with the left eye or the right eye of the observer. The diagrams are placed side by side at a specified distance apart, and when viewed with the aid of a stereoscope, the images will merge resulting in a three-dimensional picture.


Author(s):  
Jonas Koko

We propose a MATLAB implementation of the [Formula: see text] finite element method for the numerical solutions of the Poisson problem and the linear elasticity problem in two-dimensional (2D) and three-dimensional (3D). The code consists of vectorized (and short) assembling functions for the matrices (mass and stiffness) and the right-hand sides. Since for the [Formula: see text] finite element, the element mass matrix and right-hand side are simple, the implementation uses only the MATLAB function sparse on the elements volume. For the stiffness matrix, to obtain a MATLAB implementation close to the standard form, cell-arrays are used to store the gradients of the element basis functions. The assembling procedure can then use matrix/vector products on small size cell-arrays. Numerical experiments show that our implementation is fast, scalable with respect to time, and outperforms existing vectorized MATLAB FEM codes.


2012 ◽  
Vol 22 (01) ◽  
pp. 1250010 ◽  
Author(s):  
FU ZHANG ◽  
JACK HEIDEL

We show analytically that almost all three-dimensional dissipative quadratic systems of ordinary differential equations with a total of five terms on the right-hand side and one nonlinear term (namely 5-1 cases) are not chaotic except twenty one of them. Indeed we find nine systems that exhibit chaos, which were discovered by Sprott and Malasoma earlier. They are the simplest dissipative chaotic systems found so far. In this paper, we also extend Heidel–Zhang's theorem which provides sufficient conditions for solutions in the three-dimensional autonomous systems with polynomials and rational expressions on the right-hand side being nonchaotic. We then investigate the twenty one systems analytically and numerically. We show the portraits of some typical chaotic and nonchaotic solutions in phase space. For two of the systems that exhibit chaos we found stable period 1, 2, 4, 8 and 12 orbits numerically.


2011 ◽  
Vol 49 (1) ◽  
pp. 121-126
Author(s):  
B. van Loon ◽  
N. van Heerbeek ◽  
T.J.J. Maal ◽  
W.A. Borstlap ◽  
K.J.A.O. Ingels ◽  
...  

BACKGROUND: When lateral osteotomies are performed as part of a rhinoplasty, the nose and paranasal region invariably change in three dimensions. The PURPOSE of this study is to compare the effect of the percutaneous perforating and endonasal continuous osteotomy techniques concerning the degree of postoperative swelling using three dimensional (3D) stereophotogrammetry. METHODOLOGY: A prospective follow-up study was conducted. Patients requiring bilateral osteotomies were included and randomly underwent a percutaneous osteotomy on one side and an endonasal osteotomy on the other side. Pre- and postoperative 3D photos were acquired using 3D stereophotogrammetry. Volumetric measurement data were acquired from the paranasal region using 3D software. Measurements were compared using Student`s t-test and Wilcoxon signed rank test statistics. RESULTS: Twenty patients were included. A percutaneous osteotomy was performed on the right side in nine patients and on the left side in 11 patients. The total volume, the volume of the right paranasal and left paranasal region were significantly larger postoperative. No difference was found between the sides. CONCLUSIONS: No difference concerning swelling is found between the percutaneous and endonasal osteotomy technique sides. With 3D stereophotogrammetry volumetric data can be acquired and compared to evaluate soft-tissue changes.


2001 ◽  
Vol 38 (5) ◽  
pp. 476-485 ◽  
Author(s):  
K. A. Russell ◽  
S. D. Waldman ◽  
B. Tompson ◽  
J. M. Lee

Objective: The purpose of this study was to assess the ability of shape parameters of nasal morphology to predict esthetics in individuals with complete unilateral cleft lip and palate (CUCLP). Methods: This retrospective study involved 28 patients with repaired CUCLP. Nostril morphology was analyzed using nose casts and a video-imaging technique. Calculated shape parameters included area, perimeter, centroid, angle of the principal axis, major and minor moments of area, anisometry, bulkiness, lateral offset, and three-dimensional internostril angles. Esthetics was assessed using a panel of six orthodontists who rated nasal esthetics from frontal, lateral, basal, and three-quarters view slides and from nose casts. Correlations between esthetics and the shape parameters were completed using the entire group as well as using two statistically determined subsets: those with the best and those with the worst esthetics. Results: Nasal esthetics was related to only the perimeter and bulkiness parameter ratios. Symmetry of the perimeters between the right and left nostrils positively correlated with better esthetics using the entire sample group while symmetry of bulkiness between the right and left nostrils positively correlated with better esthetics using both the entire sample group and the best and worst subsets. Conclusions: Only perimeter and bulkiness showed positive correlations with nasal esthetics. The group of parameters used to assess nostril morphology had neither significant correlation with—nor predictive power for—esthetics. Thus, an assessment of the entire nasal surface topography in three dimensions needs to be completed and assessed with respect to predictability of nasal esthetics.


2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Claudio Letta ◽  
Andreas Schweizer ◽  
Philipp Fürnstahl

The purpose of this study was to accurately quantify contralateral differences of the scaphoid in three-dimensional space to evaluate the feasibility of using the healthy contralateral bone as a reconstruction template in the preoperative planning of complex mal- or nonunions. Three-dimensional surface models of the left and right scaphoids were reconstructed from computed tomography images and compared in 26 individuals. Left-right differences were quantified with respect to volume, surface area, length, and surface-to-surface deviation. The average left-right differences in volume, surface area, and length were 95.4 mm3 (SD 66.2 mm3), 32.7 mm2 (SD 22.9 mm32), and 0.28 mm (SD 0.4 mm), respectively. The average surface-to-surface deviation between the sides was 0.26 mm (SD 0.2 mm). High statistical correlation (Pearson) between the left and the right side was found in all evaluated measures.


2021 ◽  
Author(s):  
Florian Gaertner ◽  
Patricia Reis-Rodrigues ◽  
Ingrid de Vries ◽  
Miroslav Hons ◽  
Juan Aguilera ◽  
...  

Efficient immune-responses require migrating leukocytes to be in the right place at the right time. When crawling through the body amoeboid leukocytes must traverse complex three-dimensional tissue-landscapes obstructed by extracellular matrix and other cells, raising the question how motile cells adapt to mechanical loads to overcome these obstacles. Here we reveal the spatio-temporal configuration of cortical actin-networks rendering amoeboid cells mechanosensitive in three-dimensions, independent of adhesive interactions with the microenvironment. In response to compression, Wiskott-Aldrich syndrom protein (WASp) assembles into dot-like structures acting as nucleation sites for actin spikes that in turn push against the external load. High precision targeting of WASp to objects as delicate as collagen fibers allows the cell to locally and instantaneously deform its viscoelastic surrounding in order to generate space for forward locomotion. Such pushing forces are essential for fast and directed leukocyte migration in fibrous and cell-packed tissues such as skin and lymph nodes.


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