Three-Dimensional Evaluation of Soft Tissue Malar Modifications after Zygomatic Valgization Osteotomy via Geometrical Descriptors

Patients with severe facial deformities present serious dysfunctionalities along with an unsatisfactory aesthetic facial appearance. Several methods have been proposed to specifically plan the interventions on the patient’s needs, but none of these seem to achieve a sufficient level of accuracy in predicting the resulting facial appearance. In this context, a deep knowledge of what occurs in the face after bony movements in specific surgeries would give the possibility to develop more reliable systems. This study aims to propose a novel 3D approach for the evaluation of soft tissue zygomatic modifications after zygomatic osteotomy; geometrical descriptors usually involved in face analysis tasks, i.e., face recognition and facial expression recognition, are here applied to soft tissue malar region to detect changes in surface shape. As ground truth for zygomatic changes, a zygomatic openness angular measure is adopted. The results show a high sensibility of geometrical descriptors in detecting shape modification of the facial surface, outperforming the results obtained from the angular evaluation.

Guided wave propagation in functionally graded cylindrical structures with sector cross-sections

The differential equations governing guided waves in functionally graded cylindrical structures with sector cross-sections are solved by introducing the double orthogonal polynomial series method into the cylindrical coordinate system, and the wave characteristics are subsequently investigated. The validity of the present method is confirmed by way of the comparison with available references, and the convergence is discussed. The corresponding phase velocity dispersion curves, displacement distributions and Poynting vectors are illustrated. The influences of the variation in the radius to thickness ratio, angular measure and gradient index on the guided wave characteristics are discussed, which can be used as significant guidance on ultrasonic guided wave non-destructive testing for functionally graded cylindrical structures with sector cross-sections.

INVESTIGATIONS INTO THE ACCURACY OF ANGLE CALIBRATION

Technical possibilities to create equipment for the calibration of flat angles are discussed in the article. The angular standard measure, the radian, has not been realised as a standard unit until now. Nevertheless, the unit of angular measure in degrees is used as the geometric measure of length in geodesy, machine engineering and other branches of industry – by multiangular prisms – polygons with an autocollimator, rotary tables, circular scales, etc. It should be noted that these angle measures are calibrated against the upper level measures (etalons) only at the several intervals depending on the number of sides (angles) of the polygon or the other standard measure. The methods of calibration of constant angle value in full circle are used as well. At the same time geodetic instruments, rotary tables of metal cutting tools and instruments, rotary encoders have a great number of discrete values. These values between the calibrated points remain unknown during calibration. The information received during calibration relative to all the information available can be evaluated using information entropy. The equipment of calibration permitting to select significantly more information would be essential for better accuracy assurance of instruments used in machine engineering, geodesy, building structures. Theoretical and technical background for justifying and developing such equipment for angular accuracy calibration is presented here. A modern scientific and technical background validates this concept.

Angle Measures and Bisectors in Minkowski Planes

We prove that a Minkowski plane is Euclidean if and only if Busemann's or Glogovskij's definitions of angular bisectors coincide with a bisector defined by an angular measure in the sense of Brass. In addition, bisectors defined by the area measure coincide with bisectors defined by the circumference (arc length) measure if and only if the unit circle is an equiframed curve.

Do Rotation Coordinates Provide the Substrate for a Mental Protractor?

In previous studies, we have found that the accuracy in judging collinearity of lines or dots varies considerably from one subject to another as a function of the relative angle of the stimulus elements. A model of errors generally shows large excursions across several subranges of angular position. These do not appear to be motor errors, at least not ones that are well separated from perceptual mechanisms. The errors are most likely generated at primary visual cortex, or beyond. We examined and modeled accuracy in judging collinearity of dot pairs, varying the angular position of the dots through 360°, the distance between the dots (stimulus span), and the distance at which the subject was required to respond (response span). Subjects manifested idiosyncratic profiles of error across angular positions, as reported previously. But across the tested range of spans, from 4 to 8 deg, the errors tended to be the same, irrespective of stimulus or response span. This suggests that the judgments are based on a radial (angular) measure of spatial position. We discuss these results in the context of proposals that the brain maps spatial position using rotation coordinates. These new data are consistent with the hypothesis that subjects use the z-axis coordinates as a mental protractor for judging angular position and collinearity.

Systematic and Random Errors Associated with Johnston's Cephalometric Analysis

This study examined intra- and interexaminer systematic and random errors associated with Johnston's cephalometric method of assessing skeletal and dental changes from pairs of radiographs. Data were obtained from the tracings of radiographs of 30 mixed dentition subjects, who had been treated to correct a Class II malocclusion. Measurements included molar and incisor crown movements relative to basal bone, apical base change, maxillary and mandibular displacement relative to the cranial base, and total molar and overjet reduction. In addition, the change in axial inclination of the incisors and molars was determined. A paired t- test for each pair of replicates for each measure was performed to examine inter- and intra-examiner bias. Estimates of the random error, the coefficient of reliability, and confidence limits (95 per cent level) of a single determination were undertaken. No systematic errors occurred between/within examiners for any linear or angular measure. Interexaminer random errors, based on the standard deviation of the mean difference between replicates, were greater than intra-examiner random errors for 12 out of 13 parameters. Measures assessing molar correction and overjet reduction had the least amount of random error variance within and across judges, while changes in mandibular position had the greatest. Because considerable random errors occurred, the Johnston analysis when used to assess skeletal changes, as well as individual molar and incisor movements, may have limited utility in clinical practice for the individual case.

Spectroscopic Studies of Binary and Multiple Star Systems

There can be few subjects that benefit more than binary stars do from complementary approaches. Consider their orbits, for an initial example. By ‘visual’ methods — by which I mean all methods of obtaining angular resolution on the sky, including the modern techniques of optical interferometry — one can determine an orbit, but with the scale known in terms of angular measure only. By spectroscopic (radial-velocity) methods one obtains the linear scale of the orbit, but with those techniques the inclination to the line of sight is indeterminate. In order to find the complete characteristics of the orbit in three dimensions — as is essential in order to find those most important data, the masses of the component stars — one needs to utilize both methods. It is, accordingly, clearly of great value to have a meeting like this that is object-oriented rather than technique-oriented; it is a long time since there was a meeting specifically devoted to binary stars, and especially in view of the great advances that have taken place in observational techniques of all sorts in recent years it is more than timely that we should have this meeting now. We are certainly very grateful to Dr. McAlister and his colleagues for arranging it and holding it at this beautiful venue.