Shape Moments Research Articles

The effects of molecular shape and quadrupole moment on tilted smectic phase formation

Results are presented from constant NPT Monte Carlo simulations of two systems based on the biaxial internally rotated Gay-Berne (IRGB) potential. First, the effect of increasing molecular elongation is considered, and it is shown that a change in aspect ratio from 3:1 to 4:1 leads to nematic and tilted smectic J phases being replaced by smectic A and tilted smectic G phases, respectively. Second, the effect of a longitudinal electric quadrupole on the phase behaviour of the IRGB model is examined. The presence of a moderate quadrupole moment results in the smectic G phase being replaced by a smectic J; the onset pressure of the smectic J increases monotonically as the quadrupole moment is increased, although the integrity of the tilted layers improves. In addition, the region of smectic A stability is found to persist for moderate quadrupole moment values. For the largest quadrupole moment considered, domains comprising poorly defined, tilted layers are formed but fail to develop into coherent smectic structures. This observation is ascribed to the competition between the unique tilt direction favoured by the biaxial IRGB potential and the random tilt direction of the uniaxial quadrupole-quadrupole interactions.

Optimal Parallel Algorithms for Computer Vision Problems

The computational model on which the algorithms are developed is the arrays with reconfigurable optical buses (abbreviated to AROB). It integrates the advantages of both optical transmission and electronic computation. In this paper, instead of using the radix-2 system, a radix-x system can be used to represent the numbers of the intermediate results of algorithms. We first design two O(1) time basic operations for computing the prefix sums of N and N2 integers each of size O(log N)-bit on the AROB using N1+(1/c) and N×N1+(1/c) processors, respectively, where c is a constant and c⩾1. Currently, these are the best-known results. Then, based on these two basic operations, several O(1) time parallel algorithms for computer vision problems are developed. These problems include shape moment computation, histogramming, histogram modification, Hough transform and median row. Based on the product of time and the number of processors used, all proposed algorithms are time and/or cost optimal.

Two new algorithms for efficient computation of Legendre moments

Orthogonal moments have been successfully used in the field of pattern recognition and image analysis. However, the direct computation of orthogonal moments is very expensive. In this paper, we present two new algorithms for fast computing the two-dimensional (2D) Legendre moments. The first algorithm consists of transforming the pixel-based calculation of Legendre moments into the line-segment-based calculation. After all line-segment moments have been calculated, Hatamian's filter method is extended to calculate the one-dimensional Legendre moments. The second algorithm is directly based on the double integral formulation. The 2D shape is considered as a continuous region and the contribution of the boundary points is used for fast calculation of shape moments. The numerical results show that the new algorithms can decrease the computational complexity tremendously, furthermore, they can be used to treat any complicated objects.

A new computation of shape moments via quadtree decomposition

The main contribution of this paper is in designing an optimal and/or optimal speed-up algorithm for computing shape moments. We introduce a new technique for computing shape moments. The new technique is based on the quadtree representation of images. We decompose the image into a number of non-overlapped squares, since the moment computation of squares is easier than that of the whole image. The proposed sequential algorithm reduces the computational complexity significantly. By integrating the advantages of both optical transmission and electronic computation, the proposed parallel algorithm can be run in O(1) time using N× N 1+1/ c processors when the input image is complicated. If the input image is simple (i.e., the image can be represented by a few quadtree nodes), the proposed parallel algorithm can be run in O(1) time using N× N processors. In the sense of the product of time and the number of processors used, the proposed parallel algorithm is time and cost optimal and achieves optimal speed-up.

Classification of rotifers with machine vision by shape moment invariants

An automated system for the identification of rotifers under a microscope with machine vision by shape analysis has been developed, which tends to be substituted for human appraisal. A suitable image recognition algorithm was proposed and the results were discussed in detail. In this study, rotifers were classified into the exact types despite the debris, which appeared from sludge in the degraded water or from rotifer carcasses. Two stages of a discrimination model based on shape analysis were built: one was to separate debris from rotifers, and the other was to classify rotifers into three groups. A set of shape descriptors, including geometry and moment features, was extracted from the images. The set of shape descriptors had to satisfy the RST (rotation, scaling, and translation) invariance. Shape analysis was proved to be an effective approach since the classification accuracy was approx. 92%. The results from different classification approaches were also compared. The machine vision system with shape analysis and the 2-stage discrimination model had a greater effect on the reduction of manpower requirement for the classification of rotifers.

Computing horizontal/vertical convex shape's moments on reconfigurable meshes

Zero- to third-order moments are very useful tools for analysing 2-D (two-dimensional) shapes. Given an N × N digital image, this paper presents a novel constant-time parallel algorithm for computing a horizontal/vertical convex shape's moments, each row/column in the shape without holes, on an N × N reconfigurable mesh. In the sense of the product of time and the number of processors used, our algorithm is time- and cost-optimal.

Nitrogen in the isotopically enriched 12C diamond

An electron paramagnetic resonance (EPR) characterization study of isotopically enriched 12C diamond grown by General Electric has been carried out. While other commonly used techniques detect no nitrogen in this diamond, the clear EPR spectrum consistently measured a nitrogen concentration of about 0.05 ppm by calibration against a few standards. The concentration is about 2 orders of magnitude lower than that of a few natural IIa diamonds and over 4 orders of magnitude smaller than that of a typical yellow Ib diamond. The 12C diamond is evaluated to be ideal for research of diamonds under high pressure as well as irradiated diamonds. Both the experimental line shape and second moment do not support a random nitrogen distribution in this diamond. Instead, we found that nitrogen atoms tend to stay apart from one another. This uniformly dispersed nitrogen distribution is a new state of nitrogen found in diamond.

An efficient algorithm for computation of shape moments from run-length codes or chain codes

Moments are very useful for shape analysis. Zero- to third-order moments have been used for computer vision applications such as shape recognition and orientation. They can serve for composition of the well-known moment invariants used as desirable features as well as for the detection of the location and the principal axis direction of a shape. The shape is often represented by a binary image and its moments can be obtained by use of fast algorithms considering the shape as a discrete point array. In this paper a new algorithm based on the double-integral formulation is presented. The shape is considered as a continuous region and the contribution of boundary points is used for fast computation of shape moments. This method can be used to calculate moments from either the run-length codes or the chain codes of shape.

Computing a shape's moments from its boundary

Moments have been among the most commonly used tools in the analysis of 2D shapes. Important information about a shape such as its size, center location and orientation are all moment-based attributes. There is also a number of very useful shape features such as maximum and minimum moments of inertia, moment invariants, shape spreadness and shape elongation which are also derived from moments. Traditionally, moments of a shape are computed from the occupancy array representation of the shape. That is, all the shape's pixels are involved in the computation. In this paper we propose a method which computes the same set of moments using only the corner pixels along a shape's boundary. The basic approach is to construct a set of triangles using the shape's corners and the origin of the coordinate system. The moments of these triangles are computed first. The moments of the shape are then derived from the triangles' moments. We have found the suggested method to be much more efficient than the traditional occupancy array based methods.

Beam‐Column Element on Weak Winkler Foundation

In this study an efficient beam-column on elastic foundation was derived using the exact displacement function obtained from the solution of the governing differential equation. The stiffness matrix and nodal load vector of the element are derived explicitly, and the detailed equations for the determination of the deflected shape, shearing force, and bending moment are developed. Two numerical examples are used to verify the accuracy and efficiency of the formulation. Conclusions drawn from the study are presented.

Control point transforms for shape representation and measurement

A new fast transform from curve samples to least-squares normalized B-spline control points is developed and their relation to Fourier descriptors is established. Contour control point sequence scale, translation, and rotation are known to produce identical shape model variations. It is shown that under the conditions of our transform, such sequences are also directly applicable to efficient computation of many useful shape features or characteristics. First, methods for computing boundary curvature and mean contour sample from control points are presented. Then, transforms from contour control points to shape moments and projections are developed and tested.

P-wave shape and seismic moment for Ust-Kamchatsk earthquake of December 15, 1971

P-wave shape and seismic moment for Ust-Kamchatsk earthquake of December 15, 1971

Infrared intensity measurements—I. Experimental conditions and a standard band

The experimental conditions for the measurement of absolute infrared intensities of vibrational transitions have been examined using the out-of-plane CH vibration of 1,2,4,5-tetrachlorobenzone. This symmetrical band has been investigated in solution in carbon disulfide. The band was analyzed by the band shape moment analysis. The error in the experimentally determined intensity is estimated to be ±5 percent. It is suggested that this band would be useful as an intensity standard in condensed systems.

Exchange Effects in Alkali Ozonates

Resonance absorption has been observed in polycrystalline samples of potassium and cesium ozonate. The absorptions are characterized by nearly free electron spin $g$ values with line widths ranging from 26 to 49 oersteds. Analysis of line shapes based on the Anderson-Weiss model for exchange interaction between equivalent magnetic ions and calculations of line shape moment ratios based on the Van Vleck theory, strongly suggest exchange interaction narrowing. Values of exchange frequencies for potassium and cesium ozonate are estimated to be 6\ifmmode\times\else\texttimes\fi{}${10}^{11}$ rad ${\mathrm{sec}}^{\ensuremath{-}1}$ and 3\ifmmode\times\else\texttimes\fi{}${10}^{11}$ rad ${\mathrm{sec}}^{\ensuremath{-}1}$, respectively.