Camera Calibration Using Catenary

In this work, we introduce a novel calibration technique based on a hanging chain curve replacing the checkerboard-based methods. It is a known physical phenomenon that a hanging chain or a flexible rope under gravity can be modeled by a special curve called catenary. Therefore, instead of the commonly-used planar calibrator, we propose using multiple shots of a catenary-shaped chain for calibration. This approach can solve the out-of-focus problem which is faced in checkerboard calibration methods when the size of the board is not large enough. Although enlarging a planar calibrator increases the manufacturing time and cost, a simple label chain can create large planar areas as precise as a rigid checkerboard, is easily foldable and transportable. We compare the results of our proposed approach against the widely used checkerboardbased calibration as well as the state-of-the-art calibration methods and show that catenary-based calibration is much more accurate than checkerboard-based calibration by a very large margin and is also very competitive among the other approaches.<br>

Camera Calibration Using Catenary

In this work, we introduce a novel calibration technique based on a hanging chain curve replacing the checkerboard-based methods. It is a known physical phenomenon that a hanging chain or a flexible rope under gravity can be modeled by a special curve called catenary. Therefore, instead of the commonly-used planar calibrator, we propose using multiple shots of a catenary-shaped chain for calibration. This approach can solve the out-of-focus problem which is faced in checkerboard calibration methods when the size of the board is not large enough. Although enlarging a planar calibrator increases the manufacturing time and cost, a simple label chain can create large planar areas as precise as a rigid checkerboard, is easily foldable and transportable. We compare the results of our proposed approach against the widely used checkerboardbased calibration as well as the state-of-the-art calibration methods and show that catenary-based calibration is much more accurate than checkerboard-based calibration by a very large margin and is also very competitive among the other approaches.<br>

Darboux Iso-Geodesic Special Curve in Euclidean Space

In this paper, by using Darboux frame we scrutinize the issues of reconstructing surfaces with given some unusual Smarandache curves in Euclidean 3-space, we make manifest the family of surfaces as a linear combination of the components of this frame and derive the necessary and sufficient conditions for coefficients to satisfy both the iso-geodesic and iso-parametric requirements.

A Geometric Modeling of Tracheal Elements of the Chard (Beta vulgaris) Leaf

ABSTRACT: In this study, we give a geometric description of the tracheal elements of the chard (Beta vulgaris var. cicla L.), which is a widespread cultivated plant in Turkey. It is used as an edible plant and its leaves are used as antidiabetic in traditional medicine plant. We have shown that the tracheal elements, which are taxonomic value of the plant, can be considered as a surface of revolution or a tubular shape along a special curve.

Special Bertrand Curves in 4D Galilean Space

The generalization of Bertrand curves in Galilean 4-space is introduced and the characterization of the generalized Bertrand curves is obtained. Furthermore, it is proved that no special curve is a classical Bertrand curve in Galilean 4-space such that the notion of classical Bertrand curve is definite only in three-dimensional spaces.

The Statistic Definition and Research of the One Class Similar Special Curve

This paper use the statistical method to give the similar definition of common broken line. This is the first derivative function of the Linear correlation analysis which is based on the history data of Shenhu Securities Market and through the RSI index line and the closing quotation price line of the financial trading products, which reaching a result of relative analysis coefficient that all bigger than 0.8. This speak volume for that both of the height of the broken line is similar. By using the fitting nature of RSI index line and closing quotation price line, we reach the price predictor formula of financial trading products and make an empirical analysis, which will provide math support for the extreme price of financial trading products by using RS index to judge.

Body Height Correction in Scoliosis Patients for Pulmonary Function Test

We studied standing anteroposterior roentgenograms from 140 scoliosis patients and obtained a correction equation for body height by Cobb angle. This equation is applicable to patients with a double curve or special curve pattern as well as patients with a single curve. The repeatability of the method examined with this equation was higher than that with the previous correction method for body height by Cobb angle, and the difference between the corrected values and the measured values was small. Therefore, this method is considered to be more reliable.

Acoustical Dispersion in Periodic Microwave Structures

The theory, the design, and the numerical results relevant to the acoustical frequency dispersion band of periodic microwave structures are discussed. Experimental Brillouin diagrams for the acoustical band of different structures exhibit a neat fitting to a special curve. This curve coincides with the qualitative analysis of resonators chain coupled (distant coupling included) together both capacitively and inductively. Discrete points on the curve are obtained analytically using the variational theory. Those points which correspond to the eigenvalues of only one period of the structure are analyzed and explained in terms of boundary conditions. Numerical methods for calculating these eigenvalues to a high degree of accuracy are either already available or can easily be programed. These programs are easily modified so that various other design parameters may be evaluated simultaneously. The basic equations are derived and the appropriate technique developed for a model of distant coupling up to the second neighbor. Comments on the numerical procedure, on the accuracy, and on the practicality of the different operational modes are given.