Snakes with Ellipse-Reproducing Property

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortestpossible support subject to some design constraints to maximize efficiency. While the resulting snakes are versatile enough to provide a good approximation of any closed curve in the plane, their most important feature is the fact that they admit ellipses within their span. Thus, they can perfectly generate circular and elliptical shapes. These features are appropriate to delineate cross sections of cylindrical-like conduits and to outline blob-like objects. We address the implementation details and illustrate the capabilities of our snake with synthetic and real data.

Snakes With an Ellipse-Reproducing Property

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency. While the resulting snakes are versatile enough to provide a good approximation of any closed curve in the plane, their most important feature is the fact that they admit ellipses within their span. Thus, they can perfectly generate circular and elliptical shapes. These features are appropriate to delineate cross sections of cylindrical-like conduits and to outline bloblike objects. We address the implementation details and illustrate the capabilities of our snake with synthetic and real data.

ELLIPSE FITTING USING FINITE RATE OF INNOVATION PRINCIPLES

We address the problem of parameter estimation of an ellipse from a limited number of samples. We develop a new approach for solving the ellipse fitting problem by showing that the x and y coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals. Uniform samples of x and y coordinate functions of the ellipse are modeled as a sum of weighted complex exponentials, for which we propose an efficient annihilating filter technique to estimate the ellipse parameters from the samples. The FRI framework allows for estimating the ellipse parameters reliably from partial or incomplete measurements even in the presence of noise. The efficiency and robustness of the proposed method is compared with state-of-art direct method. The experimental results show that the estimated parameters have lesser bias compared with the direct method and the estimation error is reduced by 5-10 dB relative to the direct method.

Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle

Standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse. When the data are noisy and come from a partial ellipse, the state-of-the-art methods tend to produce biased ellipses. We rely on the sampling structure of the underlying signal and show that the x- and y-coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals, and that their parameters are estimable from partial data. We consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude-modulated complex exponentials. A low-pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials. The annihilating filter used in FRI approaches is applied to estimate the sampling interval in the closed form. We perform experiments on simulated and real data, and assess both objective and subjective performances in comparison with the state-of-the-art ellipse fitting methods. The proposed method produces ellipses with lesser bias. Furthermore, the mean-squared error is lesser by about 2 to 10 dB. We show the applications of ellipse fitting in iris images starting from partial edge contours, and to free-hand ellipses drawn on a touch-screen tablet.

Yielding of sensitive clays: micromechanical considerations

Test results reported on several natural sensitive soils show significant anisotropy of the yield curves, which are generally oriented along the coefficient of earth pressure at rest (K-0) axis. An attempt is made in this paper to explain the anisotropy in yielding from microstructural considerations. An elliptic pore, with particle domains aligned along the periphery of the pore, and with the major axis of the pore being oriented along the direction of the in situ major principal stress, is chosen as the unit of microstructure. An analysis of forces at the interdomain contacts around the ellipse is carried out with reference to experimentally determined yield stress conditions of one soil, and a yield criteria is defined. The analysis, with the proposed yield criteria, enables one to define the complete yield curve for any other soil from the results of only two tests (one constant eta compression test with eta close to eta(K?0), where eta is the stress ratio (= q/p) and eta(K?0) is the stress ratio corresponding to anisotropic K-0 compression, and another undrained shear test). Predicted yield curves are compared with experimental yield curves of several soils reported in the literature.

A novel conformation of valinomycin in its barium complex

Knowledge of the molecular mechanisms involved in ionophore-mediated cation transport would be valuable for under-standing many essential functions of biological membranes1−3. Cations are transported in several stages, such as formation of the ionophore−cation complex, diffusion across the cell membrane and subsequent release of the cation. Several conformational rearrangements are involved in this process, and so a detailed understanding of all the conformational possibilities of the ionophore seems to be essential for elucidating the molecular mechanism of ion transport. We are carrying out spectroscopic and crystallographic studies to explore the possible conformational stages of ionophores by complexing them, in different solvents, with cations of various sizes and charges. We report here a novel conformation of the ionophore valinomycin in its barium complex. It can be described as an extended depsipeptide chain, without internal hydrogen bonds, wound in the form of an ellipse with the two barium ions located at the foci.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

A geodesic-based triangulation technique for damage location in metallic and composite plates

Lamb-wave-based damage detection methods using the triangulation technique are not suitable for handling structures with complex shapes and discontinuities as the parametric/analytical representation of these structures is very difficult. The geodesic concept is used along with the triangulation technique to overcome the above problem. The present work is based on the fundamental fact that a wave takes the minimum energy path to travel between two points on any multiply connected surface and this reduces to the shortest distance path or geodesic. The geodesics are computed on the meshed surface of the structure using the fast marching method. The wave response matrix of the given sensor configuration for the healthy and the damaged structure is obtained experimentally. The healthy and damage response matrices are compared and their difference gives the time information about the reflection of waves from the damage. A wavelet transform is used to extract the arrival time information of the wave scattered by the damage from the acquired Lamb wave signals. The computed geodesics and time information are used in the ellipse algorithm of triangulation formulation to locate the loci of possible damage location points for each actuator-sensor pair. The results obtained for all actuator-sensor pairs are combined and the intersection of multiple loci gives the damage location result. Experiments were conducted in aluminum and composite plate specimens to validate this method.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Experimental Studies on Mass Distribution of Impinging Jets

Noting that practical impinging injectors are likely to have skewness, an experimental study has been made to understand the behavior of such jets using water as the simulant. In perfectly impinging jets, a high aspect ratio ellipse-like mass distribution pattern is obtained with major axis normal to the plane of two jets whereas in skewed jets the major axis turns from its normal position. A simple analysis shows that this angle of turn is a function of skewness fraction and impingement angle only and is independent of injection velocity. Experimental data from both mass distribution and photographic technique validate this prediction.

Bubble size measurement and error analysis in a gas liquid ejector

Bubble size in a gas liquid ejector has been measured using the image technique and analysed for estimation of Sauter mean diameter. The individual bubble diameter is estimated by considering the two dimensional contour of the ellipse, for the actual three dimensional ellipsoid in the system by equating the volume of the ellipsoid to that of the sphere. It is observed that the bubbles are of oblate and prolate shaped ellipsoid in this air water system. The bubble diameter is calculated based on this concept and the Sauter mean diameter is estimated. The error between these considerations is reported. The bubble size at different locations from the nozzle of the ejector is presented along with their percentage error which is around 18%.

Characterization of friction at three contact pairs by photoelastic Isotropic point (IP)

Friction coefficient between a circular-disk periphery and V-block surface was determined by introducing the concept of isotropic point (IP) in isochromatic field of the disk under three-point symmetric loading. IP position on the symmetry axis depends on active coefficient of friction during experiment. We extend this work to asymmetric loading of circular disk in which case two frictional contact pairs out of three loading contacts, independently control the unconstrained IP location. Photoelastic experiment is conducted on particular case of asymmetric three-point loading of circular disk. Basics of digital image processing are used to extract few essential parameters from experimental image, particularly IP location. Analytical solution by Flamant for half plane with a concentrated load, is utilized to derive stress components for required loading configurations of the disk. IP is observed, in analytical simulations of three-point asymmetric normal loading, to move from vertical axis to the boundary along an ellipse-like curve. When friction is included in the analysis, IP approaches the center with increase in loading friction and it goes away with increase in support friction. With all these insights, using experimental IP information, friction angles at three contact pairs of circular disk under asymmetric loading, are determined.