Geometric Calibration of LensUsing B-Spline Surface Fitting

A new lens calibration method which is suitable for all kinds of cameras is presented. Based on the global and local adjustable feature of B-spline surface, this method does not require the determination of distortion model of the camera lens. By applying B-spline surface fitting, all kinds of lens distortion models can be simulated. The control points of B-spline surface are estimated inversly from the feature points of detected lines. Then by moving the control points, straight line features in the image can be retrieved. Compared with traditional calibration method, this method has its unique advantage that need no corresponding points between image and scene. Experimental results show the effectiveness of the method.

NON-STATIONARY SIGNAL DENOISING USING TIME-FREQUENCY CURVE SURFACE FITTING

Based on the theory of adaptive time-frequency decomposition and Time-Frequency Dis- tribution Series (TFDS), this paper presents a novel denoising method for non-stationary signal. Ac- cording to the input signal features, an appropriate kind of elementary functions with great concen- tration in the Time-Frequency (TF) plane is selected. Then the input signal is decomposed into a linear combination of these functions. The elementary function parameters are determined by using ele- mentary function TF curve surface to fit the input signal’s TFDS. The process of curved surface fitting corresponds to the signal structure matching process. The input signal’s dominating component whose structure has the resemblance with elementary function is fitted out firstly. Repeating the fitting process, the residue can be regarded as noises, which are greatly different from the function. Selecting the functions fitted out initially for reconstruction, the denoised signal is obtained. The performance of the proposed method is assessed by means of several tests on an emulated signal and a gearbox vi- brating signal.

Applying Surface Fitting in the Medical Thermal Tomography Technology

Based on the thermal tomography technology, this thesis tries to calculate quantity and distribution of heat source in vivo from body surface temperature. A superposition temperature image of a number of point heat sources is surface fitted to get the Q of heat sources (information of cancer cells) quantitatively. The result can reflect the disease area information because cancer cell's Q value is much higher than that of normal cell. This application is a new try in the diagnosis of breast cancer, which has an important value on the early detection and diagnosis of disease source.

Image zooming via surface fitting based on edge constraint

In this paper we present a new image zooming algorithm based on surface fitting with edge constraint. In surface fitting,we consider not only the relationship of corresponding pixels between the original image and the enlarged image, but also the neighbor pixels in the enlarged image according to the local structure of original image. Furthermore, during surface fitting, more interpolation constraints are used in the new algorithm for improving the precision of the super sampling pixels. The experimental results show that the new method outperforms the previous methods which based on surface fitting.

Method for Improving Digital Elevation Model Precision of Consumer Level Unmanned Aerial Vehicles

Currently,the aerial survey system of low-altitude unmanned aerial vehicles(UAVs)has been widely used in acquiring digital map 4D products,mapping,digital linear maps,and other aspects.However,there are problems,such as low precision and weak practicability in constructing digital elevation model(DEM)products through the data collected using consumption level UAVs.Therefore,improving the accuracy of DEM products obtained by consumption level UAVs is a crucial and complex issue in the research of UAV aerial survey systems.In precision elevation measurement,the geodetic height of a certain number of ground points with reasonable distribution in the region is often obtained first.Then,the normal height of the ground points is obtained by leveling,and the elevation residual value surface of the region is fitted.Finally,the normal height of the points to be solved in the region is obtained by fitting the elevation residual surface.Therefore,the elevation residual fitting method was used to improve the accuracy of consumer UAV DEM products in this study.First,a high-quality ground point cloud was obtained by constructing the gradient filtering-cloth simulation filtering(GF-CSF)model.Second,an abnormal elevation fitting residual DEM model was constructed.Lastly,the final DEM was obtained using the DEM difference method.The experimental results show that among the 20 random sampling inspection points,the average elevation residual was 2.3 mm,and the root mean square error(RMSE)was 16.7 mm after the DEM accuracy was improved by the method.The average elevation residual without improving the DEM accuracy was 28.6 mm,and RMSE was 33.7 mm.

NON-CONTACT MEASUREMENT OF SCULPTURED SURFACE OF ROTATION

A method for measuring the sculptured surface of rotation by using coordinatemeasuring machine (CMM) and rotary table is proposed. The measurement is realized during thecontinuous rotation of the workpiece mounted on the rotary table while the probe moves along thegeneratrix of the surface step by step. This method possesses lots of advantages such as simplicityof probe motion, high reliability and efficiency. Some key techniques including calibration of theeffective radius of the probing system, determination of the position of axis of rotation,auto-centering of the workpiece, data processing algorithm, are discussed. Approaches fordetermining the coordinates on measured surface, establishing workpiece coordinate system andsurface fitting are presented in detail. The method can be used with contact or non-contact probes.Some fragile ceramic and plaster parts are measured by using the system consisting of a CMM, rotarytable, motorized head and non-contact laser triangulation probe. The measuring uncertainty is about0.02 mm which meets the general requirement in most cases.

Global Continuity Adjustment and Local Shape Optimization Technique for Complex Trimmed Surface Model

Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering. In recent years, a lot of progress has been made in smooth join of non-trimmed surface patches, while there has been seldom research on smoothly stitching trimmed surface patches together. This paper studies the problem of global continuity adjustment, damaged hole repair and local shape optimization for complex trimmed surface model, and presents a uniform scheme to deal with continuity adjustment of trimmed surfaces and geometric repair of local broken region. Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G^1 continuity, and then local shape optimization functional is adopted to reduce fitting error and improve local quality of refitted surface patch. The proposed approach is applied to a discontinuity ship hull surface model with an irregular hole, and the result demonstrates the validation of our method. Furthermore, on the premise of global continuity, the proposed locally repairing damaged surface model provides a better foundation for following research work, such as topology recovery technique for complex surface model after geometric repair.

LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING

The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.

Calculation of stratum surface principal curvature based on a moving least square method

With the east section of the Changji sag Zhunger Basin as a case study, both a principal curvature method and a moving least square method are elaborated. The moving least square method is introduced, for the first time, to fit a stratum surface. The results show that, using the same-degree base function, compared with a traditional least square method, the moving least square method can produce lower fitting errors, the fitting surface can describe the morphological characteristics of stratum surfaces more accurately and the principal curvature values vary within a wide range and may be more suitable for the prediction of the distribution of structural fractures. The moving least square method could be useful in curved surface fitting and stratum curvature analysis.

NURBS Parameterization for Medical Surface Reconstruction

InVesalius is an open-source software for reconstruction of computed tomography and magnetic resonance images, which allows the user to make analysis and segmentation of virtual anatomical models. Physical models can be printed with the aid of rapid prototyping, giving the medical community a reliable instrument to help planning surgeries. To offer the user more control over the model, this work describes a methodology and tool developed for NURBS parameterization that provides mechanisms for adjusting the shape or even selecting a particular region of interest of the surface. Furthermore, the tool gives the option to export the final results of the process to a STEP file, which allows further edition in any well-known CAD software.

Feature-Preserving Mesh Denoising via Anisotropic Surface Fitting

We propose in this paper a robust surface mesh denoising method that can effectively remove mesh noise while faithfully preserving sharp features. This method utilizes surface fitting and projection techniques. Sharp features are preserved in the surface fitting algorithm by considering an anisotropic neighborhood of each vertex detected by the normal-weighted distance. In addition, to handle the mesh with a high level of noise, we perform a pre-filtering of surface normals prior to the neighborhood searching. A number of experimental results and comparisons demonstrate the excellent performance of our method in preserving important surface geometries while filtering mesh noise.

Calculation of hydrodynamics for semi-submersibles based on NURBS

Accurate hydrodynamic calculations for semi-submersibles are critical to support modern rapid exploration and extraction of ocean resources. In order to speed hydrodynamic calculations, lines modeling structures were separated into structural parts and then fitted to Non-uniform Rational B-spline (NURBS). In this way, the bow and stern section lines were generated. Modeling of the intersections of the parts was then done with the universal modeling tool MSC.Patran. Mesh was gererated on the model in order to obtain points of intersection on the joints, and then these points were fitted to NURBS. Next, the patch representation method was adopted to generate the meshes of wetted surfaces and interior free surfaces. Velocity potentials on the surfaces were calculated separately, on basis of which the irregular frequency effect was dealt with in the calculation of hydrodynamic coefficients. Finally, the motion response of the semi-submersible was calculated, and in order to improve calculations of vertical motion, a damping term was affixed in the vertical direction. The results show that the above methods can generate fine mesh accurately representing the wetted surface of a semi-submersible and thus improve the accuracy of hydrodynamic calculations.

FITTING C1 SURFACES TO SCATTERED DATA WITH S 1 2 （△ m,n （2））

This paper presents a fast algorithm （BS2 Algorithm） for fitting C 1 surfaces to scat- tered data points. By using energy minimization, the bivariate spline space S 2 1（△ m,n （2） ） is introduced to construct a Cl-continuous piecewise quadratic surface through a set of irregularly 3D points. Moreover, a multilevel method is also presented. Some experimental results show that the accuracy is satisfactory. Furthermore, the BS2 Algorithm is more suitable for fitting surfaces if the given data points have some measurement errors.

Analytical Solution for Model-Based Dynamic Power Factor Measurement in AC Resistance Spot Welding

On the basis of welding transformer circuit model, a new measuring method was proposed. This method measures the peak angle of the welding current, and then calculates the dynamic power factor in each half-wave. An artificial neural network is trained and used to generate simulation data for the analytical solution, i.e. a high-order binary polynomial, which can be easily adopted to calculate the power factor online. The tailored sensing and computing system ensures that the method possesses a real-time computational capacity and satisfying accuracy. A DSP-based resistance spot welding monitoring system was developed to perform ANN computation. The experimental results suggest that this measuring method is feasible.

Estimation of Winds at Different Isobaric Levels Based on the Observed Winds at 850 hPa Level Using Double Fourier Series

A technique based on the double Fourier series is developed to estimate the winds at different isobaric levels forthe limited area domain, 35°E to 140°E and 30°S to 40°N, using the observed winds at 850 hPa lcvcl for the month ofJune. For this purpose the wind field at a level under consideration is taken in the ratio form with that of 850 hPa level and the coefficients of the double Fouricr series are computed. These coefficients are subsequently used to computethe winds which are compared with the actual winds. The results of the double Fourier series technique are comparedwith those of the polynomial surface fitting method developed by Bavadekar and Khaladkar (1 992). The technique isalso applied for the daily wind data of 11. June, 1979 and the validation of the technique is tested for a few radiosondestations of india. The computed winds for these radiosonde stations arc quite close to observed winds.

Lens Calibration Without Pre-Designated Distortion Model and Corresponding Points

A new lens calibration method which is suitable for all kinds of cameras is presented. Based on the linear feature in the image, this method does not require the determination of point correspondence between a scene and the image of the scene. By applying B-spline surface fitting, all kinds of lens distortion models can be simulated. The control points of B-spline surface are estimated iteratively to extract linear feature from the distorted image. Compared with traditional calibration method, which requires either corresponding point pairs or distortion model of lens, or both of them, this method has its unique advantage. Experimental results show the effectiveness of the method.

Image interpolation algorithm on a triangular grid

A new method for constructing a fitting surface on a triangular grid is presented. Assuming images are obtained by sampling from the original scene. Conventional polynomial interpolation methods generally construct the fitting surface on a square grid. Different from existing methods, the new method constructs the fitting surface on a triangular grid which can divide the original surface more detailed and improve approximation accuracy. As the quality of the image edges plays a key role in visual effects of image, the new method uses image edges as constraints to get a triangle grid. The new method constructs a cubic polynomial patch locally using image data to approximate the original surface. Experimental comparison results of the new method with other methods show that the new method can produce high-quality images and remove the zigzagging artifact.

AUTOMATIC PROGRAMMING SYSTEM WITH NURBS METHOD ON PC

This paper presents an automatic programming system on PC, it has also solved the technic problem in the combination of different curves or surfaces. The NURBS is applied to modeling and fitting complicated curves and surfaces. The circular spline is combined with the NURBS to determine the cutter path in accordance with the features of the interpolation movement of NC machine tool. Three methods have been developed to solve the overcutting problems.

Bi-Cubic B-Spline Fitting-Based Local Volatility Model with Mean Reversion Process

This paper studies the traditional local volatility model and proposes:A novel local volatility model with mean-reversion process.The larger is the gap between local volatility and its mean level,the higher will be the rate at which local volatility will revert to the mean.Then,a B-spline method with proper knot control is applied to interpolate the local volatility matrix.The bi-cubic B-spline is used to recover the local volatility surface from this local volatility matrix.Finally,empirical tests show that the proposed mean-reversion local volatility model offers better prediction performance than the traditional local volatility model.

Moving Multiple Curves/Surfaces Approximation of Mixed Point Clouds

We propose a local model called moving multiple curves/surfaces approximation to separate mixed scanning points received from a thin-wall object,where data from two sides of the object may be mixed due to measurement error.The cases of two curves(including plane curves and space curves)and two surfaces in one model are mainly elaborated,and a lot of examples are tested.