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.

ANNUAL VARIATIONS OF TEMPERATURE ON FOUR URBAN UNDERLYING SURFACES AND FITTING ANALYSIS

Based on the observed 2-year temperature data for four kinds of typical urban underlying surfaces,including asphalt, cement, bare land and grass land, the annual variations and influencing factors of landsurface temperature are analyzed. Then fitting equations for surface temperature are established. It is shownthat the annual variation of daily average, maximum and minimum temperature and daily temperature rangeon the four urban underlying surfaces is consistent with the change in air temperature. The difference oftemperature on different underlying surfaces in the summer half year (May to October) is much moreevident than that in the winter half year (December to the following April). The daily average and maximumtemperatures of asphalt, cement, bare land and grass land are higher than air temperature due to theatmospheric heating in the daytime, with that of asphalt being the highest, followed in turn by cement, bareland and grass land. Moreover, the daily average, maximum and minimum temperature on the four urbanunderlying surfaces are strongly impacted by total cloud amount, daily average relative humidity andsunshine hours. The land surface can be cooled (warmed) by increased total cloud amount (relativehumidity). The changes in temperature on bare land and grass land are influenced by both the total cloudamount and the daily average relative humidity. The temperature parameters of the four land surfaces aresignificantly correlated with daily average, maximum and minimum temperature, sunshine hours, dailyaverage relative humidity and total cloud amount, respectively. The analysis also indicates that the range offitting parameter of a linear regression equation between the surface temperature of the four kinds of typicalland surface and the air temperature is from 0.809 to 0.971, passing the F-test with a confidence level of 0.99.

Study on curved surface fitting model using GPS and leveling in local area

The height anomaly surface is fitt and the quasi-geoid can be obtained when the height anomaly is determined with the geometric analytic method. Therefore, some mathematical models to fit height anomaly surface using GPS, leveling and terrain data in a local area, including the polynomial fitting model, the multi-surface function fitting model, the motion surface fitting model and the fitting model of little flexibility deformation of thin board, are given. Then the digital characteristics are analyzed with the curved surface theory. The General curvature and the mean curvature of surface are concluded. The advantage, disadvantage and application of the above models are discussed. The effect of terrain undulation on height anomaly is considered in the surface fitting models. The practical case indicates that these models are of validity and practicability. It is concluded that the above models can give the good fitting results at the centimeter level. But the polynomial fitting model is worse than the other models.

Spectral Reflectance Characteristics of Different Snow and Snow-Covered Land Surface Objects and Mixed Spectrum Fitting

The field spectroradiometer was used to measure spectra of different snow and snow-covered land surface objects in Beijing area.The result showed that for a pure snow spectrum,the snow reflectance peaks appeared from visible to 800 nm band locations;there was an obvious absorption valley of snow spectrum near 1 030 nm wavelength.Compared with fresh snow,the reflection peaks of the old snow and melting snow showed different degrees of decline in the ranges of 300～1 300,1 700～1 800 and 2 200～2 300 nm,the lowest was from the compacted snow and frozen ice.For the vegetation and snow mixed spectral characteristics,it was indicated that the spectral reflectance increased for the snow-covered land types(including pine leaf with snow and pine leaf on snow background), due to the influence of snow background in the range of 350～1 300 nm.However, the spectrum reflectance of mixed pixel remained a vegetation spectral characteristic.In the end,based on the spectrum analysis of snow,vegetation,and mixed snow/vegetation pixels,the mixed spectral fitting equations were established,and the results showed that there was good correlation between spectral curves by simulation fitting and observed ones(correlation coefficient R2=0.950 9).

Fitting of Analytic Surfaces to Noisy Point Clouds

Fitting C2-continuous or superior surfaces to a set S of points sampled on a 2-manifold is central to reverse engineering, computer aided geometric modeling, entertaining, modeling of art heritage, etc. This article addresses the fitting of analytic (ellipsoid, cones, cylinders) surfaces in general position in . Currently, the state of the art presents limitations in 1) automatically finding an initial guess for the analytic surface F sought, and 2) economically estimating the geometric distance between a point of S and the analytic surface F. These issues are central in estimating an analytic surface which minimizes its accumulated distances to the point set. In response to this situation, this article presents and tests novel user-independent strategies for addressing aspects 1) and 2) above, for cylinders, cones and ellipsoids. A conjecture for the calculation of the distance point-ellipsoid is also proposed. Our strategies produce good initial guesses for F and fast fitting error estimation for F, leading to an agile and robust optimization algorithm. Ongoing work addresses the fitting of free-form parametric surfaces to S.

Predicting of Land Surface Temperature Distribution in Freetown City, Sierra Leone by Using Polynomial Curve Fitting Model

Global warming has attracted much concern about the worldwide organization, civil society groups, researchers, and so forth because the worldwide surface temperature has been expanding. This investigation intends to assess and compare the ability of a combination of land cover indices to predict the future distribution of land surface temperatures in Freetown using the Polynomial model analysis. Landsat satellite images of 1988, 1998, 2000, 2010, and 2018 of the Freetown Metropolitan zone were utilized for analysis. The investigation had adopted two land covers indices, Modification of normalized difference water index and Urban Index (UI) (e.g., MNDWI and UI) and applied a multi regression equation for forecasting the future LST. The stimulation results propose that the development will be accompanied by surface temperature increases, especially in Freetown’s western urban area. The temperature prevailing in the west of the metropolitan area may increase in the city somewhere in the range from 1988 to 2018. Additionally, the results of the LST prediction show that the model is perfect. Our discoveries can be represented as a helpful device for policymakers and community awareness by giving a scientific basis for sustainable urban planning and management.

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.

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.

A Gradient-Simulated Annealing Algorithm of Pre-location-Based Best Fitting of Blank to Complex Surfaces Machining

The algorithm is divided into two steps. The first step pre-locates the blank by aligning its centre of gravity and approximate normal vector with those of destination surfaces, with largest overlap of projections of two objects on a plane perpendicular to the normal vector. The second step is optimizing an objective function by means of gradient-simulated annealing algorithm to get the best matching of a set of distributed points on the blank and destination surfaces. An example for machining hydroelectric turbine blades is given to verify the effectiveness of algorithm.

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.

Ship hull plate processing surface fairing with constraints based on B-spline

The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

Irregular surface seismic forward modeling by a body-fitted rotated–staggered-grid finite-difference method

Finite-difference(FD) methods are widely used in seismic forward modeling owing to their computational efficiency but are not readily applicable to irregular topographies. Thus, several FD methods based on the transformation to curvilinear coordinates using body-fitted grids have been proposed, e.g., stand staggered grid(SSG) with interpolation, nonstaggered grid, rotated staggered grid(RSG), and fully staggered. The FD based on the RSG is somewhat superior to others because it satisfies the spatial distribution of the wave equation without additional memory and computational requirements; furthermore, it is simpler to implement. We use the RSG FD method to transform the firstorder stress–velocity equation in the curvilinear coordinates system and introduce the highprecision adaptive, unilateral mimetic finite-difference(UMFD) method to process the freeboundary conditions of an irregular surface. The numerical results suggest that the precision of the solution is higher than that of the vacuum formalism. When the minimum wavelength is low, UMFD avoids the surface wave dispersion. We compare FD methods based on RSG, SEM, and nonstaggered grid and infer that all simulation results are consistent but the computational efficiency of the RSG FD method is higher than the rest.

Reconstruction of B-spline surface by interpolating boundary curves and approximating inner points

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is： first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.

Symmetric alteration of four knots of B-spline and NURBS surfaces

Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface, the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.

G^0 and G^1 connection between two adjacent B-spline surfaces

In this paper, the smooth connection between two B-spline surfaces is discussed. First, a brief proof of some simple sufficient conditions of Go and G1 continuity is given. On this basis, a novel method for Go or G1 connection between two adjacent B-spline surfaces is presented. A reparameterization step is firstly taken for one of the surfaces such that they have the same parameterization in v direction, then, adjust their boundary control vertices to make them Go or Gl connected. The GI connection parameter is determined by an optimization problem. Compared with the existed methods, our method is simple and easy to be used in practice.

B-Spline Approximation of Ship Waves on the Free Surface

We consider the problem of a ship advancing in waves. In this method, the zone of free surface in the vicinity of body is discretized. On the discretized surface, the first-order and second-order derivatives of ship waves are represented by the B-Spline formulae. Different ship waves are approximated by cubic B-spline and the first and second order derivates of incident waves are calculated and compared with analytical value. It approves that this numerical method has sufficient accuracy and can be also applied to approximate the velocity potential on the free surface.

G^1 Continuity Conditions of B-spline Surfaces

According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a kind of sufficient conditions of G1 continuity are developed, and a kind of sufficient conditions of G1 continuity among N(N>2) patch B-spline surfaces meeting at a common corner are given at the end.

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.

Influence of Interference Fit and Surface Roughness on Contact Resistance of Tubing Connections

Within offshore installations, making tubing connections conduct electricity is a developing interest. Being able to use tubing structures to carry the drive power needed downhole avoids installation of cables and lines. The challenge is making the connection good enough with minimum possible power loss. At the same time, the connection has to secure the transfer of the rated power without any danger of overheating. An overheating can eventually result in a welded connection. Previous studies on contact design have mainly focused on low level contact force, while this study aims to find out the influence of surface roughness and connection strength, at macro level, on contact resistance of tubing connections so as to know the power transfer capability of the connection. First, the connection is simplified by ＂rolling out＂ the tubes to flat sheet metals and the voltage drop at rated current was measured at various loads. Then experiment was conducted on contact pairs with two different surface finish qualities and three different contact fits. The results show that smoother surfaces ease the flow of current while high interference fit increases the contact stability. The influence of surface topography becomes insignificantly low at high connection interference.