Bicubic B-Spline And Thin Plate Spline On Surface Appoximation

In real life, the available data points which are either 2D or 3D are normally scattered and contaminated with noise. The noise is defined as the variation in a set of data points. To fit these data points, the approximation methods are considered as a suitable mean compared to the interpolation methods. It is important for the approximation methods to preserve the shape and features of the model in the presence of any noise. B-spline and thin plate spline approximation are being studied in this thesis. The effectiveness of the modified B-spline approximation algorithm is investigated in approximating the bicubic B-spline surface from the samples of scattered data points taken from the point set model

B-Spline Surface Fitting on Scattered Points

This paper looks into the effectiveness of B-spline approximation algorithm in approximating the bicubic B-spline surface from the set of scattered data points which are taken from the scanned 3D object in the form of point sets. Using the B-spline approximation algorithm, the unknown B-spline control points are determined, followed by the reconstruction of the bicubic B-spline surface. Using a set of neighbourhood of data points, a B-spline surface patch may be constructed, which can be pieced together to form the final surface. Modification of the B-spline approximation algorithm is carried out before the reconstruction in order to fit the scattered data points closely. Here, the density of the data points is scaled down due to the sparseness of the points that may affect the smoothness. The sample of scattered data points is chosen from a specific region in the point set model by using k-nearest neighbour search method. Furthermore, to fit the sample set of scattered data points accurately, they are reoriented in the normal direction. We also observe the effect of noise in the reconstruction of bicubic B-spline surface. Experimental results demonstrate that the scattered data points are better fitted after the modification of the algorithm and the accuracy of the approximated bicubic B-spline surface is easily influenced by the presence of noise

Point Set Denoising Using Bootstrap-Based Radial Basis Function.

This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which is applied when searching for the smoothing parameters of radial basis functions, is revisited. The main contribution of this paper is a smoothing algorithm that relies on a bootstrap-based radial basis function. The proposed method incorporates a k-nearest neighbour search and then projects the point set to the approximated thin-plate spline surface. Therefore, the denoising process is achieved, and the features are well preserved. A comparison of the proposed method with other smoothing methods is also carried out in this study

The Stanford bunny point set model with a noise level of 0.25.

<p>The Stanford bunny point set model with a noise level of 0.25.</p

The noise-free bimba point set model.

<p>The noise-free bimba point set model.</p

The bimba point set model with a noise level of 0.25.

<p>The bimba point set model with a noise level of 0.25.</p

Comparison for the smoothing result from the bimba point set model with a noise level of 0.50.

<p>(a) Proposed smoothing algorithm. (b) HC Laplacian smoothing algorithm. (c) Algebraic point set surface smoothing algorithm.</p

Comparison for the smoothing result from the sphere point set model with a noise level of 0.50.

<p>(a) Proposed smoothing algorithm. (b) HC Laplacian smoothing algorithm. (c) Algebraic point set surface smoothing algorithm.</p

Comparison for the smoothing result from the Stanford bunny point set model with a noise level of 0.25.

<p>(a) Proposed smoothing algorithm. (b) HC Laplacian smoothing algorithm. (c) Algebraic point set surface smoothing algorithm.</p