三次插值样条曲线拟合多核并行算法

充分利用多核技术提升多核处理器的资源利用率,缩短执行时间,发挥多核系统的优异性能。在多核计算机上设计了解三对角方程组的奇偶约化多线程并行程序,实现了三次样条曲线拟合的快速计算。通过实验结果的加速比对比,可以看出并行后缩短了求解方程组的时间,多核资源得到充分利用。结果表明,奇偶约化多核并行算法在三次样条曲线拟合中的应用是有效及可行的。     

基于样条曲线拟合的肺区轮廓修补算法*

当肿瘤处于肺的边缘时,依据CT图像分割出的肺区有缺陷,肿瘤可能被排除在分割出的肺区外.为了解决这一问题,根据肺区外侧轮廓的形状特征,抽取多个控制点,使用Cardinal样条曲线拟合肺区轮廓.拟合后的边界成功地把肿瘤包含在肺区内.     

基于多值样条拟合曲线搜索的医学图像分割

针对肾组织切片图像的复杂特点,提出了一种基于拟合曲线搜索的肾小球分割方法,克服了边界增强方法中由于边界大量缺损而导致的肾小球区域提取不全的困难。首先在小波低频区域使用LOG滤波器获得含噪声较少的边界二值图像,在该二值图像中采用三次样条拟合方法构造闭合曲线,然后通过遗传算法在小波构造的低分辨率图像中搜索边界的最佳拟合曲线,在高分辨率图像中对该曲线进行精细化调整。实践证明了这一方法的正确性和有效性。     

Cone spline approximation via fat conic spline fitting

Fat conic section and fat conic spline are defined. With well established properties of fat conic splines, the problem of approximating a ruled surface by a tangent smooth cone spline can then be changed as the problem of fitting a plane fat curve by a fat conic spline. Moreover, the fitting error between the ruled surface and the cone spline can be estimated explicitly via fat conic spline fitting. An efficient fitting algorithm is also proposed for fat conic spline fitting with controllable tolerances. Several examples about approximation of general developable surfaces or other types of ruled surfaces by cone spline surfaces are presented.     

Intrinsic spline curve with local control

A new spline algorithm that uses arc length as parameter and generates a curve in terms of the quantities ‘relative curvature’ and ‘relative torsion’ is described. The tangent and curvature vectors at each datapoint are estimated and the spline is built up span by span. This allows local changes without affecting the whole curve and facilitates the incorporation of derivative discontinuities. Unless discontinuities are specifically requested, the solution obtained is curvature continuous.     

Cubic curve update

The author considers the problem of cataloging all the shapes that can be generated by a cubic equation. In response to a letter commenting on an earlier column, he corrects an error in his listing of all the combinations of factorizations that could make degenerate curves, pointing out that all type 5's are really the same shape and all type 7's are really the same shape. He provides additional considerations on the possible shapes of nondegenerate curves     

Hybrid curve fitting

We consider a parameterized family of closed planar curves and introduce an evolution process for identifying a member of the family that approximates a given unorganized point cloud {p _i } _{i =1,..., N} . The evolution is driven by the normal velocities at the closest (or foot) points (f _i ) to the data points, which are found by approximating the corresponding difference vectors p _i -f _i in the least-squares sense. In the particular case of parametrically defined curves, this process is shown to be equivalent to normal (or tangent) distance minimization, see [3], [19]. Moreover, it can be generalized to very general representations of curves. These include hybrid curves, which are a collection of parametrically and implicitly defined curve segments, pieced together with certain degrees of geometric continuity.     

Cubic B-spline curve approximation by curve unclamping

A new approach for cubic B-spline curve approximation is presented. The method produces an approximation cubic B-spline curve tangent to a given curve at a set of selected positions, called tangent points, in a piecewise manner starting from a seed segment. A heuristic method is provided to select the tangent points. The first segment of the approximation cubic B-spline curve can be obtained using an inner point interpolation method, least-squares method or geometric Hermite method as a seed segment. The approximation curve is further extended to other tangent points one by one by curve unclamping. New tangent points can also be added, if necessary, by using the concept of the minimum shape deformation angle of an inner point for better approximation. Numerical examples show that the new method is effective in approximating a given curve and is efficient in computation.     

Moment computation for objects with spline curve boundary

A new approach is proposed for computation of area and geometric moments for a plane object with a spline curve boundary. The explicit formulae are obtained for area and low order moment calculation. The complexity of calculation depends on the moment order, spline degree, and the number of control points used in spline representation. The formulae proposed use the advantage that the sequence of spline control points is cyclic. It allowed us to reduce substantially the number of summands in them. The formulae might be useful in different applications where it is necessary to perform measurements for shapes with a smooth boundary.     

Fairing of Parametric Cubic B-spline Curves and Bicubic B-spline Surfaces

ＦａｉｒｉｎｇｏｆＰａｒａｍｅｔｒｉｃＣｕｂｉｃＢｓｐｌｉｎｅＣｕｒｖｅｓａｎｄＢｉｃｕｂｉｃＢｓｐｌｉｎｅＳｕｒｆａｃｅｓＭｕＧｕｏｗａｎｇ，ＺｈｕＸｉｎｘｉｏｎｇ，ＬｅｉＹｉａｎｄＴｕＨｏｕｊｉｅＤｅｐａｒｔｍｅｎｔｏｆＭａｎｕｆａｃｔｕｒｉ...     

Towards perceptual video cropping with curve fitting

Coming with the proliferation of mobile devices, the issue of displaying videos with varying resolutions and aspect ratios has become emerging. To this end, state-of-the-art works typically resort to video retargeting or cropping, i.e. adaptively adjusting the display regions and contents within each video frame to fit for the mobile device screens. However, most existing approaches retain on evaluating the objective visual statistics to select salient parts to be cropped within each frame, with time-consuming constraints to ensure the temporal consistency, which is indeed unsuitable to cope with the massive videos uploaded daily from user-contributed platforms. In this paper, we propose an efficient yet robust video cropping algorithm which merits in two-fold: First, a perceptual Region of Interest selection approach is proposed by employing a novel Interesting Region Score, which is a linear combination of Rate of Focused Attention, Total Saliency Score, and Bias from Center Penalty. Second, we adopt fast curve fitting to seek for an optimal cropping sequence over a set of consecutive video frames within a shot, which avoids the complex optimization with temporal constraints among adjacent frames. Experiments on video sequences from Backkom cartoon and Iron Man II with comparisons against several alternative approaches demonstrate the efficiency and robustness of the proposed algorithm.     

Data fitting with a spline using a real-coded genetic algorithm

To obtain a good approximation for data fitting with a spline, frequently we have to deal with knots as variables. The problem to be solved then becomes a continuous nonlinear and multivariate optimization problem with many local optima. Therefore, it is difficult to obtain the global optimum. In this paper, we propose a method for solving this problem by using a real-coded genetic algorithm. Our method can treat not only data with a smooth underlying function, but also data with an underlying function having discontinuous points and/or cusps. We search for the best model among candidate models by using the Bayes Information Criterion (BIC). With this, we can appropriately determine the number and locations of knots automatically and simultaneously. Five examples of data fitting are given to show the performance of our method.     

Cubic spline interpolation based ultrasound scan conversion algorithm

Digital scan conversion is employed in medical ultrasound imaging system to display scanned vector data in Cartesian coordinate that are acquired with polar coordinate. Interpolation is applied to estimate gray values of unsampled pixels in digital scan conversion. A cubic spline interpolation based scan conversion algorithm is proposed for ultrasound vector data processing. Cubic spline interpolation is efficient to provide more accurate result images for both nature and ultrasonic images. Experimental results indicate that the result images of the proposed algorithm are more accurate than those of the nearest neighbor interpolation, linear interpolation and cubic convolution interpolation based algorithm.     

基于组合方法对图像的双三次多项式拟合

提出了基于图像数据构造拟合曲面的新方法.假设给定的图像数据所对应的原场景曲面能用分片二次多项式曲面表示,原场景曲面称为原曲面.现有方法通常是用图像数据作为插值数据构造原曲面的拟合曲面,而新方法以图像数据生成公式为约束,通过反向采样过程来构造对图像数据拟合的曲面,从而使拟合曲面具有更好的逼近精度.由于图像边缘处的质量对图像的视觉效果起着关键的作用,我们也把图像边缘做为约束条件用于拟合曲面的构造.对于每一个数据点及其邻近区域,新方法以采样公式和图像边缘作为约束条件局部地构造一张二次多项式曲面片,该曲面片具有二次多项式精度.所有的二次多项式曲面片的加权组合形成逼近原曲面的拟合曲面.对算法比较的实验表明,由新方法生成的放大图像具有较高的精度和较好的视觉效果.     

Constrained curve fitting on manifolds

When designing curves on surfaces the need arises to approximate a given noisy target shape by a smooth fitting shape. We discuss the problem of fitting a B-spline curve to a point cloud by squared distance minimization in the case that both the point cloud and the fitting curve are constrained to lie on a smooth manifold. The on-manifold constraint is included by using the first fundamental form of the surface for squared distance computations between the point cloud and the fitting curve. For the solution we employ a constrained optimization algorithm that allows us to include further constraints such as one-sided fitting or surface regions that have to be avoided by the fitting curve. We illustrate the effectiveness of our algorithm by means of several examples showing different applications.     

用于曲线拟合的种群再分布遗传算法

针对简单遗传算法在曲线拟合应用中局部搜索能力差、收敛精度低的特点,提出了一种新的基于种群再分布的改进遗传算法。该算法在遗传算法进行的过程中,根据最优解的优劣,调整种群在最优解附近的分布,从而增强了算法的局部搜索能力。实验证明,该方法对于曲线拟合问题能取得优于简单遗传算法和传统数值迭代方法的结果。     

Parametric and nonparametric curve fitting

We are concerned with convergence issues in the identification of a static nonlinear function. Our investigation focuses on properties of the input signal that ensure convergence of the estimate. Both parametric and nonparametric approaches are considered. In the parametric case, we offer sufficient conditions under which the estimated parameters converge to their true values almost surely. For the nonparametric case, we offer necessary and sufficient conditions under which the estimated function converges almost surely to the true nonlinearity.