准均匀B样条曲面的多分辨率表示及应用

在多分辨率曲线和曲面造型中，B样条小波已经得到了广泛应用。曲线和曲面的多分辨率造型成为一个研究热点。通过阐述准均匀B样条曲线曲面的基于小波分解的多分辨率表示的数学原理，给出了具体的曲线和曲面小波分解算法和实验结果，说明了准均匀B样条曲面多分辨表示的优点及其在工业上的应用。     

任意NUBS曲线的小波分析和造型技术

为了对任意NUBS曲线进行精确的分解和重构，提出了半正交B样条小波分解和重构的新算法，同时给出了处理非均匀B样条曲线的非整数阶分辨率的小波分解和重构算法，并实现了任意非均匀B样条曲线的多分辨率表示，对于任意非均匀B样条或NUBS曲线，无论它有多少个控制点，均可以对它进行半正交分解和重构，而不受控制点数必须等于2＋3的限制，从这个意义上讲，该方法不仅可以实现连续分辨率水平（continuous-resolutionlevel)的非均匀B样条曲线造型，还可以对非均匀B样条和NURBS曲线进行精确的分解和重构，这对于B样条曲线曲面的多分辨率造型与显示具有重大应用价值。     

NURBS曲线曲面的多分辨率几何建模

针对均匀和准均匀B样条小波多分辨率建模表示能力和适应性的不足,基于离散内积和非均匀B样条节点插入算法建立了一种非均匀半正交B样条小波,并进一步论述了其在非均匀B样条曲线曲面中的多分辨率设计.最后通过实例对非均匀B样条曲线曲面中的多分辨率建模进行了说明和验证.     

基于小波的B样条曲线多分辨表示及编辑

多分辨表示方法为曲线提供了更为灵活的表达方式,使得我们可以在不同分辨率下对曲线进行编辑,小波技术是实现曲线多分辨表示的一种新颖方法,已有许多论文从理论上论述了这项技术,文中从几何概念出发,由浅入深地论述了基于小波的准均匀三次B样条曲线多分辨表示的原理及其实现,并通过实例描述了B样条曲线的多分辨编辑。     

基于双正交非均匀B样条小波的曲线逼近方法

针对B样条曲线逼近有序数据点在应用最小二乘法时出现的计算量较大问题,提出一种基于双正交非均匀B样条小波的曲线逼近方法。其基本思想是：先用最小二乘法生成初始B样条逼近曲线,再用细节曲线逼近误差向量,接着将细节曲线叠加于原逼近曲线得到新的B样条曲线,这个过程是迭代的。细节曲线的基函数是双正交非均匀B样条小波。与传统最小二乘法相比,该方法仅需计算新增线性系统,避免重复计算原系统,降低了计算量,提高了运算效率;此外,给出了B样条逼近曲线的一种多分辨率表示形式。     

小波方法光顺的B样条模糊系统及其应用

为了减少不准确数据对模糊系统的影响, 本文利用准均匀B样条小波方法光顺了B样条模糊系统. 首先将B样条模糊系统的多分辨率表示转化为准均匀B样条函数的多分辨率表示, 接着利用准均匀B样条小波分解方法对相应的准均匀B样条函数进行分解就得到了一系列光顺性逐渐增强、规则个数逐渐减少的模糊系统, 即基于小波方法的光顺B样条模糊系统. 最后, 仿真结果表明, 小波方法光顺的B样条模糊系统构造的模糊控制器在改善原来B样条模糊系统构造的模糊控制器性能的同时, 大大提高了原来控制器的运行效率.     

基于B样条多分辨率表示的一种数字水印方法

本文根据B样条多分辨率表示的特点提出了一种盲数字水印方法,把原图像做二次小波分解,在低频子图像上用Harris特征点检测算法选取特征点,在以特征点为圆心的同心圆上选点的灰度值作为控制顶点建立B样条曲线,对B样条曲线做多分辨率分解,在低分辨率系数中嵌入水印。由于小波分解后选特征点以及Harris特征点具有几何变换不变性,试验表明该方法对JPEG压缩、缩放、旋转、平移、剪切、滤波等具有较强的抵抗力。     

基于曲率单调变化的空间非均匀三次B样条曲线的构造方法

B样条曲线在目前CAD系统中得到广泛应用,针对B样条曲线的光顺问题,给出并证明了具有曲率单调变化的非均匀三次B样条曲线的构造方法.首先通过给定非均匀三次B样条曲线的中间控制边矢量及相关初始条件,然后计算初始和结尾控制边矢量,由此得到的非均匀三次B样条曲线具有单调变化的曲率.实验在Windows系统下基于VC++语言实现,相关实例验证了该构造方法的有效性及实用性.     

一种B样条曲线描述图像边界的算法

型值点的个数与分布对B样条曲线的形状有直接影响,为了让B样条曲线能很好地描述图像区域边缘,研究了一种自适应3次非均匀B样条曲线插值算法。利用B样条曲线在型值点处曲率较大的性质,调整型值点的位置和个数,通过B样条曲线与图像边缘的误差,对型值点进一步优化,使B样条曲线贴合边缘。实验结果表明,该方法得到的B样条曲线能很好地描述区域边缘。     

基于小波的非均匀B样条曲线自动光顺算法

为了更好地对曲线进行自动光顺,针对一般的非均匀B样条曲线,提出一种基于非均匀B样条小波的曲线光顺算法.首先将曲线分解为尺度部分和细节部分,并把细节部分再次分解为小波尺度部分和小波细节部分;然后通过自动设定阈值对小波细节部分进行修复,并通过小波重构得到新的控制顶点;最后对新的控制顶点进行迭代计算,直至达到满意的光顺效果.通过设定光顺误差限,采用该算法可以在计算机上对曲线进行自动光顺操作.实例验证表明,文中算法比其他基于小波的曲线光顺方法具有更好的光顺效果.     

Multiresolution for Algebraic Curves and Surfaces using Wavelets

This paper describes a multiresolution method for implicit curves and surfaces. The method is based on wavelets, and is able to simplify the topology. The implicit curves and surfaces are defined as the zero-valued piece-wise algebraic isosurface of a tensor-product uniform cubic B-spline. A wavelet multiresolution method that deals with uniform cubic B-splines on bounded domains is proposed. In order to handle arbitrary domains the proposed algorithm dynamically adds appropriate control points and deletes them in the synthesis phase.     

Multiresolution video object extraction fitted to scalable wavelet-based object coding

To enable content based functionalities in video processing algorithms, decomposition of scenes into semantic objects is necessary. A semi-automatic Markov random field based multiresolution algorithm is presented for video object extraction in a complex scene. In the first frame, spatial segmentation and user intervention determine objects of interest. The specified objects are subsequently tracked in successive frames and newly appeared objects/regions are also detected. The video object extraction algorithm includes discrete wavelet transform decomposition multiresolution Markov random field (MRF)-based spatial segmentation with emphasis on border smoothness at different resolutions, and an MRF-based backward region classification that determines the tracked objects in the scene. Finally, a motion constraint, embedded in the region classifier, determines the newly appeared objects/regions and completes the proposed algorithm towards an efficient video segmentation algorithm. The results are applicable for generic segmentation applications, however the proposed multiresolution video segmentation algorithm supports scalable object-based wavelet coding in particular. Moreover, compared to traditional object extraction algorithms, it produces smoother and more visually pleasing shape masks at different resolutions. The proposed effective multiresolution video object extraction method allows for larger motion, better noise tolerance and less computational complexity     

基于多分辨率马尔可夫随机场运动目标分割

提出一种基于三维时空小波变换和马尔可夫随机场(MarkovRandomField)模型的多分辨率运动目标分割算法。该算法利用三维时空小波变换对图像序列进行分解得到多分辨率的图像序列,并在此基础上建立多分辨率的马尔可夫随机场模型,构造相应的能量函数。通过条件迭代模型优化算法(IteratedConditionalModes)求解能量函数的最优解,得出标记场,提取出运动目标。实验结果证明,该算法能够很好地消除了单一分辨率的MRF运动检测结果中"空洞"现象,对运动目标分割具有很好的分割效果。     

Multiresolution-based watersheds for efficient image segmentation

This paper presents an efficient method for image segmentation based on a multiresolution application of a wavelet transform and watershed segmentation algorithm. The procedure toward complete segmentation consists of four steps: pyramid representation, image segmentation, region merging and region projection. First, pyramid representation creates multiresolution images using a wavelet transform. Second, image segmentation segments the lowest-resolution image of the pyramid using a watershed segmentation algorithm. Third, region merging merges the segmented regions using the third-order moment values of the wavelet coefficients. Finally, the segmented low-resolution image with label is projected into a full-resolution image (original image) by inverse wavelet transform. Experimental results of the presented method can be applied to the segmentation of noise or degraded images as well as reduce over-segmentation. In addition, we applied our method to human face detection with accurate and closed boundaries.     

Genetic B-Spline approximation on combined B-reps

We present a genetic algorithm for approximating densely sampled curves with uniform cubic B-Splines suitable for Combined B-reps. A feature of this representation is altering the continuity property of the B-Spline at any knot, allowing to combine freeform curves and polygonal parts within one representation. Naturally there is a trade-off between different approximation properties like accuracy and the number of control points needed. Our algorithm creates very accurate B-Splines with few control points, as shown in Fig.?1. Since the approximation problem is highly nonlinear, we approach it with genetic methods, leading to better results compared to classical gradient based methods. Parallelization and adapted evolution strategies are used to create results very fast.     

MRF-based texture segmentation using wavelet decomposed images

In recent textured image segmentation, Bayesian approaches capitalizing on computational efficiency of multiresolution representations have received much attention. Most of the previous researches have been based on multiresolution stochastic models which use the Gaussian pyramid image decomposition. In this paper, motivated by nonredundant directional selectivity and highly discriminative nature of the wavelet representation, we present an unsupervised textured image segmentation algorithm based on a multiscale stochastic modeling over the wavelet decomposition of image. The model, using doubly stochastic Markov random fields, captures intrascale statistical dependencies over the wavelet decomposed image and intrascale and interscale dependencies over the corresponding multiresolution region image.     

基于区域分割的小波分解运动补偿编码算法

为了提高视频运动估值的速度和运动矢量编码的效率，提出了一种基于区域分割的小波分解运动补偿的视频编码算法，该算法的几个核心部分的特点如下：（1）运动估值部分，在基本的可变块多分辨率运动估值算法的基础上，充分利用了小波分解后各子带所表征的运动结构相关性，因而提高了运动矢量的编码效率，同时提出了基于区域分割的多分辨率运动估值算法，因而在有效减少运动估值时间消耗的同时，进一步提高了运动矢量的编码效率；（2）在量化部分，提出了一种基于人的视觉系统的量化方法；（3）采用改进的高效的零树小波编码算法对帧内和帧间信息进行编码，实验结果表明，所提出的算法是有效的。     

利用分水岭分割的多分辨率遥感图像融合算法

对全色图像和多光谱图像进行融合可以获得更加清晰的图像信息。提出了一种基于分水岭分割和小波变换的多分辨率图像融合算法。利用正交小波变换得到原图像的小波金字塔表示。对近似图像进行分水岭分割,并且用小波逆变换把原始分割结果逐步映射回更高的分辨率层。通过联合区域分析,得到各层的联合区域分割图,并用此图来指导各层小波系数的融合。对融合系数进行小波逆变换,得到融合的图像。实验结果表明,该法对遥感图像的融合十分有效,能很好地兼顾融合图像的光谱质量和空间清晰度。     

Construction of uniformly symmetric bi-frames based on multiresolution template algorithm

In this paper, we focus on the construction of wavelet bi-frames with three generators and uniform symmetry which play an important role in the applications for curve multiresolution processing. We first establish some templates of the decomposition and reconstruction algorithm corresponding to wavelet bi-framelet by several iterative steps. These templates allow parameterization of wavelet bi-framelet filter banks with three symmetric generators. Then the parameters in the filter can be determined by solving systems of nonlinear equations related to the sum rules for the refinement mask and the vanishing moments of framelets, which led to the wavelet bi-frames with desired properties. Some examples of uniform symmetry bi-frames with three generators are presented to illustrate efficient of our methods.     

Unsupervised multiscale segmentation of color images

This paper proposes a new multiresolution technique for color image representation and segmentation, particularly suited for noisy images. A decimated wavelet transform is initially applied to each color channel of the image, and a multiresolution representation is built up to a selected scale 2^J. Color gradient magnitudes are computed at the coarsest scale 2^J, and an adaptive threshold is used to remove spurious responses. An initial segmentation is then computed by applying the watershed transform to thresholded magnitudes, and this initial segmentation is projected to finer resolutions using inverse wavelet transforms and contour refinements, until the full resolution 2⁰ is achieved. Finally, a region merging technique is applied to combine adjacent regions with similar colors. Experimental results show that the proposed technique produces results comparable to other state-of-the-art algorithms for natural images, and performs better for noisy images.