基于四元素插值的空间曲线边界约束变形方法

曲线形状的变形技术在计算机动画和产品造型设计中有着重要的应用。以单位球面四元素插值为基础建立非线性的局部变换，通过在中间帧重构方程引进边界控制条件，提出了具有边界约束的空间曲线和平面曲线形状的变形方法。该方法在曲线形状渐变序列中具有保周长的线性变化，适合一般曲线的渐变和骨架行走的特征。还给出了建立渐变序列的边界曲线算法，通过实例说明了造型和编辑边界曲线能得到良好的拼接效果。实验表明,该算法在空间曲线变形中具有良好的视觉效果和应用前景，算法具有简易性和统一性。     

基于内在插值的多重形状渐变方法

推广了基于内在形状插值的多边形渐变算法,提出了具有边界约束的多重形状变形方法.通过在约束方程中引进边界控制条件得到适合一般曲线形状的插值算法,并利用具有指定边界约束的变换和形状插值器的构造,使该算法适合具有任意指定边界的多重曲线形状的混合变形,并给出了3D曲线形状边界约束的最优方程.通过2D形状渐变实验表明该算法的视觉效果良好.     

基于形状插值与移动最小二乘变形的图像渐变

针对已有图像渐变方法难以处理较大几何变化的问题,提出一种基于形状插值与移动最小二乘变形的图像渐变方法.给定一幅源图像和一幅目标图像,用户首先通过在图像上放置开或者封闭的曲线(称为"特征曲线"),对齐源和目标图像中的几何特征;然后提出一种基于重心的线条外观模型,以提取表示一组特征曲线的形状及其所传达的视觉外观,并建立一种双层结构的形状插值算法,实现源特征曲线到目标特征曲线的保形状过渡;最后以中间过渡特征曲线为约束,通过保刚性的移动最小二乘变形把2幅图像的几何特征融合在一起,生成保外观的中间过渡图像帧.实验结果表明,该方法能够实时生成自然且视觉真实的图像渐变序列,即使当源和目标图像中对应几何特征的形状差别较大时,也能够充分保持这些特征的外观和属性.     

曲面浅浮雕生成算法

为了在三维网格上快速生成曲面浅浮雕造型,提出一种利用三维模型半自动生成曲面浅浮雕的算法.首先利用图像的边缘检测方法来获取模型在透视场景中的边缘点,并将其与被贴的曲面载体进行位置匹配,获得Poisson方程的Dirichlet边界值;然后对模型高度场的梯度值进行压缩;最后利用确定边界条件的Poisson方程对模型压缩后的梯度场进行求解,还原生成浮雕模型.利用文中算法可以生成贴于曲面上的浅浮雕模型.     

基于压缩存储技术求解压力Poisson方程的BiCGSTAB算法

基于投影算法所得压力Poisson方程进行数值离散,对离散系统形成的稀疏线性方程组,由于线性方程组的系数矩阵存在大量的零元素,为降低内存存储,本文以一维稀疏存储结构对大规模的系数矩阵进行压缩处理,只存储非零元素。同时,以具有优化性质的BiCGSTAB算法求解压力Poisson方程,显著的提高了计算效率。在相同初始条件下,利用Fortran90完成超松弛迭代法的程序求解压力Poisson方程数值离散所得到的线性方程组进行求解对比。结果表明基于压缩存储的BiCGSTAB算法在求解稀疏线性方程组具有明显的优势,该算法求解速度快、高效、可靠。     

基于多层次特征结构的二维形状渐变

二维形状渐变在二维角色动画、模式匹配、几何造型中有着重要的应用.已有方法大多根据边长、角度、面积等局部几何属性来完成形状之间的最佳对应和渐变,忽略了形状的内在特征结构.为此,提出一种基于多层次特征结构的二维形状渐变方法,首先将源形状和目标形状分解为若干个视觉显著性特征,并通过一种用户启发式的半自动方法建立2个形状的特征对应关系;然后根据形状的特征信息构建源形状和目标形状的多层次特征结构,分别表示形状特征的整体位置和朝向、形状特征的局部朝向和形状特征的局部细节;最后组合不同特征层次上的插值结果,重构出中间形状.在源形状到目标形状的渐变过程中,针对不同层次上的特征信息分别使用近似保刚性插值、边角插值以及弹性线性插值方法进行过渡.实验结果表明,该方法简单高效,有效地避免了形状的内部扭曲,保持了形状的局部特征,可产生自然、光滑且视觉真实的形状渐变序列.     

具有边界约束的多重形状变形方法

推广了基于内在形状插值的多边形渐变算法,提出了具有边界约束的多重形状变形方法.基于内在形状插值是公认的对2D形状插值具有良好效果,但是该算法仅适合于闭多边形的插值,不适合曲线形状的插值.通过在约束方程中引进边界控制条件得到适合一般曲线形状的插值算法,并利用具有指定边界约束的变换和形状插值器的构造,使该算法适合具有任意指定边界的多重2D曲线形状的混合变形.实验表明该算的视觉效果良好,可直接用于角色动画设计系统.     

约束条件下的人脸五官替换算法

针对医学美容以及数字娱乐领域中的特定应用,提出了基于图像的人脸五官替换算法。该算法将人脸特征提取与图像复合相结合,无需3维人脸模型重建,自动合成具有源图像主要五官特征的结果图像。系统允许用户调整权重,在源五官与目标五官间进行插值,控制结果图像与二者的相似程度。进一步地,以鼻子附近的拉普拉斯算子为约束,求解泊松方程以去除阴影影响。实验结果表明,该算法效率高,合成效果达到了实用的要求。     

一种新的图像插值算法的研究

针对现有的形状插值算法不易保持模型的尖锐特征,形状过渡序列易产生体积收缩等问题,本文提出了一种新的泊松形状插值算法,采用适合三角网格的局部仿射变换矩阵来描述两个兼容模型之间的关系,对网格中的每个三角面片直接进行插值,而整体插值效果由泊松求解器完成.     

基于局部单射的平面形状插值形变

在只给出用简单多边形表示的两输入形状的情况下,实现一种简单易用、自然高效的形状插值方法.首先利用基于形状感知的特征匹配算法生成源形状和目标形状之间的匹配;之后在源形状上构造三角剖分,并通过求解映射到目标形状上的尽量刚体的局部单射得到同构三角剖分;最后利用扭曲有界的插值方法得到中间序列.实验结果表明,该方法构造的形变结果能较好地体现源形状和目标形状的特征对应信息,形变过程自然,扭曲较小.     

Videoshop: A new framework for spatio-temporal video editing in gradient domain

This paper proposes a new framework for video editing in gradient domain. The spatio-temporal gradient fields of target videos are modified and/or mixed to generate a new gradient field which is usually not integrable. We compare two methods to solve this “mixed gradient problem”, i.e., the variational method and loopy belief propagation. We propose a 3D video integration algorithm, which uses the variational method to find the potential function whose gradient field is closest to the mixed gradient field in the sense of least squares. The video is reconstructed by solving a 3D Poisson equation. The main contributions of our framework lie in three aspects: first, we derive a straightforward extension of current 2D gradient technique to 3D space, thus resulting in a novel video editing framework, which is very different from all current video editing software; secondly, we propose using a fast and accurate 3D discrete Poisson solver which uses diagonal multigrids to solve the 3D Poisson equation, which is up to twice as fast as a simple conventional multigrid algorithm; finally, we introduce a set of new applications, such as face replacement and painting, high dynamic range video compression and graphcut based video compositing. A set of gradient operators is also provided to the user for editing purposes. We evaluate our algorithm using a variety of examples for image/video or video/video pairs. The resulting video can be seamlessly reconstructed.     

Blending Quadric Surfaces with Piecewise Algebraic Surfaces

Given several algebraic surfaces and corresponding auxiliary planes, a scheme for constructing a piecewise algebraic surface to blend the given surfaces is presented along the intersection curves of the given surfaces and their corresponding auxiliary planes. The algorithm starts with the suitable partition of the 3D space into tetrahedrons or prisms in which the algebraic surface patches are defined. Then a smooth piecewise algebraic surface of low degree is constructed which meets the initial surfaces with a certain order of geometric continuity. Examples are provided to demonstrate the detailed construction process and to compare our method with previous approaches. The results show some advantages of the new blending method.     

3D shape metamorphosis based on T-spline level sets

We propose a new method for 3D shape metamorphosis, where the in-between objects are constructed by using T-spline scalar functions. The use of T-spline level sets offers several advantages: First, it is convenient to handle complex topology changes without the need of model parameterization. Second, the constructed objects are smooth (C² in our case). Third, high quality meshes can be easily obtained by using the marching triangulation method. Fourth, the distribution of the degrees of freedom can be adapted to the geometry of the object. Given one source object and one target object, we firstly find a global coordinate transformation to approximately align the two objects. The T-spline control grid is adaptively generated according to the geometry of the aligned objects, and the initial T-spline level set is found by approximating the signed distance function of the source object. Then we use an evolution process, which is governed by a combination of the signed distance function of the target object and a curvature-dependent speed function, to deform the T-spline level set until it converges to the target shape. Additional intermediate objects are inserted at the beginning/end of the sequence of generated T-spline level sets, by gradually projecting the source/target object to the initial/final T-spline level set. A fully automatic algorithm is developed for the above procedures. Experimental results are presented to demonstrate the effectiveness of our method.     

2D shape morphing via automatic feature matching and hierarchical interpolation

The paper presents a new method to interpolate a pair of 2D shapes that are represented by piecewise linear curves. The method addresses two key problems in 2D shape morphing process: feature correspondence and path interpolation. First, a robust feature metric is defined to measure the similarity of a pair of 2D shapes in terms of visual appearance, orientation and relative size. Based on the metric, an optimal problem is defined and solved to associate the features on the source shape with the corresponding ones on the target shape. Then, a two-level hierarchical approach is proposed to solve the corresponding features interpolation trajectory problem. The algorithm decomposes the input shapes into a pair of corresponding coarse polygons and several pairs of corresponding features. Then the corresponding coarse polygons are interpolated in an as-rigid-as-possible plausible way; meanwhile the corresponding features are interpolated using the intrinsic method. Thus interior distortions of the intermediate shapes could be avoided and the feature details on the input shapes could be well preserved. Experimental results show that the method can generate smooth, natural and visually pleasing 2D shape morphing effects.     

An approximation approach of the clothoid curve defined in the interval [0, π/2] and its offset by free-form curves

We propose an algorithm to approximate the clothoid curve defined in the interval [0, π/2] and its offset curves with Bézier curves and the approximation errors converge to zero as the degree of the Bézier curves is increased. Secondly, we discuss how to approximate the clothoid curve by B-spline curves of low degrees. By employing our method, the clothoid curve and its offset can be efficiently incorporated into CAD/CAM systems, which are important for the development of 3D civil engineering CAD systems, especially for 3D highway road design systems. The proposed method has been implemented on AutoCAD R14.     

Light field morphing using 2D features

We present a 2D feature-based technique for morphing 3D objects represented by light fields. Existing light field morphing methods require the user to specify corresponding 3D feature elements to guide morph computation. Since slight errors in 3D specification can lead to significant morphing artifacts, we propose a scheme based on 2D feature elements that is less sensitive to imprecise marking of features. First, 2D features are specified by the user in a number of key views in the source and target light fields. Then the two light fields are warped view by view as guided by the corresponding 2D features. Finally, the two warped light fields are blended together to yield the desired light field morph. Two key issues in light field morphing are feature specification and warping of light field rays. For feature specification, we introduce a user interface for delineating 2D features in key views of a light field, which are automatically interpolated to other views. For ray warping, we describe a 2D technique that accounts for visibility changes and present a comparison to the ideal morphing of light fields. Light field morphing based on 2D features makes it simple to incorporate previous image morphing techniques such as nonuniform blending, as well as to morph between an image and a light field.     

A Ray Tracing Approach to Diffusion Curves

Diffusion curves [ [OBW*08] ] provide a flexible tool to create smooth‐shaded images from curves defined with colors. The resulting image is typically computed by solving a Poisson equation that diffuses the curve colors to the interior of the image. In this paper we present a new method for solving diffusion curves by using ray tracing. Our approach is analogous to final gathering in global illumination, where the curves define source radiance whose visible contribution will be integrated at a shading pixel to produce a color using stochastic ray tracing. Compared to previous work, the main benefit of our method is that it provides artists with extended flexibility in achieving desired image effects. Specifically, we introduce generalized curve colors called shaders that allow for the seamless integration of diffusion curves with classic 2D graphics including vector graphics (e.g. gradient fills) and raster graphics (e.g. patterns and textures). We also introduce several extended curve attributes to customize the contribution of each curve. In addition, our method allows any pixel in the image to be independently evaluated, without having to solve the entire image globally (as required by a Poisson‐based approach). Finally, we present a GPU‐based implementation that generates solution images at interactive rates, enabling dynamic curve editing. Results show that our method can easily produce a variety of desirable image effects.     

着色双面2.5D图形算法研究

2.5D图形算法是计算机卡通动画生成的关键技术。通过将扩散曲线方法引入双面2.5D图形,提出着色双面2.5D图形技术。该技术首先读入矢量表示的图形色源曲线,再根据用户指定的操作对色源曲线进行折叠处理,由矢量曲线所对应的色源颜色对2.5D图形的正反面局部层区域进行扩散着色,最终生成具有渐变着色效果的2.5D图形。实验表明,该方法绘制出的2.5D图形颜色过渡自然,视觉效果好,克服了传统2.5D矢量图形绘制效果颜色单一、颜色过渡生硬等问题。该方法可用于生成静态2.5D图像或动态2.5D动画。