图像插值技术综述

图像插值是图像处理中最基本的技术之一,得到了广泛研究和应用.将图像插值技术分为传统插值、基于边缘的插值和基于区域的插值3类,介绍了各类技术的一般实现方法和典型算法;从原理上分析了各类算法的科学性;并对不同算法进行了对比实验和讨论.实验结果表明,基于区域的插值方法原理更科学,插值图像的主观和客观质量最好;最后,给出了图像插值的发展形式及前景.     

一种基于4对图像对应点的欧氏重建方法

摄像机自标定算法通常是非线性的，为了得到线性的方法，提出了一种在RANSAC框架下由4对图像对应点线性标定摄像机并对场景进行鲁棒性欧氏重建的方法。当摄像机作两组平移运动时，若在两组平移运动之间摄像机具有不同的姿态，则从4对图像对应点可以线性地重建场景的欧氏几何。模拟实验和真实图像实验均证明了本文方法的可行性。     

基于断层间切片图像的插值方法研究

断层间图像插值是三维重建的一个关键步骤,研究了传统的插值方法,并对其进行了分析。在此基础上提出了一种基于距离变换的目标图像插值方法,该方法首先对断层图像进行阈值分割得到目标图像并对图像进行中心配准,然后运用欧几里德距离变换法求取目标图像的距离图像,采用加权平均线性插值方法得到目标图像间的插值图像;对ICT切片图像进行了实验研究,取得了令人满意的效果。     

基于核的图像欧氏距离人脸识别

引进了两幅图像之间的一种新的距离度量方法——图像欧氏距离,该距离是利用核函数对传统的欧氏距离进行改进而得到的。在此基础上,设计了一种新的分类识别方法——基于核的图像欧氏距离人脸识别方法,并应用于人脸识别中。为验证该算法的可行性,对人脸图像进行DCT变换得到预处理样本,并在ORL和Yale人脸库上进行多角度的比较实验。分析实验结果表明,该方法优于其它距离分类器算法。     

根据轮廓寻找匹配对应点的断层图像插值方法

插值是三维重建的一个重要步骤。目前常用的直接灰度插值会使得图像边界模糊。针对这一问题,提出一种基于轮廓寻找匹配点的插值方法：首先对两幅图像进行形状插值,得到插值图像的轮廓;再根据轮廓寻找插值图像在两幅源图像上的对应点,并根据匹配准测,找到最佳匹配点;最后对匹配点的灰度进行插值,得到插值像素点的灰度值。试验结果表明,和已有的算法比较,新算法较好地提高了插值图像的质量。     

基于密切多项式近似的多项式插值算法框架

多项式插值技术是近似理论中一种常见的近似方法,被广泛用于数值分析、信号处理等领域。但传统的多项式插值技术大多是基于数值分析与实验结果相结合得到的,没有统一的理论描述和规律性的解决方案。为此,根据密切多项式近似理论为图像的多项式插值算法提出一个统一的理论框架。密切多项式近似的理论框架包括采样点数目、密切阶数和导数近似规则三个部分,它既可以用于分析现有的多项式插值算法,也可以用于开发新的多项式插值算法。分析了主流多项式插值技术在密切多项式近似理论框架下的表现形式,并以四点二阶密切多项式插值算法为例详细描述了利用密切多项式插值的理论框架开发新的多项式插值算法的一般流程。理论分析和数值实验表明大多数主流插值算法都属于密切多项式插值算法,它们的处理效果与采样点数目、密切阶数和导数近似规则有紧密的关系。     

一种基于小波与双三次插值的CCD图像超分辨方法*

为了尽可能地保持CCD图像的原始信息,提高图像的空间分辨率,有利于对图像的细节信息进行观察分析,对各种超分辨方法进行研究,提出了一种改进的基于小波和双三次插值的超分辨方法：对低分辨率图像进行灰度变换,并把它作为小波逆变换的低分辨率图像,对图像进行恢复,再与低分辨图像的双三次插值图像求平均。将该方法应用于CCD图像,从视觉上空间分辨率有提高,并可以获得25.524 4 dB的峰值信噪比。实验结果表明,该算法得到了比全小波双三次插值、原图像作为低频图像小波双三次插值和双线性插值更高的峰值信噪比及更好的图像细节     

解析法图像重建中的插值技术研究

为了给图像重建中插值方法的选择提供依据,研究了线性插值和样条插值对重建图像的质量影响.分析了常用的插值技术,从一维插值的角度,从理论和实验两个方面分析了线性插值和样条插值的性能,将两种方法应用到滤波反投影法图像重建中,分析了两种方法在不同的投影采样间隔的情况下对重建图像的质量影响.结果发现在一维信号插值时,样条插值精度高,但在图像重建时,采用更精确的样条插值反而使得重建图像的质量下降.最后指出图像重建时应该采用能更好的抑制振荡噪声的线性插值方法.     

基于结构张量的图像插值方法

提出了一种新的图像插值算法，该算法利用局部结构张量所描述的图像几何特征增强了图像的边缘而不会产生伪影。在仿真实验中，应用该方法能够得到比传统的双线性和双三次插值方法更优的结果，特别是在边缘区域。而且该方法采用的插值格式能有效地减小计算量，适合实时应用。就提出的插值模型和一种基于变分的插值方法之间的关系进行了讨论，分析表明后者只是该模型的一个特例。     

基于二元树复小波的图像插值超分辨率算法

根据二元树复小波理论和图像插值的特点,将二元树复小波变换与基于边缘插值方法相结合,得到一个放大的插值图像,然后将插值后的图像进行一级小波分解,将分解后的高频子带再做小波变换,并修正变换后的高颊子带系数,进行图像重构后得到最终的插值图像.实验结果表明,该方法能够提高图像的分辨率,_同时消除边缘处的"振铃"效应.     

Manifold-valued Thin-Plate Splines with Applications in Computer Graphics

We present a generalization of thin‐plate splines for interpolation and approximation of manifold‐valued data, and demonstrate its usefulness in computer graphics with several applications from different fields. The cornerstone of our theoretical framework is an energy functional for mappings between two Riemannian manifolds which is independent of parametrization and respects the geometry of both manifolds. If the manifolds are Euclidean, the energy functional reduces to the classical thin‐plate spline energy. We show how the resulting optimization problems can be solved efficiently in many cases. Our example applications range from orientation interpolation and motion planning in animation over geometric modelling tasks to color interpolation.     

Diffusion tensor interpolation profile control using non-uniform motion on a Riemannian geodesic

Tensor interpolation is a key step in the processing algorithms of diffusion tensor imaging (DTI), such as registration and tractography. The diffusion tensor (DT) in biological tissues is assumed to be positive definite. However, the tensor interpolations in most clinical applications have used a Euclidian scheme that does not take this assumption into account. Several Rie-mannian schemes were developed to overcome this limitation. Although each of the Riemannian schemes uses different metrics, they all result in a ‘fixed’ interpolation profile that cannot adapt to a variety of diffusion patterns in biological tissues. In this paper, we propose a DT interpolation scheme to control the interpolation profile, and explore its feasibility in clinical applications. The profile controllability comes from the non-uniform motion of interpolation on the Riemannian geodesic. The interpolation experiment with medical DTI data shows that the profile control improves the interpolation quality by assessing the reconstruction errors with the determinant error, Euclidean norm, and Riemannian norm.     

Tensor scale: An analytic approach with efficient computation and applications

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods.     

显式重定向的扩散张量图像配准

扩散张量图像配准算法是近年图像配准研究的热点与难点之一.针对配准中容易出现的局部极值和张量重定向问题,以欧氏距离为相似性测度,将张量重定向显式融入目标函数,采用模拟退火算法与Powell算法法相结合的混合优化策略,对临床使用的扩散张量图像DTI(Diffusion Tensor Images)进行配准实验.实验结果表明,该算法稳定性良好,在对扩散张量图像进行配准时,能有效保持扩散张量主特征方向与纤维走向的一致性,同时成功解决了局部极值的困扰,是一种实用的扩散张量图像配准方法.     

A Riemannian Framework for Tensor Computing

Tensors are nowadays a common source of geometric information. In this paper, we propose to endow the tensor space with an affine-invariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries (null eigenvalues are at the infinity), the geodesic between two tensors and the mean of a set of tensors are uniquely defined, etc. We have previously shown that the Riemannian metric provides a powerful framework for generalizing statistics to manifolds. In this paper, we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation, filtering, diffusion and restoration of missing data. For instance, most interpolation and Gaussian filtering schemes can be tackled efficiently through a weighted mean computation. Linear and anisotropic diffusion schemes can be adapted to our Riemannian framework, through partial differential evolution equations, provided that the metric of the tensor space is taken into account. For that purpose, we provide intrinsic numerical schemes to compute the gradient and Laplace-Beltrami operators. Finally, to enforce the fidelity to the data (either sparsely distributed tensors or complete tensors fields) we propose least-squares criteria based on our invariant Riemannian distance which are particularly simple and efficient to solve.     

A generic approach to diffusion filtering of matrix-fields

Summary Diffusion tensor magnetic resonance imaging, is a image acquisition method, that provides matrix- valued data, so-called matrix fields. Hence image processing tools for the filtering and analysis of these data types are in demand. In this article, we propose a generic framework that allows us to find the matrix-valued counterparts of the Perona–Malik PDEs with various diffusivity functions. To this end we extend the notion of derivatives and associated differential operators to matrix fields of symmetric matrices by adopting an operator-algebraic point of view. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our novel matrix-valued Perona–Malik diffusion filters. The Dutch Organization NWO is gratefully acknowledged for financial support. The German Organization DFG is gratefully acknowledged for financial support.     

3D space-varying coefficient models with application to diffusion tensor imaging

The present methodological development and the primary application field originate from diffusion tensor imaging (DTI), a powerful nuclear magnetic resonance technique which enables the quantification of microscopical tissue properties. The current analysis framework of separate voxelwise regressions is reformulated as a 3D space-varying coefficient model (SVCM) for the entire set of diffusion tensor images recorded on a 3D voxel grid. The SVCM unifies the three-step cascade of standard data processing (voxelwise regression, smoothing, interpolation) into one framework based on B-spline basis functions. Thereby strength is borrowed from spatially correlated voxels to gain a regularization effect right at the estimation stage. Two SVCM variants are conceptualized: a full tensor product approach and a sequential approximation, rendering the SVCM numerically and computationally feasible even for the huge dimension of the joint model in a realistic setup. A simulation study shows that both approaches outperform the standard method of voxelwise regression with subsequent regularization. Application of the fast sequential method to real DTI data demonstrates the inherent ability to increase the grid resolution by evaluating the incorporated basis functions at intermediate points. The resulting continuous regularized tensor field may serve as basis for multiple applications, yet, ameloriation of local adaptivity is desirable.     

基于线性插值的张量步态识别算法*

提出一种新的基于线性插值的张量步态识别算法。为了能将测试步态序列与注册的相匹配,必须使测试序列的维数与注册的一致,首先将一个周期内的步态帧经相邻帧线性插值归一到一定数目,那么单个的步态样本表现成张量的形式。张量分析采用多重线性主成分分析算法,在CASIA(B)步态数据库上实验,确定单个步态张量选择一个周期比半个周期更有效。该方法得到了令人鼓舞的识别效果。     

三幅图像中的曲率估计

从前两幅图像的图像特征中估计第3幅图像的特征,在计算机视觉领域中有着广泛的应用,例如,视觉识别,基于模型的视觉动画、视图合成、目标检测和跟踪。Faugeras和Robert指出第3幅图像的特征可以通过前面两个摄像机图像的双线性函数来进行估计,其基本上是通过基础矩阵来计算的,因而他们的方法在实际计算过程中有很大的缺陷。为此提出了一种新的估计方法,即从三焦点张量中来估计第3幅图像的特征。这一方法继承和发展了Faugeras等的方法。此外还给出了一个定理说明了本文的条件与Faugeras给出的条件是等价的,但本方法简单目更加系统。实验结果证明了该方法的可靠性。