Tensor scale: A local morphometric parameter with applications to computer vision and image processing

Scale is a widely used notion in image analysis that evolved in the form of scale-space theory whose key idea is to represent and analyze an image at various resolutions. Recently, the notion of localized scale—a space-variant resolution scheme—has drawn significant research interest. Previously, we reported local morphometric scale using a spherical model. A major limitation of the spherical model is that it ignores structure orientation and anisotropy, and therefore fails to be optimal in many imaging applications including biomedical ones where structures are inherently anisotropic and have mixed orientations. Here, we introduce a new concept called “tensor scale”—a local morphometric parameter yielding a unified representation of structure size, orientation, and anisotropy. Also, a few applications of tensor scale in computer vision and image analysis, especially, in image filtering are illustrated. At any image point, its tensor scale is the parametric representation of the largest ellipse (in 2D) or ellipsoid (in 3D) centered at that point and contained in the same homogeneous region. An algorithmic framework to compute tensor scale at any image point is proposed and results of its application on several real images are presented. Also, performance of the tensor scale computation method under image rotation, varying pixel size, and background inhomogeneity is studied. Results of a quantitative analysis evaluating performance of the method on 2D brain phantom images at various levels of noise and blur, and a fixed background inhomogeneity are presented. Agreement between tensor scale images computed on matching image slices from two 3D magnetic resonance data acquired simultaneously using different protocols are demonstrated. Finally, the application of tensor scale in anisotropic diffusive image filtering is presented that encourages smoothing inside a homogeneous region and also along edges and elongated structures while discourages blurring across them. Both qualitative and quantitative results of application of the new filtering method have been presented and compared with the results obtained by spherical scale-based and standard diffusive filtering methods.     

基于张量的XML相似度计算方法

扩展标记语言(XML) 带有一定的结构和语义信息, 与普通文本相比, XML具有描述精确、表现形式丰富等特点, 但同时也使得传统的自然语言处理和数据挖掘等技术不能直接应用. 根据XML内容和结构并非独立, 内容影响结构, 结构作用于内容, 提出一种基于张量的XML特征降维及综合相似度计算方法. 针对XML文档, 使用张量表示并采用基于最大互信息的方法对其进行降维, 采用将XML结构和内容相融合的综合相似度度量方法确定结构和内容的内在联系及共同作用方式, 提高XML综合相似度计算性能. 实验及结果分析验证了所提出方法的有效性.

     

Invariant crease lines for topological and structural analysis of tensor fields

We introduce a versatile framework for characterizing and extracting salient structures in three-dimensional symmetric second-order tensor fields. The key insight is that degenerate lines in tensor fields, as defined by the standard topological approach, are exactly crease (ridge and valley) lines of a particular tensor invariant called mode. This reformulation allows us to apply well-studied approaches from scientific visualization or computer vision to the extraction of topological lines in tensor fields. More generally, this main result suggests that other tensor invariants, such as anisotropy measures like fractional anisotropy (FA), can be used in the same framework in lieu of mode to identify important structural properties in tensor fields. Our implementation addresses the specific challenge posed by the non-linearity of the considered scalar measures and by the smoothness requirement of the crease manifold computation. We use a combination of smooth reconstruction kernels and adaptive refinement strategy that automatically adjust the resolution of the analysis to the spatial variation of the considered quantities. Together, these improvements allow for the robust application of existing ridge line extraction algorithms in the tensor context of our problem. Results are proposed for a diffusion tensor MRI dataset, and for a benchmark stress tensor field used in engineering research.     

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.     

Visualizing second-order tensor fields with hyperstreamlines

A method developed to help scientists visualize 3D tensor data is presented. The method is based on the concept of a hyperstreamline, the simplest continuous tensor structure that can be extracted from a tensor field. Hyperstreamlines for a particular case of symmetric tensor fields are introduced, and a structural depiction of symmetric tensor fields is derived from the representation of many hyperstreamlines. A method for visualizing unsymmetric tensor data by encoding an additional vector field along the trajectory of the hyperstreamlines is discussed     

Oriented and Vectorial Patterning of Cardiac Myocytes Using a Microfluidic Dielectrophoresis Chip—Towards Engineered Cardiac Tissue With Controlled Macroscopic Anisotropy

Recently, the ability to create engineered heart tissues with a preferential cell orientation has gained much interest. Here, we present a novel method to construct a cardiac myocyte tissue-like structure using a combination of dielectrophoresis and electro-orientation via a microfluidic chip. The device includes a top home-made silicone chamber containing microfluidic channels and bottom integrated microelectrodes which are patterned on a glass slide to generate dielectrophoresis force and orientation torque. Using the interdigitated-castellated microelectrodes, the induction of a mutually attractive dielectrophoretic force between cardiac myocytes can lead to cells moving close to each other and forming a tissue-like structure with orientation along the alternating current (ac) electric field between the microelectrode gaps. Both experiments and analysis indicate that a large orientation torque and force can be achieved by choosing an optimal frequency around 2 MHz and decreasing the conductivity of medium to a relatively low level. Finally, electromechanical experiments and biopolar impedance measurements were performed to demonstrate the structural and functional anisotropy of electro-oriented structure     

Fracture Patterns Design for Anisotropic Models with the Material Point Method

Physically plausible fracture animation is a challenging topic in computer graphics. Most of the existing approaches focus on the fracture of isotropic materials. We proposed a frame-field method for the design of anisotropic brittle fracture patterns. In this case, the material anisotropy is determined by two parts: anisotropic elastic deformation and anisotropic damage mechanics. For the elastic deformation, we reformulate the constitutive model of hyperelastic materials to achieve anisotropy by adding additional energy density functions in particular directions. For the damage evolution, we propose an improved phase-field fracture method to simulate the anisotropy by designing a deformation-aware second-order structural tensor. These two parts can present elastic anisotropy and fractured anisotropy independently, or they can be well coupled together to exhibit rich crack effects. To ensure the flexibility of simulation, we further introduce a frame-field concept to assist in setting local anisotropy, similar to the fiber orientation of textiles. For the discretization of the deformable object, we adopt a novel Material Point Method(MPM) according to its fracture-friendly nature. We also give some design criteria for anisotropic models through comparative analysis. Experiments show that our anisotropic method is able to be well integrated with the MPM scheme for simulating the dynamic fracture behavior of anisotropic materials.     

基于非局部结构张量的SSIM图像质量评价方法

针对基于局部运算的图像质量评价方法的局限性,提出一种基于非局部结构张量的SSIM图像质量评价方法。图像在各像素点的非局部结构张量的主特征值大小很好地反映了该像素点的结构强度信息,特别是纹理结构等细节信息; 主特征向量的方向反映了该像素点的结构方向信息。利用退化图像和参考图像的非局部结构张量的主特征值相似度刻画结构强度相似度,利用主特征向量夹角的余弦刻画结构方向相似度。数值实验结果显示,利用文中方法对TID2008数据库中的图像进行评价的平均运算时间为778.43s,且评价结果与主观评价接近。     

The mechanical design of a novel Schönflies-motion generator

The design of a novel Schönflies-motion generator (SMG) is the focus of the paper. Schönflies motions are characterized by four degrees of freedom: three independent translations and one rotation about one axis of fixed orientation. The two driving modules of the manipulator are intended to produce, each, two independent motions, pan and tilt. The design philosophy and the layout of the SMG are discussed, along with the design procedure, which includes: (i) part-modelling and visualization, with animation of the device; (ii) evaluation of the main parameters and the characteristics of the different structural realizations, as well as the selection of one single structure meeting best the design specifications; (iii) the design of the main components for the selected variant of the structure; (iv) the structural and modal analyses and determination of the inertial and elastic parameters of the device and its components; and (v) the production of detailed manufacturing drawings. Further results of structural and modal analyses of the SMG are considered, while the link geometry is defined based on the design specifications.