Anisotropic noise injection for input variables relevance determination

There are two archetypal ways to control the complexity of a flexible regressor: subset selection and ridge regression. In neural-networks jargon, they are, respectively, known as pruning and weight decay. These techniques may also be adapted to estimate which features of the input space are relevant for predicting the output variables. Relevance is given by a binary indicator for subset selection, and by a continuous rating for ridge regression. This paper shows how to achieve such a rating for a multilayer perceptron trained with noise (or jitter). Noise injection (NI) is modified in order to penalize heavily irrelevant features. The proposed algorithm is attractive as it requires the tuning of a single parameter. This parameter controls the complexity of the model (effective number of parameters) together with the rating of feature relevances (effective input space dimension). Bounds on the effective number of parameters support that the stability of this adaptive scheme is enforced by the constraints applied to the admissible set of relevance indices. The good properties of the algorithm are confirmed by satisfactory experimental results on simulated data sets.     

噪声影响的泛空间上的学习理论关键定理

关键定理是统计学习理论的重要组成部分,但目前其研究主要集中在概率空间上且假设样本不受噪声的影响。鉴于此,提出了泛空间上样本受噪声影响的期望风险泛函、经验风险泛函以及经验风险最小化原则的定义,给出并证明了泛空间上样本受噪声影响的学习理论的关键定理。     

Anisotropic quadrangulation

Quadrangulation methods aim to approximate surfaces by semiregular meshes with as few extraordinary vertices as possible. A number of techniques use the harmonic parameterization to keep quads close to squares, or fit parametrization gradients to align quads to features. Both types of techniques create near-isotropic quads; feature-aligned quadrangulation algorithms reduce the remeshing error by aligning isotropic quads with principal curvature directions. A complementary approach is to allow for anisotropic elements, which are well-known to have significantly better approximation quality.In this work we present a simple and efficient technique to add curvature-dependent anisotropy to harmonic and feature-aligned parameterization and improve the approximation error of the quadrangulations. We use a metric derived from the shape operator which results in a more uniform error distribution, decreasing the error near features.     

反常声电光调制器

介绍了一种新型反常声电光调制器，它可以用电光效应实现激光强度的调制，而使用声光效应来控制调制光的偏转方向。也可用声光效应实现激光强度的调制，而用电光效应来控制器件的中心频率。器件的性能更加灵活。     

Separable Anisotropic Diffusion

Anisotropic diffusion has many applications in image processing, but the high computational cost usually requires accuracy trade-offs in order to grant its applicability in practical problems. This is specially true when dealing with 3D images, where anisotropic diffusion should be able to provide interesting results for many applications, but the usual implementation methods greatly scale in complexity with the additional dimension. Here we propose a separable implementation of the most general anisotropic diffusion formulation, based on Gaussian convolutions, whose favorable computational complexity scales linearly with the number of dimensions, without any assumptions about specific parameterizations. We also present variants that bend the Gaussian kernels for improved results when dealing with highly anisotropic curved or sharp structures. We test the accuracy, speed, stability, and scale-space properties of the proposed methods, and present some results (both synthetic and real) which show their advantages, including up to 60 times faster computation in 3D with respect to the explicit method, improved accuracy and stability, and min–max preservation.     

Practical Anisotropic Geodesy

The computation of intrinsic, geodesic distances and geodesic paths on surfaces is a fundamental low‐level building block in countless Computer Graphics and Geometry Processing applications. This demand led to the development of numerous algorithms – some for the exact, others for the approximative computation, some focussing on speed, others providing strict guarantees. Most of these methods are designed for computing distances according to the standard Riemannian metric induced by the surface's embedding in Euclidean space. Generalization to other, especially anisotropic, metrics – which more recently gained interest in several application areas – is not rarely hampered by fundamental problems. We explore and discuss possibilities for the generalization and extension of well‐known methods to the anisotropic case, evaluate their relative performance in terms of accuracy and speed, and propose a novel algorithm, the Short‐Term Vector Dijkstra. This algorithm is strikingly simple to implement and proves to provide practical accuracy at a higher speed than generalized previous methods.     

井下WLAN位置指纹样本自相关滤波降噪方法研究

为了解决井下WLAN位置指纹库中噪声样本对井下人员定位精度的影响,提出了用于消减位置指纹数据库中噪声样本的基于采样间隔τ的自相关滤波算法。研究表明,虽然在同一个参考点处使用同一个采集设备在不同时刻采集到的接收信号强度(received signal strength,RSS)序列都不完全一样,但噪声样本与其他样本的RSS序列相比有着较为显著的差异值。利用这一特点,基于采样间隔τ的自相关滤波算法使用样本均值作为两个样本间波动差值的平衡参照,使得噪声样本的异常特性被放大,进而使可能存在的噪声样本更精确地被滤除。滤除噪声样本的位置指纹库能够更好地表征各参考点处的RSS分布。实验结果表明,以90%置信概率为参照标准,使用自相关滤波后的位置指纹样本分别进行静态和动态人员定位的定位误差为3 m和3.5 m,比使用原始位置指纹样本的定位误差分别减小了1 m和0.5 m。     

Anisotropic Point Set Surfaces

Point Set Surfaces define smooth surfaces from regular samples based on weighted averaging of the points. Because weighting is done based on a spatial scale parameter, point set surfaces apply basically only to regular samples. We suggest to attach individual weight functions to each sample rather than to the location in space. This extends Point Set Surfaces to irregular settings, including anisotropic sampling adjusting to the principal curvatures of the surface. In particular, we describe how to represent surfaces with ellipsoidal weight functions per sample. Details of deriving such a representation from typical inputs and computing points on the surface are discussed.     

Anisotropic mesh adaptation for finite element solution of Anisotropic Porous Medium Equation

Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived for APME for time-independent diffusion. Anisotropic mesh adaptation for linear finite element solution of APME is discussed and numerical results for two dimensional examples are presented. The solution errors using anisotropic adaptive meshes show second order convergence.     

Anisotropic generalized Procrustes analysis

Generalized Procrustes analysis is a popular method for matching several configurations by translations, rotations/reflections and scaling constants. It aims at producing a group average from these Euclidean similarity transformations followed by bi-linear approximation of this group average for graphical inspection. An extension that allows for anisotropic scaling (i.e. different scaling of different dimensions) is proposed. This method is illustrated using two real data sets from sensory analysis.     

全局各向异性四边形主导网格重建方法

四边形网格的结构特点要求网格单元满足全局一致性,难以取得网格质量与表达效率之间的平衡.为此,提出一种基于全局的各向异性四边形主导网格重建方法,可生成网格质量好且冗余程度低的四边形网格.重建过程以主曲率线为基本采样单元,首先计算模型表面的主曲率场并对主曲率场积分,得到密集的主曲率线采样;再根据贪心算法,利用几何形体自身的各向异性找出冗余度最高的主曲率线并予以删除;如此循环,直至达到理想的采样密度.该重建方法适用于任意拓扑网格模型,所得到的各向异性四边形主导网格在网格模型分辨率下降时,由于始终保留重要主曲率线,从而可以更好地保持模型特征.同时,在基于贪心算法的渐进式主曲率线删除过程中,可产生分辨率连续可调的四边形主导网格.     

各向异性的分形地形生成方法研究

传统的分形地形生成方法得到的地形是各向同性的,为了使生成的分形地形具有各向异性特征,提出了一种新的分形地形生成方法,该方法利用组合分形布朗曲面模型,将具有不同特征的两种分形布朗曲面相融合,使得生成的地形具有各向异性特征.对组合分形布朗曲面算法进行了仿真实验,生成了最终的分形地形.对仿真结果的分析表明,生成的分彤地形的特征具有各向异性特征,和实际的自然地形特征相符合,从而证明了该算法的有效性.     

全局各向异性四边形主导网格重建方法?

四边形网格的结构特点要求网格单元满足全局一致性,难以取得网格质量与表达效率之间的平衡。为此,提出一种基于全局的各向异性四边形主导网格重建方法,可生成网格质量好且冗余程度低的四边形网格。重建过程以主曲率线为基本采样单元,首先计算模型表面的主曲率场并对主曲率场积分,得到密集的主曲率线采样;再根据贪心算法,利用几何形体自身的各向异性找出冗余度最高的主曲率线并予以删除;如此循环,直至达到理想的采样密度。该重建方法适用于任意拓扑网格模型,所得到的各向异性四边形主导网格在网格模型分辨率下降时,由于始终保留重要主曲率线,从而可以更好地保持模型特征。同时,在基于贪心算法的渐进式主曲率线删除过程中,可产生分辨率连续可调的四边形主导网格。     

Anisotropic Textures with Arbitrary Orientation

We present a Markov random field (MRF) model for digital imagescapable of representing anisotropic textures with arbitraryorientations. The discrete Hamiltonian is obtained through finitedifference discretization of a continuous elliptic operator on ²;, together with a polynomial perturbation.We present the solution of a non-linear system of algebraicequations that estimates the orientation angle and theelliptic operator parameters in terms of the estimated discreteHamiltonian parameters.We perform experiments of simulation and retrieval of parametersusing, respectively, the Gibbssampler algorithm and the variational estimators for MRF. Weuse also the estimation algorithm to identify relative rotationof digital images of the same realisticpicture scanned at various different orientations.     

各向异性尺度空间图象增强

文章讨论了各向异性热传导系数尺度空间理论在图象增强中的应用。尺度空间的生成可以通过热传导方程来获得,传统的理论采用各向同性的热传导系数。为了在对图象噪声进行平滑的同时,保持图象的细节,采用了各向异性的热传导方程。考虑到旋转不变性,对各向异性的热传导方程的计算方法进行改进,不仅考虑了垂直和水平方向的影响,而且考虑对角方向上象素点的影响。实验证明算法是有效的。     

Image Compression with Anisotropic Diffusion

Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec.     

各向异性扩散的研究

各向异性扩散是有选择性的平滑过程,这种平滑过程在均匀的区域不受限制,而在跨越边界部分被抑制,因此在平滑噪声的同时保持图像的边缘特征。同样,双边滤波既可以达到滤波的效果又可以保持图像的高频细节,它是一种非线性、非迭代的、局部的和简单的滤波,它是数字图像非线性滤波的代表。论文利用稳健统计方法,分析了各向异性扩散与双边滤波之间的关系,扩大了数字图像非线性滤波与非线性扩散之间的关联。