Shift,Rotation and Limited Scale Invariant Pattern Recognition Using Synthetic Discriminant Functions

Making use of the idea of synthetic discriminant functions (SDF), a simple way to synthesize a shift, rotation and limited size correlation filter is proposed. The SDF is synthesized by superimposing four 2nd order circular harmonics of a training reference pattern in 4 different sizes. Computer simulation experiments have shown that the filter is indeed shift, full rotation and limited size invariant over a size range from 1 to 1.82. The invariant range can be increased if more training patterns are used.     

主成分分析排序和模糊线性判别分析的生菜近红外光谱分类

贮存时间是影响生菜品质的一项重要因素,传统的贮存时间鉴别方法主要依靠人工经验,但是这种方法的准确率和可信度并不高。研究的目标是建立一种基于模糊识别的模型进行生菜光谱分析以实现生菜贮存时间的鉴别,并与其他鉴别方法作比较。为此,在当地超市购买60份新鲜生菜样品,存放于冰箱中待用。首先,通过AntarisⅡ近红外光谱检测仪采集生菜样品的近红外光谱数据,每隔12小时检测一次,每个样本检测重复三次,并取三次平均值作为实验数据。其次,利用多元散射校正(MSC)减少近红外光谱中的冗余信息。为了进一步去除近红外光谱中的无用信息以及简化随后的数据分类过程,分别运用主成分分析(PCA)和排序主成分分析(PCA Sort)。其中,PCA Sort通过改进对主成分的排序方法能提高分类准确率,同时便于模糊线性鉴别分析(FLDA)进一步提取特征。PCA和PCA Sort的计算仅运用了前15个主成分(能充分反映光谱的主要信息)。最后,利用模糊线性鉴别分析算法(FLDA)和K近邻算法(KNN)进一步分类所得的低维数据。基于PCA和KNN算法的模型鉴别准确率达到43%,而基于PCA, FLDA和KNN算法的模型鉴别准确...     

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

A spectral classification of general one‐dimensional binary aperiodic crystals (BACs) based on both their diffraction patterns and energy spectrum measures is introduced along with a systematic comparison of the zeroth‐order energy spectrum main features for BACs belonging to different spectral classes, including Fibonacci‐class, precious means, metallic means, mixed means and period doubling based representatives. These systems are described by means of mixed‐type Hamiltonians which include both diagonal and off‐diagonal terms aperiodically distributed. An algebraic approach highlighting chemical correlation effects present in the underlying lattice is introduced. Close analytical expressions are obtained by exploiting some algebraic properties of suitable blocking schemes preserving the atomic order of the original lattice. The existence of a resonance energy which defines the basic anatomy of the zeroth‐order energy spectra structure for the standard Fibonacci, the precious means and the Fibonacci‐class quasicrystals is disclosed. This eigenstate is also found in the energy spectra of BACs belonging to other spectral classes, but for specific particular choices of the corresponding model parameters only. The transmission coefficient of these resonant states is always bounded below, although their related Landauer conductance values may range from highly conductive to highly resistive ones, depending on the relative strength of the chemical bonds.     

Optical classification of random image fields using spectral synthetic discriminant functions

It is shown that the problem of classification of images that have the perfectly random nature may be solved with the help of synthetic discriminant functions being synthesized by least-squares technique to separate linearly the power spectra of the corresponding random image fields. The realization of the proposed method by means of an optical technique is discussed, and its efficiency is illustrated by two examples of real-life texture classification.     

基于分类的红外云层背景弱小目标检测方法

提出了一种新的基于模糊分类的红外云层背景弱小目标检测方法.根据红外成像的特点,将红外云层背景弱小目标图像分为三类:边缘类、净空及云中类、弱小目标类;对不同类别图像进行分析,建立了分类模型,并定义了方向特征矢量,将其作为类别的特征矢量;根据模糊分类的理论,定义了类相似系数来判别图像中每一个像素的类别属性,保留弱小目标类的像素点完成检测.实验结果表明,该方法能够对红外弱小目标图像中不同类型的区域进行准确的分类,从而较好的实现了对低信杂比的复杂云层背景图像中的弱小目标检测.     

On the Distribution of the Information Density of Gaussian Random Vectors: Explicit Formulas and Tight Approximations

Based on the canonical correlation analysis, we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as a general formula to calculate the central moments. Using the general results, we give closed-form expressions of the PDF and CDF and explicit formulas of the central moments for important special cases. Furthermore, we derive recurrence formulas and tight approximations of the general series representations, which allow efficient numerical calculations with an arbitrarily high accuracy as demonstrated with an implementation in Python publicly available on GitLab. Finally, we discuss the (in)validity of Gaussian approximations of the information density.