What a histogram can really tell the classifier

This paper presents a simple and efficient clustering technique based on the partitioning of the data histogram. The clustering technique was developed in the context of a study of possible unsupervized classification procedures for multispectral earth imagery. The ultimate goal was on-board data compression, the algorithmic production of thematic maps.

The incoming raw spectral data is first reduced to its two principal (Karhunen-Loêve) components, the histogram of which is then partitioned into natural classes on the sole weight of evidence of the global statistics of the imagery. During the course of the study, it became clear that some connection existed between the proposed philosophy and professor Thom's novel theory of “catastrophes”.⁽¹⁾ A simple metric is added to the histogram topology. The metric uses both Shannon's and Fisher's notions of self information. In the domain of definition of the histogram, zones corresponding to the natural classes become separated by a no man's land, an inter-class zone. Under the same formulation, the metric is “Euclidean” on the class zone, “non-Euclidean”, i.e. “Lorentz” on the inter-class zone. This methodology and the underlying philosophy were tested in practice, and encouraging results were obtained.     

Unsupervised texture segmentation using Gabor filters

This paper presents a texture segmentation algorithm inspired by the multi-channel filtering theory for visual information processing in the early stages of human visual system. The channels are characterized by a bank of Gabor filters that nearly uniformly covers the spatial-frequency domain, and a systematic filter selection scheme is proposed, which is based on reconstruction of the input image from the filtered images. Texture features are obtained by subjecting each (selected) filtered image to a nonlinear transformation and computing a measure of “energy” in a window around each pixel. A square-error clustering algorithm is then used to integrate the feature images and produce a segmentation. A simple procedure to incorporate spatial information in the clustering process is proposed. A relative index is used to estimate the “true” number of texture categories.     

Color enhancement of highly correlated images. I. Decorrelation and HSI contrast stretches

Conventional enhancements for the color display of multispectral images are based on independent contrast modifications or “stretches” of three input images. This approach is not effective if the image channels are highly correlated or if the image histograms are strongly bimodal or more complex. Any of several procedures that tend to “stretch” color saturation while leaving hue unchanged may better utilize the full range of colors for the display of image information. Two conceptually different enhancements are discussed: the “decorrelation stretch”, based on principal-component (PC) analysis, and the “stretch” of “hue”-“saturation”-intensity (HSI) transformed data. The PC transformation is scene-dependent, but the HSI transformation is invariant. Examples of images enhanced by conventional linear stretches, decorrelation stretch, and by stretches of HSI transformed data are compared. Schematic variation diagrams or two- and three-dimensional histograms are used to illustrate the “decorrelation stretch” method and the effect of the different enhancements.     

联合结构化图学习与l1范数谱嵌入的鲁棒聚类算法

谱聚类算法存在两个不足:a)将图的构造与谱分解割裂成两个独立的阶段,导致了结果的次优性;b)常用的基于l₂范数度量谱特征向量的相似性具有噪声敏感性。为了克服上述两点不足,提出基于联合结构化图学习与l₁范数谱嵌入的鲁棒聚类算法(记为CLRL1)。在该算法框架下,一方面图的学习过程与聚类过程可以有效结合起来进行协同优化,另一方面l₁范数的使用可以很好地约束谱特征向量的相似性以提升算法的鲁棒性。在多个常用数据集上进行的实验结果表明,改进算法聚类性能得到了明显提升。     

On two-sided infinite fixed points of morphisms

Let Σ be a finite alphabet, and let h:Σ^* → Σ^* be a morphism. Finite and infinite fixed points of morphisms—i.e., those words w such that h(w)=w—play an important role in formal language theory. Head characterized the finite fixed points of h, and later, Head and Lando characterized the one-sided infinite fixed points of h. Our paper has two main results. First, we complete the characterization of fixed points of morphisms by describing all two-sided infinite fixed points of h, for both the “pointed” and “unpointed” cases. Second, we completely characterize the solutions to the equation h(xy)=yx in finite words.     

Constrained multibody system dynamics an automated approach

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. Specifically, the “closed loop” problem of multibody chain systems is addressed.

The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. This modification, which is based upon a solution of the constraint equations obtained through a “zero eigenvalues theorem,” is, in effect, a contraction of the dynamical equations.

It is observed that, for a system with n generalized coordinates and m constraint equations, the coefficients in the constraint equations may be viewed as “constraint vectors” in n-dimensional space. Then, in this setting the system itself is free to move in the n−m directions which are “orthogonal” to the constraint vectors.     

A note on web intelligence, world knowledge and fuzzy logic

Existing search engines––with Google at the top––have many remarkable capabilities; but what is not among them is deduction capability––the capability to synthesize an answer to a query from bodies of information which reside in various parts of the knowledge base.

In recent years, impressive progress has been made in enhancing performance of search engines through the use of methods based on bivalent logic and bivalent-logic-based probability theory. But can such methods be used to add nontrivial deduction capability to search engines, that is, to upgrade search engines to question-answering systems? A view which is articulated in this note is that the answer is “No.” The problem is rooted in the nature of world knowledge, the kind of knowledge that humans acquire through experience and education.

It is widely recognized that world knowledge plays an essential role in assessment of relevance, summarization, search and deduction. But a basic issue which is not addressed is that much of world knowledge is perception-based, e.g., “it is hard to find parking in Paris,” “most professors are not rich,” and “it is unlikely to rain in midsummer in San Francisco.” The problem is that (a) perception-based information is intrinsically fuzzy; and (b) bivalent logic is intrinsically unsuited to deal with fuzziness and partial truth.

To come to grips with fuzziness of world knowledge, new tools are needed. The principal new tool––a tool which is briefly described in this note––is Precisiated Natural Language (PNL). PNL is based on fuzzy logic and has the capability to deal with partiality of certainty, partiality of possibility and partiality of truth. These are the capabilities that are needed to be able to draw on world knowledge for assessment of relevance, and for summarization, search and deduction.     

基于广义积分平方误差谱选择的图像分割

谱聚类算法中并不是所有的顶层谱都含有聚类信息,对于实际含噪声数据的聚类,由于谱数据分布复杂,谱的选择是必要的。文中推广积分平方误差散度,验证所提出的广义积分平方误差散度可用来估计数据分布的模态,以及度量谱所含的聚类信息量,并提出一种基于谱选择的谱聚类算法。自然图像分割实验结果表明,提出的算法比以往的谱聚类算法更为简单有效。     

Fuzzy spectral clustering with robust spatial information for image segmentation

In recent years, spectral clustering has become one of the most popular clustering algorithms in areas of pattern analysis and recognition. This algorithm uses the eigenvalues and eigenvectors of a normalized similarity matrix to partition the data, and is simple to implement. However, when the image is corrupted by noise, spectral clustering cannot obtain satisfying segmentation performance. In order to overcome the noise sensitivity of the standard spectral clustering algorithm, a novel fuzzy spectral clustering algorithm with robust spatial information for image segmentation (FSC_RS) is proposed in this paper. Firstly, a non-local-weighted sum image of the original image is generated by utilizing the pixels with a similar configuration of each pixel. Then a robust gray-based fuzzy similarity measure is defined by using the fuzzy membership values among gray values in the new generated image. Thus, the similarity matrix obtained by this measure is only dependent on the number of the gray-levels and can be easily stored. Finally, the spectral graph partitioning method can be applied to this similarity matrix to group the gray values of the new generated image and then the corresponding pixels in the image are reclassified to obtain the final segmentation result. Some segmentation experiments on synthetic and real images show that the proposed method outperforms traditional spectral clustering methods and spatial fuzzy clustering in efficiency and robustness.     

Recognizing image “style” and activities in video using local features and naive Bayes

The goal of this paper is to offer a framework for classification of images and video according to their “type”, or “style”––a problem which is hard to define, but easy to illustrate; for example, identifying an artist by the style of his/her painting, or determining the activity in a video sequence. The paper offers a simple classification paradigm based on local properties of spatial or spatio-temporal blocks. The learning and classification are based on the naive Bayes classifier. A few experimental results are presented.     

A heuristic grouping procedure for component family formation in a cellular manufacturing environment

A heuristic clustering procedure is introduced for grouping purposes in a cellular manufacturing environment. The procedure uses the concepts of “edge-cut” and “cut-set” of graph theory in combination with a similarity measure to group the objects. An experiment was conducted to compare twelve different variations of the procedure when used for component family identification. Two measures of performance are used to select the most suitable variation of the procedure and a numerical example is given for the variation.     

A small gain theorem for linear stochastic systems

A well-known result in linear control theory is the so-called “small gain” theorem stating that if given two plants with transfer matrix functions T₁ and T₂ in H^∞ such that T₁ < γ and T₂ < 1/γ, when coupling T₂ to T₁ such that u₂ = y₁ and u₁ = y₂ one obtains an internally stable closed system. The aim of the present paper is to describe a corresponding result for stochastic systems with state-dependent white noise.     

Large-scale simulations of self-organizing neural networks on parallel computers: application to biological modelling

In this contribution we report about a study of a very versatile neural network algorithm known as “Self-organizing Feature Maps” and based on earlier work of Kohonen [1,2]. In its original version, the algorithm addresses a fundamental issue of brain organization, namely how topographically ordered maps of sensory information can be formed by learning.

This algorithm is investigated for a large number of neurons (up to 16 K) and for an input space of dimension d900. To meet the computational demands this algorithm was implemented on two parallel machines, on a self-built Transputer systolic ring and on a Connection Machine CM-2.

We will present below

1. (i) a simulation based on the feature map algorithm modelling part of the synaptic organization in the “hand-region” of the somatosensory cortex,

2. (ii) a study of the influence of the dimension of the input-space on the learning process,

3. (iii) a simulation of the extended algorithm, which explicitly includes lateral interactions, and

4. (iv) a comparison of the transputer-based “coarse-grained” implementation of the model, and the “fine-grained” implementation of the same system on the Connection Machine.

     

Finite-element technique for solving problems formulated by Hamilton''s principle

The finite element technique is applied to functional which govern dynamical problems, where time is an independent variable.

The present paper demonstrates improved accuracy in mass-spring-damper systems and exemplifies “rendevous problems” of a “travelling” particle in a medium. The motion is governed by Hamilton's principle. The time interval is fixed.

Functionals are constructed from Hamilton's extended principle and appropriate conditions stating the various constraints.

Initial value problems may be incorporated by writing a functional in accordance with Gurtin's method.

Shape functions are polynomials in time and can be extended to other spatial variables when present.

As a result of a variation to the functional, a system of algebraic (not necessarily linear) equations is formed. This system is solved simultaneously to yield its motion within the boundaries of the given time interval.     

Applying abstraction and formal specification in numerical software design

Numerical software development tends to struggle with an increasing complexity. This is, on the one hand, due to the integration of numerical models, and on the other hand, due to change of hardware. Parallel computers seem to fulfill the need for more and more computer resources, but they are more complex to program.

The article shows how abstraction is used to combat complexity. It motivates that separating a specification, “what,” its realisation, “how,” and its implementation, “when, where,” is of vital importance in software development. The main point is that development steps and levels of abstraction are identified, such that the obtained software has a clear and natural structure.

Development steps can be cast into a formal, i.e., mathematical framework, which leads to rigourous software development. This way of development leads to accurate and unambiguous recording of development steps, which simplifies maintenance, extension and porting of software. Portability is especially important in the field of parallel computing where no universal parallel computer model exists.     

Combined effects of in-plane boundary conditions and stiffening on buckling of eccentrically stringer-stiffened cylindrical panels

Donnel type stability equations for buckling of stringer stiffened cylindrical panels under combined axial compression and hydrostatic pressure are solved by the displacement approach of [6], The solution is employed for a parametric study over a wide range of panel and stringer geometries to evaluate the combined influence of panel configurations and boundary conditions along the straight edges on the buckling behavior of the panel relative to a complete “counter” cylinder (i.e. a cylinder with identical skin and stiffener parameters).

The parametric studies reveal a “sensitivity” to the “weak in shear”, N_x = N_xφ = 0, along the straight edges, SS1 boundary conditions type where the panel buckling loads are always smaller than those predicted for a complete “counter” cylinder. In the case of “classical”, SS3 B.Cs., there always exist values of panel width, 2φ₀, for which ρ = 1, i.e. the panel buckling load equals that of the complete “counter” cylinder. For SS2 and SS4 B.Cs. types, the nature by which the panel critical load approaches that of the complete cylinder appears to be panel configuration dependent.

Utilization of panels for the experimental determination of a complete cylinder buckling load is found to be satisfactory for relatively very lightly and heavily stiffened panels, as well as for short panels, (L/R) = 0.2 and 0.5. Panels of moderate length and stiffening have to be debarred, since they lead to nonconservative buckling load predictions.     

利用广义信息熵谱选择的图像分割

谱聚类算法中图上拉普拉斯矩阵的特征向量(谱)决定聚类结果,如何选择谱至关重要.为了解决这一问题,基于广义信息熵,定义谱的区分性、谱的区分有效性和谱的区分度这3个指标.谱的区分性指标用于衡量谱所含聚类信息的显著程度;谱的区分有效性指标用于剔除聚类结果无效的谱;谱的区分度指标用于构建基于贡献力的选择性聚类集成方案.进而提出基于谱选择的谱聚类算法.各种自然图像分割实验表明文中算法简单有效.     

基于空间特征的谱聚类含噪图像分割

为克服传统谱聚类算法应用到含噪图像分割时易受到图像中噪声影响的问题,提出一种基于空间特征的谱聚类含噪图像分割算法。该方法利用图像各个像素的灰度信息、局部空间邻接信息及非局部空间信息设计像素的三维特征,通过引入空间紧致性函数建立像素特征点与其K个最近邻之间的相似性,进而利用谱聚类算法得到图像的最终分割结果。实验中采用含噪的人工图像、自然图像及合成孔径雷达图像与空间模糊聚类、规范切谱聚类和Nystrm方法3种算法进行对比实验,实验结果验证文中方法能克服图像中噪声影响并取得较满意的分割效果。