Geometry Machines: From AI to SMC
The existing techniques and software tools for automated geometry theorem proving (GTP) are examined and reviewed. The underlying ideas of various approaches are explained with a set of selected examples. Comments and analyses are provided to illustrate the encouraging success of GTP which interrelates AI and SMC. We also present some technological applications of GTP and discuss its challenges ahead.

title: A simple method for implicitizing rational curves and surfaces
abstract: This paper presents a simple method for converting rational parametric equations of curves and surfaces into implicit equations. The method proceeds via writing out the implicit polynomial F of estimated degree with indeterminate coefficients u i , substituting the rational expressions for the given parametric curve or surface into F to yield a rational expression g / h in the parameter s (or s and t ), equating the coefficients of g in terms of s (and t ) to 0 to generate a sparse, partially triangular system of linear equations in u i with constant coefficients, and finally solving the linear system for u i . If a nontrivial solution is found, then an implicit polynomial is obtained; otherwise, one repeats the same process, increasing the degree of F . Our experiments show that this simple method is efficient. It performs particularly well in the presence of base points and may detect the dependency of parameters incidentally.

title: Reasoning about Surfaces Using Differential Zero and Ideal Decomposition
abstract: This paper presents methods for zero and ideal decomposition of partial differential polynomial systems and the application of these methods and their implementations to deal with problems from the local theory of surfaces. We show how to prove known geometric theorems and to derive unknown relations automatically. In particular, an algebraic relation between the first and the second fundamental coefficients in a very compact form has been derived, which is more general and has smaller degree than a relation discovered previously by Z. Li. Moreover, we provide symmetric expressions for Li's relation and clarify his statement. Some examples of theorem proving and computational difficulties encountered in our experiments are also discussed.

title: GEOTHER: A Geometry Theorem Prover

title: Automated Generation of Diagrams with Maple and Java
abstract: This note shows how to draw diagrams automatically from the predicate specification of a given set of geometric relations among a set of points in the plane. It is done first in Maple by translating the geometric relations into polynomial equations, decomposing the obtained system of polynomials into irreducible representative triangular sets, and finding an adequate numerical solution from each triangular set. A Java class coding the solution and the polynomials in each triangular set is generated, compiled, and then executed with the main Java programs to draw a diagram. The whole process combining symbolic elimination in Maple with numerical computation, graphic drawing, and letter labeling in Java is fully automatic. The drawn diagrams may be animated and fine-tuned by mouse click and dragging and saved as PostScript files. We present the drawing method, discuss some techniques of implementation, and give several sample diagrams drawn by our program.

title: On Wu's Method for Proving Constructive Geometric Theorems
abstract: In 1977 Wu Wen-tsiin discovered an efficient method for mechanical theorem proving. This method has been applied to prove and discover theorems in various kinds of geometries. Based on an extension of one of Wu's algorithmic procedures, the author implemented a prover CPS for proving so-called constructive geometric theorems, as well as a general theorem prover PS. Using this prover we proved more than one hundred non-trivial theorems and discovered also a number of interesting ones. This paper is a summarization of our early work, as a abbreviation of the chapter 2 from my Chinese doctoral dissertation.

title: Identifying reasoning strategies in medical decision making: A methodological guide
abstract: Reasoning strategies are a key component in many medical tasks, including decision making, clinical problem solving, and understanding of medical texts. Identification of reasoning strategies used by clinicians may prove critical to the optimal design of decision support systems. This paper presents a formal method of cognitive-semantic analysis for the identification and characterization of reasoning strategies deployed in medical tasks and demonstrates its use through specific examples. Although semantic analysis was originally developed in the investigation of knowledge structures, it can also be applied to identify the reasoning and decision processes used by physicians and medical trainees in clinical tasks. Assumptions underlying the methods, as well as illustrations of their use in diagnostic explanation tasks, are presented. We discuss semantic analysis in the context of the current interests in developing medical ontologies and argue that a frame-based propositional analytic methodology can provide a systematic way of addressing the construction of such ontologies. Although the application of propositional analysis methods has some limitations, we show how such limitations are being addressed and present some examples of information tools that have been developed to ease, and make more systematic, the process of analysis.

title: Segmentation of medical images using LEGION
abstract: Advances in visualization technology and specialized graphic workstations allow clinicians to virtually interact with anatomical structures contained within sampled medical-image datasets. A hindrance to the effective use of this technology is the difficult problem of image segmentation. In this paper, the authors utilize a recently proposed oscillator network called the locally excitatory globally inhibitory oscillator network (LEGION) whose ability to achieve fast synchrony with local excitation and desynchrony with global inhibition makes it an effective computational framework for grouping similar features and segregating dissimilar ones in an image. The authors extract an algorithm from LEGION dynamics and propose an adaptive scheme for grouping. They show results of the algorithm to two-dimensional (2-D) and three-dimensional (3-D) (volume) computerized topography (CT) and magnetic resonance imaging (MRI) medical-image datasets. In addition, the authors compare their algorithm with other algorithms for medical-image segmentation, as well as with manual segmentation. 's computational and architectural properties make it a promising approach for real-time medical-image segmentation.

title: IMDS: intelligent malware detection system
abstract: The proliferation of malware has presented a serious threat to the security of computer systems. Traditional signature-based anti-virus systems fail to detect polymorphic and new, previously unseen malicious executables. In this paper, resting on the analysis of Windows API execution sequences called by PE files, we develop the Intelligent Malware Detection System (IMDS) using Objective-Oriented Association (OOA) mining based classification. IMDS is an integrated system consisting of three major modules: PE parser, OOA rule generator, and rule based classifier. An OOA_Fast_FP-Growth algorithm is adapted to efficiently generate OOA rules for classification. A comprehensive experimental study on a large collection of PE files obtained from the anti-virus laboratory of King-Soft Corporation is performed to compare various malware detection approaches. Promising experimental results demonstrate that the accuracy and efficiency of our IMDS system out perform popular anti-virus software such as Norton AntiVirus and McAfee VirusScan, as well as previous data mining based detection systems which employed Naive Bayes, Support Vector Machine (SVM) and Decision Tree techniques.

title: Oriented statistical nonlinear smoothing filter
abstract: This paper presents a nonlinear smoothing method which is based on an orientation-sensitive probability measure. By incorporating geometrical constraints through the coupling structure, we obtain a robust nonlinear smoothing algorithm. Even when noise is substantial the proposed smoothing algorithm can still preserve salient boundaries. Compared with anisotropic diffusive approaches, the proposed nonlinear algorithm not only performs better in preserving boundaries but also has a non-uniform stable state, whereby reliable results are available within a fixed number of iterations independent of images. A system using the proposed method and LEGION network has been developed and applied in noisy image segmentation and hydrographic feature extraction from digital ortho-photo quadrangles. Experimental results using synthetic and real images are provided.

title: Perceptual organization based on temporal dynamics
abstract: This paper presents a computational model for perceptual organization. A figure-ground segregation network is proposed based on a novel boundary pair representation. The system solves the figure-ground segregation problem through temporal evolution. Gestalt-like grouping rules are incorporated by modulating connections, which determines the temporal behavior and thus the perception of the system. The results are then fed to a surface completion module based on local diffusion. Different perceptual phenomena, such as modal and a modal completion, virtual contours, grouping and shape decomposition are explained by the model with a fixed set of parameters. Computationally, the system eliminates combinatorial optimization, which is common to many existing computational approaches. It also accounts for more examples that are consistent with psychological experiments. In addition, the boundary-pair representation is consistent with well-known on- and off-center cell responses and thus biologically more plausible.