Z.C. Li

Analysis and recognition of alphanumeric handprints by parts

An advanced hierarchical model has been proposed to produce a more effective character recognizer based on the probability of occurrence of the patterns. New definitions such as crucial parts, efficiency ratios, degree of confusion, similar character pairs, etc. have also been given to facilitate pattern analysis and character recognition. Using these definitions, computer algorithms have been developed to recognize the characters by parts, including halves, quarters, and sixths. The recognition rates have been analyzed and compared with those obtained from subjective experiments. Based on the results of both computer and human experiments, a detailed analysis of the crucial parts and the Canadian standard alphanumeric character set has been made revealing some interesting fundamental characteristics of these handprint models. The results should be useful for pattern analysis and recognition, character understanding, handwriting education, and human-computer communication.<<ETX>>

Splitting-integrating method for normalizing images by inverse transformations

The splitting-integrating method is a technique developed for the normalization of images by inverse transformation. It does not require solving nonlinear algebraic equations and is much simpler than any existing algorithm for the inverse nonlinear transformation. Moreover, its solutions have a high order of convergence, and the images obtained through T/sup -1/ are free from superfluous holes and blanks, which often occur in transforming digitized images by other approaches. Application of the splitting-integrating method can be extended to supersampling in computer graphics, such as picture transformations by antialiasing, inverse nonlinear mapping, etc. >

Splitting-shooting methods for nonlinear transformations of digitized patterns

New splitting-shooting methods are presented for nonlinear transformations T: ( xi , eta ) to (x,y) where x=x( xi , eta ), y=y( xi , eta ). These transformations are important in computer vision, image processing, pattern recognition, and shape transformations in computer graphics. The methods can eliminate superfluous holes or blanks, leading to better images while requiring only modest computer storage and CPU time. The implementation of the proposed algorithms is simple and straightforward. Moreover, these methods can be extended to images with gray levels, to color images, and to three dimensions. They can also be implemented on parallel computers or VLSI circuits. A theoretical analysis proving the convergence of the algorithms and providing error bounds for the resulting images is presented. The complexity of the algorithms is linear. Graphical and numerical experiments are presented to verify the analytical results and to demonstrate the effectiveness of the methods. >

SHAPE TRANSFORMATION MODELS AND THEIR APPLICATIONS IN PATTERN RECOGNITION

This paper presents linear and bilinear shape transformations including basic transformations, analyzes their geometric properties, and provides computer algorithms. The shape transformations can be used to simplify the recognition of Roman letters, Chinese characters and other pictorial patterns by normalizing their shapes to the standard forms. Important theoretical analyses have been performed to illustrate that the linear and bilinear transformations are applicable to computer recognition of digitized patterns. A number of pictorial examples have been computed to confirm the analyses and conclusions made.

A comparative study of nonlinear shape models for digital image processing and pattern recognition

Four nonlinear shape models are presented: polynomial, Coons, perspective, and projective modes. Algorithms and some properties of these models are provided. For a given physical model, such as a perspective model, comparisons are made with other mathematical models. It is proved that, under certain conditions, the perspective models can be replaced by the Coons models. Problems related to substitution and approximation of practical models that facilitate digital image processing are raised and discussed. Experimental results on digital images are presented. >

Switching control of image based visual servoing with laser pointer in robotic assembly systems

In this paper, a switching control of Image Based Visual Servoing (IBVS) with laser pointer is introduced to control the pose of the end effector with respect to the stationary object in a robotic assembly system so that the image features observed by the camera reach the desired image features as fast as possible. The simple off-the-shelf laser pointer is adopted to realize the depth estimation for obtaining the image Jacobian matrices. By using a laser spot as an image feature and the partition Degree-Of-Freedom (DOF) method, the proposed switching control algorithm decouples the rotational and translational motion control of the robotic end effector to avoid the inherent drawbacks of traditional IBVS, such as image singularities, image local minima and relative long trajectory in Cartesian space. The experimental results on a robotic assembly system are given to verify the effectiveness of the proposed method.

The simplified hybrid-combined methods for Laplace's equation with singularities

Abstract In Li and Liang (1983), the simplified hybrid-combined method is presented for combining the Ritz-Galerkin method and the finite-element method. In this paper we will apply this method to solve singularity problems of Laplaces equation. Error bounds and stability analyses will be provided while taking into account the integration approximation along the coupling boundary. A significant coupling relation between the Ritz-Galerkin and the finite-element method has been found for the Laplace equation with singularities. An optimal rate of convergence has also been achieved. Numerical experiments have been carried out for solving the benchmark problem: Motzs problem to verify the theoretical results.

Harmonic models of shape transformations in digital images and patterns

A harmonic model of shape transformations is presented. In this model, harmonic functions are governed by the Laplace equation. This model can convert all image or a pattern to another with arbitrary shapes. The transformation process is harmonic, without abruptness and discontinuity. This model can be used to generate and recognize handwritten Roman letters and Chinese characters, fingerprints, and other types of digitized images and patterns. The algorithms of the harmonic models involve partial differential equations and their numerical solutions. Therefore, an intrinsic link between pattern images and numerical methods is presented.<<ETX>>

Coupling techniques in boundary-combined methods

Abstract Three coupling strategies in matching the Ritz-Galerkin method and the finite element method are introduced for general elliptic equations and useful numerical techniques are provided. Numerical experiments have been carried out for solving the typical, singular Motz problem, which shows that optimal convergence rates of numerical solutions can be achieved by using the combined methods and coupling techniques provided in this paper.

Penalty-combined method and applications in solving elliptic problems with singularities

Abstract The simplest penalty technique is proposed for matching the Ritz-Galerkin and finite elements methods in solving elliptic problems with multiple singularities. The advantage of this method over the nonconforming combination is its simplicity, without dealing with direct constraints. Error bounds are provided to guide the choice of the penalty constant Pc. Moreover, when Pc is chosen properly large, the numerical solutions from the penalty combined method will approach those from the nonconforming combination. Numerical experiments are carried out for Motzs problem to justify the proposed coupling technique. This technique is also applied to the study of potential flow of wind over buildings where there exist multiple singularities and multiple coupling interfaces among different numerical methods. On the whole, the penalty combined method is useful for solving complicated engineering problems.