B. G. Mertzios

A new class of Zernike moments for computer vision applications

A Modified Direct Method for the computation of the Zernike moments is presented in this paper. The presence of many factorial terms, in the direct method for computing the Zernike moments, makes their computation process a very time consuming task. Although the computational power of the modern computers is impressively increasing, the calculation of the factorial of a big number is still an inaccurate numerical procedure. The main concept of the present paper is that, by using Stirlings Approximation formula for the factorial and by applying some suitable mathematical properties, a novel, factorial-free direct method can be developed. The resulted moments are not equal to those computed by the original direct method, but they are a sufficiently accurate approximation of them. Besides, their variability does not affect their ability to describe uniquely and distinguish the objects they represent. This is verified by pattern recognition simulation examples.

Real-time computation of two-dimensional moments on binary images using image block representation

This work presents a new approach and an algorithm for binary image representation, which is applied for the fast and efficient computation of moments on binary images. This binary image representation scheme is called image block representation, since it represents the image as a set of nonoverlapping rectangular areas. The main purpose of the image block representation process is to provide an efficient binary image representation rather than the compression of the image. The block represented binary image is well suited for fast implementation of various processing and analysis algorithms in a digital computing machine. The two-dimensional (2-D) statistical moments of the image may be used for image processing and analysis applications. A number of powerful shape analysis methods based on statistical moments have been presented, but they suffer from the drawback of high computational cost. The real-time computation of moments in block represented images is achieved by exploiting the rectangular structure of the blocks.

On the analysis of discrete linear time-invariant singular systems

The discrete singular equation over an interval can represent a two-point boundary-value problem or it can be considered as a dynamical relation developing forward in time. A theory is provided, by giving analytic solutions and discussing system properties in both cases, that encompasses both interpretations. The singular system fundamental matrix is used to provide analytic solutions to a time-invariant discrete singular equation defined over an interval. The two distinct cases in which the singular relation is interpreted as a two-point boundary-value problem or as a forward dynamical system on the interval are both considered. Also considered is the case in which the singular relation is considered as a backward dynamical system, and the relationship between the index of nilpotence and the Laurent series coefficients resulting from the solutions of certain state-space equations is shown. Reachability and observability are discussed, and the point is made that these properties are different, depending on how the singular relation is interpreted. >

A decomposition theorem and its implications to the design and realization of two-dimensional filters

It is shown that an arbitrary rational 2-D transfer function can be expanded in first order terms, each one of which is a function of only one of the two variables. This method leads naturally to reconfigurable filters with great modularity and parallelism, which can realize any rational transfer function up to a given order.

Leverrier's algorithm for singular systems

An algorithm is presented which allows the computation of the transfer function of a singular system from its state-space description, without inverting a polynomial matrix. This algorithm is an extension of the Leverrier algorithm for the more general case of singular systems and it reduces the computational cost.

SHAPE RECOGNITION WITH A NEURAL CLASSIFIER BASED ON A FAST POLYGON APPROXIMATION TECHNIQUE

Abstract A method is presented for the fast recognition of two-dimensional (2D) binary shapes with complicated form, like islands on a map or medical images. The proposed method is based on a new polygon approximation technique, which extracts suitable feature vectors with specified dimension, which characterizes a given shape. These feature vectors are used as inputs in an efficient neural based classifier for the fast recognition of the shape. The proposed technique is characterized by high speed performance, which is desired for real time applications.

Statistical pattern recognition using efficient two-dimensional moments with applications to character recognition

Abstract A new set of efficient two-dimensional (2D) moments is introduced, which are normalized with respect to standard deviation. They are invariant under rotation, translation and scale of the image, less sensitive to noise and appear to have better classification performance over the existing sets of moments. Application of the proposed technique to optical character recognition is given.

On the generalized Cayley-Hamilton theorem

The Cayley-Hamilton theorem is extended to the case where two A and B n \times n matrices are involved. Results similar to the regular case are presented. The results are useful for problems that concern the analysis as well as the synthesis of singular systems, for the definition of a function of two matrices f(A, B) and in various other problems in linear algebra.

Pattern classification by using improved wavelet Compressed Zernike Moments

In this paper, an improved Feature Extraction Method (FEM), which selects discriminative feature sets able to lead to high classification rates in pattern recognition tasks, is presented. The resulted features are the wavelet coefficients of an improved compressed signal, consisting of the Zernike moments amplitudes. By applying a straightforward methodology, it is aimed to construct optimal feature vectors in the sense of vector dimensionality and information content for classification purposes. The resulting surrogate feature vector is of lower dimensionality than the original Zernike moment feature vector and thus more appropriate for pattern recognition tasks. Appropriate validation tests have been arranged, in order to investigate the performance of the proposed algorithm by measuring the discriminative power of the new feature vectors despite the information loss.

Direct controllability and observability time domain conditions of singular systems

Controllability and observability criteria for singular systems using direct formulas in the time domain are introduced. The method used is based on a direct expansion of the transfer function matrix via a Leverrier-type algorithm. Hence, no decomposition of the state-space model is needed and the criteria are implementable on a digital computer. The compact form of the matrices might be helpful in other analysis as well as synthesis problems in singular systems. >