A study on improving the performance of the real-coded genetic algorithm for electromagnetic inverse scattering of two-dimensional perfectly conducting cylinders is presented. Three schemes, namely, the penalty function approach, the closed cubic B-splines local shape function approach and the adaptive hybrid algorithm approach are proposed to deal with the problem. These schemes can be used separately or be combined to improve the performance. Numerical examples validate the schemes.

A generic multilevel quality-of-service (QoS) model for distributed multimedia applications is presented. QoS mapping mechanisms are required to translate the QoS parameters among the hierarchical levels. One QoS mapping mechanism based on the spline functions is proposed, hence two splines are compared. One is natural splines and the other is B-splines. QoS measurement experiments were conducted, and it is found that the B-splines give more accurate mapping results than the natural splines once the knots for the splines are selected appropriately.

This paper proposes a fast method for the calculation of exponential B-splines sampled at regular intervals. This algorithm is based on a combination of FIR and IIR filters which enables a fast decomposition and reconstruction of a signal. When complex values are selected for the parameters of the exponentials, complex trigonometric functions are obtained. Only the real part of these functions are used for the interpolation of real signals, leading less bandlimited signals when they are compared with the polynomial B-spline counterparts. These characteristics were verified with 1-D and 2-D examples. This paper also discusses the effectiveness of exponential B-splines, when they are applied to image processing.

This paper proposes a novel fast algorithm for the decomposition and reconstruction of two-dimensional (2-D) signals by box splines. The authors have already proposed an algorithm to calculate the discrete box splines which enables the fast reconstruction of 2-D signals (images) from box spline coefficients. The problem still remains in the decomposition process to derive the box spline coefficients from an input image. This paper first investigates the decomposition algorithm which consists of the truncated geometric series of the inverse filter and the steepest descent method with momentum (SDM). The reconstruction process is also developed to correspond to the enlargement of images. The proposed algorithm is tested for the expansion of several natural images. As a result, the peak signal-to-noise ratio (PSNR) of the reconstructed images became more than 50 dB, which can be considered as enough high level. Moreover, the property of box splines are discussed in comparison with 2-D (the tensor product of) B-splines.

This paper presents an accurate method for finding the 3D control points of the B-Spline curves. This method can automatically fit a set of data points with piecewise geometrically continuous cubic B-Spline curves. Iterating algorithm has been used for finding the 2D control points. And a new approach for shape reconstruction based on the control points of the curves on the object's surface is proposed. B-Spline patch, the extension of the B-Spline curves to surface, provides recovering the shape of the object in 2D approach. The 3D control points of the cubic B-Spline curves are computed from the factor decomposition of the measurement matrix of 2D control points. The multiple object approach is also proposed to reconstruct the 3D shape of each curves of an object. Some experiments are demonstrated to confirm the effectiveness of our proposed method.

It is very difficult to obtain a linearizing feedback and a coordinate transformation map, even though the system is feedback linearizable. It is known that finding a desired transformation map and feedback is equivalent to finding an integrating factor for an annihilating one-form. In this paper we develop a numerical algorithm for an integrating factor involving a set of partial differential equations and corresponding zero-form using the C.I.R method. We employ a tensor product splines as an interpolation method to data which are resulted from the numerical algorithm in order to obtain an approximate integrating factor and a zero-form in closed forms. Next, we obtain a coordinate transformation map using the approximate integrating factor and zero-form. Finally, we construct a stabilizing controller based on a linearized system with the approximate coordinate transformation.

This paper presents a fast algorithm for calculating box splines sampled at regular intervals. This algorithm is based on the representation by directional summations, while splines are often represented by convolutions. The summation-based representation leads less computational complexity: the proposed algorithm requires fewer additions and much fewer multiplications than the algorithm based on convolutions. The proposed algorithm is evaluated in the sense of the number of additions and multiplications for three- and four-directional box splines to see how much those operations are reduced.

An approximate scheme for decomposing and reconstructing a continuous-time signal as a linear combination of the B-splines is studied. It is an oversampling discrete-time implementation derived by substituting the multifold RRS functions for the B-splines. The RRS functions are multifold discrete convolution of the sampled rectangular functions. Analysis of the scheme yields conditions for the circuit parameters to assure stability and required precision. A design example is presented that makes the error less than 1% in the supremal norm by the oversampling ratio of 512. Its numerical simulation is also presented.

Unlike the time-consuming contour tracking method of snakes [5] which requires a considerable number of iterated computations before contours are successfully tracked down, we present a faster and accurate model-based landmarks" tracking method where a single iteration of the dynamic programming is sufficient to obtain a local minimum to an integral measure of the elastic and the image energy functionals. The key lies in choosing a relatively small number of salient land-marks", or features of objects, rather than their contours as a target of tracking within the image structure. The landmarks comprising singular points along the model contours are tracked down within the image structure all inside restricted search areas of 41 41 pixels whose respective locations in image structure are dictated by their locations in the model. A Manhattan distance and a template corner detection function of Singh and Shneier [7] are used as elastic energy and image energy respectively in the algorithm. A first approximation to the image contour is obtained in our method by applying the thin-plate spline transformation of Bookstein [2] using these landmarks as fixed points of the transformation which is capable of preserving a global shape information of the model including the relative configuration of landmarks and consequently surrounding contours of the model in the image structure. The actual image contours are further tracked down by applying an active edge tracker using now simplified line search segments so that individual differences persisting between the mapped model contour are substantially eliminated. We have applied our method tentatively to portraits of a class album to demonstrate the effectiveness of the method. Our experiments convincingly show that using only about 11 feature points our method provides not only a much improved computational complexity requiring only 0.94sec. in CPU time by SGI's indigo2 but also more accurate shape representations than those obtained by the snakes methods. The method is powerful in a problem domain where the model-based approach is applicable, possibly allowing real time processing because a most time consuming algorithm of corner template evaluation can be easily implemented by parallel processing firmware.

A new global method for constructing a C2 piecewise quartic polynomial curve is presented. The coefficient matrix of equations which must be solved to construct the curve is tridiagonal. The joining points of adjacent curve segments are the given data points. The constructed curve reproduces exactly a polynomial of degree four or less. The results of experiments to test the efficiency of the new method are also shown.

In this paper a method of recognizing waveform based on the Discrete Wavelet Transform (DWT) presented by us is applied to detecting the K-complex in human's EEG which is a slow wave overridden by fast rhythms (called as spindle). The features of K-complex are extracted in terms of three parameters: the local maxima of the wavelet transform modulus, average slope and the number of DWT coefficients in a wave. The 4th order B-spline wavelet is selected as the wavelet basis. Two channels at different resolutions are used to detect slow wave and sleep spindle contained in the K-complex. According to the principle of the minimum distance classification the classifiers are designed in order to decide the thresholds of recognition criteria. The EEG signal containing K-complexes elicited by sound stimuli is used as pattern to train the classifiers. Compared with traditional method of waveform recognition in time domain, this method has the advantage of automatically classifying duration ranks of various waves with different frequencies. Hence, it specially is suitable to recognition of signals which are the superimposition of waves with different frequencies. The experimental results of detection of K-complexes indicate that the method is effective.

The Paper describes a comprehensive system for image recognition based on the technique of boundary spline matching. It can be used to accurately compare two objects and determine whether they are identical or not. The result is extremely satisfactory for comparing planar objects as revealed from the illustrative example presented in this paper. In real practice, images of the same scene object can easily be considered as belonging to different objects if the objects are viewed from different orientations and ranges. Thus, image recognition calls for choosing the proper geometric transformation functions to match images as the initial step so that recognition by template matching can be done as the second step. However, there are a large variety of transformation functions available and the subsequent evaluation of transformation parameters is a highly nonlinear optimisation procedure which is both time consuming and not solution guaranteed, making real-time estimation impossible. This paper describes a new method that represents the boundary of each of two image objects by B-splines and matches the B-splines of two image objects to determine whether they belong to the same scene object. The algorithm developed in this paper concentrates on solving linear simultaneous equations only when handling the geometric transformation functions, which takes almost negligible computational time by using the standard Gaussian Elimination. Representation of the image boundary by B-splines provides a flexible and continuous matching environment so that the level of accuracy can be freely adjusted subject to the requirement of the user. The non-linear optimisation involves only one parameter, i.e. the starting point of each boundary under B-spline simulation, thus guaranteeing a very high speed computational system. The real time operation is deemed possible even there is a wide choice of proper transformation functions.

In the band-limited signal space, the mutual relation between continuous time signal and discrete time signal is expressed by the sampling theorem of Whittaker-Someya-Shannon. This theorem consists of an orthonormal expansion formula using sinc functions. In that formula, the expansion coefficients are identical to the sample values of signals. In general, the bandlimited signal space is not always suited to model the signals in nature. The authors have proposed a new model for signal processing based on finite times continuously differentiable functions. This paper aims to complete the sampling theorem for the spline signal spaces, which corresponds to the sampling theorem of Whittaker-Someya-Shannon in the band-limited signal space. Since the obtained sampling theorem gives the simplest representation of signals, it is considered to be the most fundamental characterization of spline functions used for signal processing. The biorthonormal basis derived in this paper is considered to be a system of delta functions at sampling points with some continuous differentiability.

We use the B spline function and apply the Oslo algorithm to minimize the number of control points in electrocardiogram (ECG) waveform compression under the limitation of evaluation indexes. This method is based on dynamic programming matching to transfer the control points of a reference ECG waveform to the succeeding ECG waveforms. This reduces the execution time for beat-to-beat processing. We also reduced the processing time at several compression stages. When the difference percent normalized root mean square difference is around 10, our method gives the highest compression ratio at a sampling frequency of 250 Hz.

In this paper, the characteristics of microstrip lines near the edge of dielectric substrate are analyzed by improving the rectangular boundary division method. The numerical results indicate the changes of the characteristics of a microstrip line when the strip conductor is closely located to the edge. When the distance the dielectric substrate edge to the strip conductor is less than the thickness of dielectric substrate, the effects of the edge on the line characteristics are no longer negligible. The numerical results in this paper show high computation accuracy without increasing computation time. Our improvement is effective for the analysis of the microstrip lines both for the narrow strip conductor and the strip conductor close to the edge. The relative errors between the numerical results and the measured values are less than 1.2%.