Lihua Yang

Characterization of Dirac-structure edges with wavelet transform

This paper aims at studying the characterization of Dirac-structure edges with wavelet transform, and selecting the suitable wavelet functions to detect them. Three significant characteristics of the local maximum modulus of the wavelet transform with respect to the Dirac-structure edges are presented: (1) slope invariant: the local maximum modulus of the wavelet transform of a Dirac-structure edge is independent on the slope of the edge; (2) grey-level invariant: the local maximum modulus of the wavelet transform with respect to a Dirac-structure edge takes place at the same points when the images with different grey-levels are processed; and (3) width light-dependent: for various widths of the Dirac-structure edge images, the location of maximum modulus of the wavelet transform varies lightly under the certain circumscription that the scale of the wavelet transform is larger than the width of the Dirac-structure edges. It is important, in practice, to select the suitable wavelet functions, according to the structures of edges. For example, Haar wavelet is better to represent brick-like images than other wavelets. A mapping technique is applied in this paper to construct such a wavelet function. In this way, a low-pass function is mapped onto a wavelet function by a derivation operation. In this paper, the quadratic spline wavelet is utilized to characterize the Dirac-structure edges and a novel algorithm to extract the Dirac-structure edges by wavelet transform is also developed.

Signal period analysis based on Hilbert-Huang transform and its application to texture analysis

An approach to analyze the period of a signal based on Hilbert-Huang transform is presented in this paper. For an approximately periodic signal which contains plenty of high frequency components, the relation between its period and its main frequency is established. Our main result is that, for an approximately periodic signal which contains plenty of high frequency components, its period can be estimated accurately according to its main-frequency distribution. By applying the technique on texture analysis, a novel method to extract the periodicity features of a texture image is developed, which can be used in texture classification, segmentation, recognition and other applications.

An EMD-based recognition method for Chinese fonts and styles

This paper presents a novel method to recognize Chinese fonts based on empirical mode decomposition (EMD). By analyzing and comparing a great number of Chinese characters, five basic strokes have been selected to characterize the stroke features of Chinese fonts. Based on them, stroke feature sequences of a given text block are calculated. By decomposing them with EMD, some intrinsic mode functions are produced and then the first two, which are of the highest frequencies, are used to produce the so-called stroke high frequency energies, which is the average energy of the two intrinsic mode functions over the length of the sequence. By calculating the stroke high frequency energies for all the five basic strokes and combining them with the averages of the five residues, which are called stroke low frequency energies, a 10-dimensional feature vector is formed. Finally, the minimum distance classifier is used to recognize the fonts and encouraging experimental results have been obtained. The main advantages of our algorithm are that (1) the feature dimension is very low; (2) less samples are needed to train the classifier; (3) finally and most importantly, it is the first attempt to apply the new theory of Hilbert-Huang transform to document analysis and recognition.

EDGE EXTRACTION OF IMAGES BY RECONSTRUCTION USING WAVELET DECOMPOSITION DETAILS AT DIFFERENT RESOLUTION LEVELS

This paper describes a novel method for edge feature detection of document images based on wavelet decomposition and reconstruction. By applying the wavelet decomposition technique, a document image becomes a wavelet representation, i.e. the image is decomposed into a set of wavelet approximation coefficients and wavelet detail coefficients. Discarding wavelet approximation, the edge extraction is implemented by means of the wavelet reconstruction technique. In consideration of the mutual frequency, overlapping will occur between wavelet approximation and wavelet details, a multiresolution-edge extraction with respect to an iterative reconstruction procedure is developed to ameliorate the quality of the reconstructed edges in this case. A novel combination of this multiresolution-edge results in clear final edges of the document images. This multi-resolution reconstruction procedure follows a coarser-to-finer searching strategy. The edge feature extraction is accompanied by an energy distribution estimation from which the levels of wavelet decomposition are adaptively controlled. Compared with the scheme of wavelet transform, our method does not incur any redundant operation. Therefore, the computational time and the memory requirement are less than those in wavelet transform.

Discrimination of similar handwritten numerals based on invariant curvature features

This paper studies the discrimination of similar handwritten numerals based on invariant curvature features. High-order B-splines are used to calculate the curvature of the contours of handwritten numerals. The concept of a distribution center is introduced so that a one-dimensional periodic signal can be normalized as shift invariant. Consequently, the curvature of the contour of a character becomes rotation invariant. To reduce the dimension of the features, wavelet basis decomposition is used to produce more compact features. Finally, artificial neural network (ANN) and support vector machines (SVM) are employed to train the features and design classifiers of high recognition rates.

Detection of Spindles in Sleep EEGs Using a Novel Algorithm Based on the Hilbert-Huang Transform

A novel approach for detecting spindles from sleep EEGs (electroencephalograph) automatically is presented in this paper. Empirical mode decomposition (EMD) is employed to decompose a sleep EEG, which are usually typical nonlinear and non-stationary data, into a finite number of intrinsic mode functions (IMF). Based on these IMFs, the Hilbert spectrum of the EEG can be calculated easily and provides a high resolution time-frequency presentation. An algorithm is developed to detect spindles from a sleep EEG accurately, experiments of which show encouraging detection results.

A width-invariant property of curves based on wavelet transform with a novel wavelet function

This paper is an improvement on the characterization of edges. Using a novel wavelet function, it is proven that the maximum moduli of the wavelet transform (MMWT) of a curve produces two new symmetrical curves on both sides of the original with the same direction. The distance between the two curves is shown to be independent of the width d of the original curve if the scale s of the wavelet transform satisfies s/spl ges/d. This property provides a novel method of obtaining the skeletons of the curves in an image.

Optimal averages for nonlinear signal decompositions-Another alternative for empirical mode decomposition

The empirical mode decomposition (EMD) is an algorithm pioneered by Huang et al. as an alternative technique to the traditional Fourier and wavelet methods for analyzing nonlinear and non-stationary signals. It aims at decomposing a signal, via an iterative sifting procedure, into several intrinsic mode functions (IMFs), and each of the IMF has better behaved instantaneous frequency analysis. This paper presents an alternative approach for EMD. The main idea is to replace the average of upper and lower envelopes in the sifting procedure of EMD by a local average obtained by variational optimization framework. Therefore, an IMF can be produced by simply subtracting the average from the signal without iteration. Our numerical examples illustrate that the resulting decomposition is convergent and robust against noise. HighlightsLet Mx be the average of a given signal x , it has been proved that M ( x - Mx ) = 0 , at some extent.Do not need to predefined the class of functions, to calculate the average of a signal.The model we proposed can avoid the global influence and robust to noise perturbations.

A novel envelope model based on convex constrained optimization

Abstract The concept of envelope has been used widely in signal analysis. However a good mathematical definition of suitable envelope remains an issue. In this paper, we present a novel model to estimate the envelope of a signal by using the convex constrained optimization. This model is based on the commonly accepted knowledge about envelope which makes it coincide with the geometric envelope of the signal. The envelope based on the new model is smooth and has no undershoots. Experiments comparing with the existing typical models of envelope are also implemented and discussed.

An improved envelope algorithm for eliminating undershoots

According to the drawbacks of current envelope algorithms, we present an improved envelope algorithm based on cubic spline and monotone piecewise cubic polynomial interpolations. The new envelope can eliminate the undershoots and meanwhile keep the smoothness property. In addition, we show that the developed method is valid when it is applied to the Empirical Mode Decomposition for non-stationary signal processing.