WAVELET TRANSFORM FOR TEXTURAL IMAGE CLASSIFICATION

INTRODUCTION

Texture analysis is still considered an interesting but challenging problem in image processing field. In computer vision, several approaches have been proposed in the past for texture analyse. Recently researchers are motivated by human version system to develop multiresolution space/scale texture models such as Gabor filter and wavelet tansforu. Gabor filters require proper tuning of filter parameters at different scales; their transformations are usually not reversible, and finally, there is a significant correlation between their texture features. Wavelet transform on the other hand, has the ability to perform local analysis fur revealing various aspects of data like trends, breakdown points, discontinuities in higher derivatives, and self-similarities. A major drawback of two-dimensional wavelets is their limited capability in capturing directional information which has a significant role in analysts of the images, including feature extraction and classification. 

To overcome this deficiency,a new family of wavelet methods that can capture the intrinsic geometrical structures such as curvelet transform and eontourlet transform. Curvelets are very successful in detecting image activities along curves, while analyzing images at multiple scales, locations, and orientations. Contourlet transform proposed by Do and Vetterli , uses a structure similar to that of curvelets, except at discrete domain. The contourlet expansion is composed of basis images oriented at various directions in multiple scales, with flexible aspect ratios which effectively capture smooth contours of images.

In many remote sensing applications such as aerial or satellite photography, and underwater acoustic imaging systems. textural images that may be acquired from the same scene but with different slope, direction. distance. noise level and illumination, should be classified consistently. It was shown that wavelet transform is suitable for this task. However, computer vision literature has paid less attention to the contourlet domain texture segmentation and classification.

WAVELET TRANSFORM

The transform of a signal is just another form of representing the signal. It does not change the information content present in the signal. The Wavelet Transform provides a time-frequency representation of the signal. It was developed to overcome the short coming of the Short Time Fourier Transform (STFT), which can also be used to analyze non-stationary signals. While STFT gives a constant resolution at all frequencies, the Wavelet Transform uses multi-resolution technique by which different frequencies are analyzed with different resolutions. A wave is an oscillating function of time or space and is periodic. In contrast, wavelets are localized waves. They have their energy concentrated in time or space and are suited to analysis of transient signals. While Fourier Transform and STFT use waves to analyze signals, the Wavelet Transform uses wavelets of finite energy.

The wavelet analysis is done similar to the STFT analysis. The signal to be analyzed is multiplied with a wavelet function just as it is multiplied with a window function in STFT, and then the transform is computed for each segment generated. However, unlike STFT, in Wavelet Transform, the width of the wavelet function changes with each spectral component. The Wavelet Transform, at high frequencies, gives good time resolution and poor frequency resolution, while at low frequencies, the Wavelet Transform gives good frequency resolution and poor time resolution.