Wavelet Theory And Its Application To The Edge Detection Of Images

Wavelet theory is a new analysis theory developed rapidly in last two decades. It is a versatile tool with very rich mathematical content and great applications. It has been employed in many fields and applications, such as signal processing, image analysis, pattern recognition, biomedical imaging, radar, fractal, computer vision, theoretical mathematics, digital television, and endless other areas. The edge of image is often considered as the fundamental feature of the image. It has been widely used in pattern recognition and computer vision and image processing and analyzing technologies such as feature description, image segmentation,image enhancement and image data compression, etc.The application of wavelet analysis to the edge detection of images is the main topic of this thesis. The main contributions in this paper can be summarized as follows: The basic wavelet analysis theory and algorithms are introduced. The basic principles of applying wavelet transform to analyse the singularities of signals and basic methods of applying wavelet transform to edge detection are discussed. The boder extentions problems in wavelet transforms are discussed detailedly, two theorems concerned are given and proved, and a concrete example and some experiments are taked to illustrate the border extensions in wavelet transform. We are making good use of the properties of multiscale edge information and wavelet transform, design the cubic B-spline smoothing filter operator and combine it with the embedded confidence to detect edges. Furthermore, we study the edge detection method for those images badly contaminated by noises, according to the sensitivity of human visual system. The experimental results show that the proposed method can detect the edges of images accurately and efficiently. By the analysis of HSV visual model, making good use of the properties of multiscale edge information and wavelet transform and multiscale fundamental forms, a new edge detection technique is presented, which is based on HSV color space, applying the multiscale fundamental forms to multiscale edge detection of color images. The experimental results show that the proposed method can efficiently and accurately detect the edges of color images.