Image Edge Detection Algorithm Based On Multi-scales Wavelet Transform

Image edge detection algorithm is currently divided into two categories, gradient-based edge detection and Laplace transform-based edge detection. In the algorithms of gradient-based edge detection, we use smoothing filter to calculate the predictive value of gradient magnitude and find the location of the edge by the predictive value. The principle of Laplace of Gaussian algorithm is by finding the second derivative of zero to determine the image edge in images. The main disadvantage of gradient based edge detection algorithm is particularly sensitive to noise. It is necessary to propose an adaptive edge detection algorithm. The algorithm can adapt to changes of noise level in image. It is able to identify the contents of those images effectively and exclude the introduction of the pseudo-noise video content to reduce the noise. It is important of the image preprocessing. Preprocessing can be divided into two ways, filter the image using Gaussian function or a smooth function.In practice, most of the signal is time domain signal. Most of the cases are the most information of the signal information hidden in the signal spectrum. Fourier transform of signal gives frequency domain information. But we can not know what spectral components exist in time. Wavelet transform is calculating each value of a single frequency to overcome the problem of resolution. Window length is changing. Edge can be considered as a transitional stage of the signal or mathematically defined as a local singularity. Fourier transform is not suited to the overall transformation of local singularities. Wavelet is a local time-frequency analysis. Wavelet edge detection technology is the discrete wavelet transform. Filter is to find a local maximum in the wavelet domain. Wavelet transform provides a multi-scale analysis. Multi-scale analysis can be applied to edge detection.The principle of edge detection based on wavelet transform is using smoothing function to smooth the detected signal at different scales. Use the first or second derivative to find its mutation. When the selected wavelet function equal to the first order differential of the smooth function, the extreme values of coefficients of the wavelet transform can be use to edge detection. The first order derivative of the smooth function is used as the mother wavelet for wavelet transform. The wavelet transform coefficients in each scale correspond to the signal modulus maxima point mutation. In large scale, the noise is smoothed. Extreme points are relative stability. In small scale, the smooth function smoothes small areas. Modulus maxima of wavelet coefficients correspond exactly to the location of the mutations. Therefore when we use module maximum method to determine signal mutation, it is necessary to combine the multi scales.B-splines wavelet has good performance in edge detection. In 4th part of this paper, B-splines is used as approximation of gauss filter. And 3 times B-splines wavelet is selected to detect the edge of the image LENA. Using the multi scales property of wavelet, we extract edge detail information such as pupil in small scales. We extract long smoothed edge chain such as columns. Then we compare the wavelet edge detection algorithms with other classic edge detection algorithms. The conclusion is that wavelet edge detection can detect the image contours clearly. It is convinced that the wavelet edge detection have good performance. It has successfully suppressed noise, and extract edges more exquisitely.