基于不可分加性小波与形态学梯度的图像边缘提取方法

针对传统的图像边缘提取方法只强调图像中的水平和垂直边缘的不足，提出了一种基于不可分加性小波和形态学梯度相结合的图像边缘提取方法。根据二维不可分小波理论构造了低通滤波器，利用它对原图像进行加性小波多尺度分解；对低频子图像求形态学梯度，对增强后的高频子图像取模极大值；将所得梯度图与边缘图作加性小波逆变换，得重构后的边缘梯度图；并利用二值形态学方法对其进行处理，得最终结果边缘图。实验结果表明，本文算法可获得较好的边缘图像，与经典的边缘提取方法相比，该方法具有完整性、多方向性、平移不变性和快速性的特点。

Image Edge Detection Method Based on Nonseparable Additive Wavelet and Morphological Gradient

In order to solve the problem that the traditional image edge detection techniques can only emphasize the horizontal and vertical edges, a new image edge extraction method combining the multi-resolution analysis of nonseparable additive wavelet transform and the mathematical morphology has been proposed. A low-pass filter of nonseparable wavelet is constructed and the source image is decomposed into a low-frequency sub-image and high-frequency sub-images. The low-frequency sub-image is filtered to obtain morphological gradient map. The high-frequency sub-images are added to form an enhanced high-frequency edge map by using modulus maxima value method. Inverse transform of nonseparable additive wavelet transform is performed on the gradient map and the edge map and an edge-gradient map is produced. The final edge map is got by binarizing the edge-gradient map. The experimental results show that the proposed method has good visual effect. When compared with the traditional image edge detection techniques, it can extract image edges with integrity, multidirection, shift invariance and high speed.