结合四元数与小波的彩色图像边缘检测算法*

针对岩石节理裂隙图像噪声多、分割困难等问题，提出一种使用四元数卷积，由反对称小波系数加权的彩色图像边缘检测算法。该算法将彩色图像的R、G、B三个分量表示为四元数的三个虚部，通过四元数卷积后，其方向产生了一定角度的旋转;将旋转后的四元数与水平方向和垂直方向的结果相加，得到相应的幅值和角度;使用反对称双正交小波系数对这些幅值和角度加权后，再使用Otsu阈值并进行模极大抑制，即可得到彩色图像边缘。通过对常用彩色图像和岩石节理裂隙图像的实验结果表明，本算法对彩色图像边缘检测具有较好的效果。

Color edge detector combining quaternion convolution and wavelet transform

Because the rock fracture image was noisy, this paper presented a color edge detection algorithm using quaternion convolution which was weighted by wavelet coefficients. The R, G and B components of a color pixel could be denoted by quaternion. After convoluted the pixel, its direction might be changed. And then added to the corresponding result in the horizontal and vertical directions. After computed the magnitude, also computed the edge strength and direction using the magnitudes. Last, obtained the color edge image via Otsu threshold and modulus maxima suppression. Experimental results show the proposed approach is efficient and robust for general color images and rock fracture images.