Haar小波数值解原理在图像边缘检测算法中的应用

Application of Haar wavelet numerical solution principle in image edge detection algorithm

在计算机视觉领域中,提取出的图像边缘信息不仅可以简要表示整幅图像信息,且能充分体现出物体的特征,因此边缘检测算法的重要性日益凸显。文中针对传统图像边缘检测算法中存在的抗噪性能差和边缘定位不明显等问题,提出了一种基于非均匀Haar小波变换的图像边缘检测算法。利用Haar小波滤波器将原始图像分解为4个子分量图像,其中水平与垂直高频子分量图像采用Canny算子进行边缘检测,低频子分量图像则利用修正形态算子进行形态学边缘检测。然后对处理后的所有子分量图像进行逆向重构操作,从而实现精准的边缘检测操作。最终,基于Lena图像验证了所提算法的性能。实验结果表明,所提算法的峰值信噪比与均方误差分别为6.3338和15217.52,且边缘检测效果明显优于其他相关对比算法。

In the field of computer vision,the extracted image edge information can not only simply represent the entire image information,but also fully reflect the characteristics of the object.Therefore,the importance of edge detection algorithm is increasingly prominent.In this paper,an image edge detection algorithm based on non⁃uniform Haar wavelet transform is presented to solve the problems of poor noise resistance and unclear edge positioning in traditional image edge detection algorithms.The original image is decomposed by Haar wavelet filter to produce four sub⁃component images.The horizontal and vertical high frequency sub⁃component images are edge detected by Canny operator,while the low frequency sub⁃component images are edge detected by modified morphological operator.Then all the processed sub⁃component images are reconstructed in reverse order to achieve accurate edge detection.Finally,the performance of the proposed algorithm is verified based on the Lena image.The experimental results show that the Power Signal⁃to⁃Noise Ratio(PSNR)and Mean Square Error(MSE)of the proposed algorithm are 6.3338 and 15217.52,respectively,and the edge detection performance is significantly better than other related comparison algorithms.