基于多尺度边缘表示的图像增强快速算法

低对比度结构广泛存在于各种数字图像之中，研究如何通过后期处理增强数字图像的对比度是很有意义的。灰度图像对比度的高低总是与图像灰度梯度幅值的大小相联系，受这种思想的启发，提出了一种基于图像多尺度边缘表示的，利用对信号小波变换模极大值的拉伸和Hermite插值多项式实现的图像增强快速算法。此算法可以实现对噪声的抑制和对图像中不同尺度特征的增强。数值实验结果表明，该算法增强效果明显，运算速度快，是一种实用性较强的图像对比度增强算法。

A Fast Image Enhancement Algorithm Based on Multi-scale Edges Representation of Images

Low contrast structure can be found in many kinds of digital images, and it is a meaningful work to find out how to enhance these raw images through digital post-processing. A novel enhancement algorithm based on multi-scale edges representation of images is proposed. This algorithm is motivated by the connection between the contrast of a grayscale image and the gradient magnitude of intensity edges in the neighborhood where the contrast is measured. The undecimated dyadic wavelet transform of the original image is computed firstly by treating the columns and lines of the image separately, and then the local maxima of wavelet transform coefficients are selected out. The reconstruction of the image can be interpreted as an interpolation process, which recovers the wavelet coefficients between two consecutive modulus maxima and then calculates the inverse wavelet transform. As we know, the first derivatives of the modulus maxima are zero, and the Hermite polynomial requires the value of derivatives at the given nodes. Based on these two facts, the wavelet coefficients can be reconstructed using Hermite interpolation polynomial of degree 3 between any two adjacent maxima. By means of stretching those maxima at different levels and interpolating them with Hermite interpolation polynomials, the image can be enhanced effectively, and the different stretching factors on different levels can provide various kinds of enhancing effects, while this kind of enhancing flexibility cannot be found in other algorithms easily. This algorithm also offers abilities to control noise magnification and to enhance features of certain size within the images. Numerical experiments show that, the method can get fairly well enhancement result and the computing complexity can be low, so it is a practical fast enhancement algorithm.