Image Denoising Via Control Of Curvature Continuity And Its Application

Image denoising is one of the fundamental operations in image processing, and it always serves as a basis for many applications in image processing and computer vision. As an image is in fact a discrete surface, in this paper we define a new local metric for smoothness measurement for images. Along with the new metric, a system of representation equations is established for noise free images. Based on the noise free image model and the new metric, we propose two new algorithms for image denoising. The main features of our new algorithms are: (1) they can be used for removal of noises of any kinds; (2) image features are preserved with no reduction of image intensities. This article involves mainly three parts as follows:In the first part, we propose a new algorithm for image denoising via control of curvature continuity. We define a sharpness factor according to the ratio of discrete normal curvature that can be used to depict local smoothness of an image. With the sharpness factor, we propose a criterion to differentiate the noise pixels and smooth pixels in an image. Then we compute new intensities for noisy pixels by bounded sharpness factors and the representation equations for noise free images. This new algorithm can be used to remove any kinds of noises with detail and feature preservation. When all sharpness factors lie in a permitted interval, the image surface will be unchanged, and the final image surface suffers no shrinkage either.In the second part, we propose homogeneous bilateral filter which takes advantage of feature preservation by bilateral filter and curvature continuity control by sharpness factor. Different from its linear part, homogeneous bilateral filter evaluate new pixel intensities based on curvature continuity. Then, wider ranges of noises can be removed by the new filter than the traditional bilateral filter in case the filtering parameters are the same. Even with many times of iterations, there is no salient blurring of details or blocking within the images.In the third part, we apply two new denoising algorithms in image interpolation and edge detection. Compared with bilinear interpolation and bi-cubic interpolation, our method keeps more features of original images. After we use our new denoising algorithms for pre-processing of images, we use the Canny operator to detect edges within the filtered images. The results show that the noises within the original image have been removed efficiently while the features/edges are preserved well.