SIViP DOI 10.1007/s11760-011-0253-5 ORIGINAL PAPER Bilateral filtering with adaptation to phase coherence and noise E. Farzana · M. Tanzid · K. M. Mohsin · M. I. H. Bhuiyan Received: 28 November 2010 / Revised: 14 July 2011 / Accepted: 14 July 2011 © Springer-Verlag London Limited 2011 Abstract In this paper, a bilateral filter with adaptive domain and range parameter is introduced for image deno- ising. Since the objective of denoising is to reduce noise as much as possible while preserving the perceptually impor- tant details, the parameters are adjusted in accordance with perceptual significance of pixels and noise level. The domain parameter is obtained by using the maximum and minimum moments of local phase coherence for being the represen- tative of image details such as edges and corners of an image. The range parameter is estimated from the intensity- homogeneity measurements for their ability to represent the underlying noise. In addition, the filter is applied in an iter- ative manner to reduce the residual noise. Experiments are carried out using various standard images, and the results show that the proposed method is more effective in reducing additive white Gaussian noise as compared to several recently introduced denoising techniques in terms of the peak signal- to-noise ratio, structural similarity index and visual quality. In addition, experiments performed using real noisy images reveal the ability of the proposed filter to provide denoised images of better visual quality. E. Farzana · M. Tanzid · K. M. Mohsin · M. I. H. Bhuiyan (B ) Department of Electrical and Electronics Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh e-mail: imamul@eee.buet.ac.bd E. Farzana e-mail: Li.eee05@gmail.com M. Tanzid e-mail: mihika193@gmail.com K. M. Mohsin e-mail: Mohsin.eee@gmail.com Keywords Bilateral filter · Range and domain filtering parameters · Homogeneity measurements · Local phase coherence · Additive white Gaussian noise 1 Introduction Noise arises during various phases of image processing such as acquisition and transmission of images. Presence of noise destroys important image details and hampers image pro- cessing tasks such as compression, segmentation and de- mosaicing. Hence, extracting underlying image information from a noisy image is a very important problem. Traditional linear Gaussian low-pass filter suppresses noise but at the cost of blurring the edges due to the assumption of low signal variation. Various nonlinear filters have been intro- duced to mitigate this limitation of linear filters. A pop- ular class of nonlinear filter is bilateral filter introduced by Tomasi and Manduchi [1], which smoothes an image while preserving the edges. In this filtering method, each pixel is replaced by a weighted mean of nearby pixels, the weights being set considering both geometrical and photo- metrical distances among the pixels. Dependency on pixel intensities in addition to their closeness makes the filter more effective in comparison with other nonlinear filters. However, performance of the bilateral filter greatly depends on the domain and range parameters; selecting large-val- ued parameters blurs the texture details, whereas noise is not reduced effectively with the small-valued ones. In [1], the parameters are set rather arbitrarily, and one has to change their values from image to image and at differ- ent noise levels to get a satisfactory filtering result. Sev- eral approaches of adaption are reported in the literature [2–6]. In [2], the parameters are set according to the local phase coherence [7] of an image. However, only the edge 123