Image Smoothing with Exponential Functions

Noise reduction in images, also known as image smoothing, is an essential and first step before further processings of the image. The key to image smoothing is to preserve important features while removing noise from the image. Gaussian function is widely used in image smoothing. Recently it has been reported that exponential functions (value of the exponent is not equal to 2) perform substantially better than Gaussian functions in modeling and preserving image features. In this paper we propose a family of exponential functions, that include Gaussian when the value of the exponent is 2, for image smoothing. We experiment with a variety of images, artificial and real, and demonstrate that optimal results are obtained when the value of the exponent is within a certain range.

[1]  Peder A. Olsen,et al.  Power Exponential Densities for the Training and Classification of Acoustic Feature Vectors in Speech Recognition , 2001 .

[2]  Song-Chun Zhu,et al.  Learning generic prior models for visual computation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[3]  Song-Chun Zhu,et al.  GRADE: Gibbs reaction and diffusion equations , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[4]  Mitra Basu,et al.  Image enhancement using a human visual system model , 1997, Pattern Recognit..

[5]  Mitra Basu,et al.  A Gaussian Derivative Operator for Authentic Edge Detection and Accurate Edge Localization , 1999, Int. J. Pattern Recognit. Artif. Intell..

[6]  Arthur R. Weeks.  Fundamentals of electronic image processing , 1996, SPIE/IEEE series on imaging science and engineering.

[7]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.