Quasi-random nonlinear scale space

A novel nonlinear scale space framework is proposed for the purpose of multi-scale image representation. The scale space decomposition problem is formulated as a general Bayesian least-squares estimation problem. A quasi-random density estimation approach is introduced for estimating the posterior distribution between consecutive scale space realizations. In addition, the application of the proposed nonlinear scale space framework for edge detection is proposed. Experimental results demonstrate the effectiveness of the proposed scale space framework for constructing scale space representations with significantly better structural localization across all scales when compared to state-of-the-art scale space frameworks such as anisotropic diffusion, regularized nonlinear diffusion, complex nonlinear diffusion, and iterative bilateral scale space methods, especially under scenarios with high noise levels.

[1]  Pierre Vandergheynst,et al.  Multiresolution segmentation of natural images: from linear to nonlinear scale-space representations , 2004, IEEE Transactions on Image Processing.

[2]  Jong-Sen Lee.  Speckle suppression and analysis for synthetic aperture radar images , 1986 .

[3]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[4]  J. Koenderink.  The structure of images , 2004, Biological Cybernetics.

[5]  Yehoshua Y. Zeevi,et al.  Image enhancement and denoising by complex diffusion processes , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Tohru Ishizaka,et al.  Segmentation of natural images using anisotropic diffusion and linking of boundary edges , 1998, Pattern Recognit..

[7]  R. Manmatha,et al.  A scale space approach for automatically segmenting words from historical handwritten documents , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  David A. Clausi,et al.  Intervertebral Disc Segmentation and Volumetric Reconstruction From Peripheral Quantitative Computed Tomography Imaging , 2009, IEEE Transactions on Biomedical Engineering.

[10]  Alan C. Bovik,et al.  Smoothing low-SNR molecular images via anisotropic median-diffusion , 2002, IEEE Transactions on Medical Imaging.

[11]  Steven W. Zucker,et al.  Local Scale Control for Edge Detection and Blur Estimation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Kirk H. Stone.  Scale, Scale, Scale? , 1968 .

[13]  Yuzhong Shen,et al.  Noise reduction and edge detection via kernel anisotropic diffusion , 2008, Pattern Recognit. Lett..

[14]  Zia-ur Rahman,et al.  A multiscale retinex for bridging the gap between color images and the human observation of scenes , 1997, IEEE Trans. Image Process..

[15]  Tony Lindeberg,et al.  Edge Detection and Ridge Detection with Automatic Scale Selection , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[16]  J.H. Elder,et al.  Scale space localization, blur, and contour-based image coding , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[17]  Tony Lindeberg.  Edge Detection and Ridge Detection with Automatic Scale Selection , 2004, International Journal of Computer Vision.

[18]  Yongmin Kim,et al.  Edge-guided boundary delineation in prostate ultrasound images , 2000, IEEE Transactions on Medical Imaging.

[19]  I. Sobol.  Uniformly distributed sequences with an additional uniform property , 1976 .

[20]  Guillermo Sapiro,et al.  Robust anisotropic diffusion , 1998, IEEE Trans. Image Process..

[21]  Guy Gilboa,et al.  Nonlinear Scale Space with Spatially Varying Stopping Time , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

[23]  E. Nezry,et al.  Structure detection and statistical adaptive speckle filtering in SAR images , 1993 .