A New Class of Wavelet-Based Metrics for Image Similarity Assessment

In this paper, we propose a new class of image similarity metrics based on a wavelet decomposition. By suitably combining weighted contributions of the different dyadic frequency bands, we define a class of similarity measures and we prove it is a metric. Moreover, we discuss the theoretical relationship between the novel class of metrics and the well-known structural similarity index (SSIM) and its multiscale versions (MSSSIM and CWSSIM). By using standard benchmark indexes over a reference database in the literature (the TID2013 database), we test the efficiency of the newly defined metrics in performing similarity assessment. We compare the performance of our metric with other well-known indexes in the literature, such as SSIM, FPH, MSSSIM, CWSSIM and PSNR, to demonstrate its improvement over the current state of the art, which becomes more evident when the query image is the one identified by the worst level of degradation which is perceived by the human visual system, as coded by the standard mean opinion score stored in the database.

[1]  Zhou Wang,et al.  Structural Approaches to Image Quality Assessment , 2005 .

[2]  Vishal Monga,et al.  Perceptual Image Hashing Via Feature Points: Performance Evaluation and Tradeoffs , 2006, IEEE Transactions on Image Processing.

[3]  W. Hendee.  The Perception of Visual Information , 1993, Springer New York.

[4]  Krzysztof Okarma.  Colour Image Quality Assessment Using Structural Similarity Index and Singular Value Decomposition , 2008, ICCVG.

[5]  Zhou Wang,et al.  On the Mathematical Properties of the Structural Similarity Index , 2012, IEEE Transactions on Image Processing.

[6]  D. Salomon.  A Guide to Data Compression Methods , 2002, Springer New York.

[7]  Jianqi Zhang,et al.  New metrics for clutter affecting human target acquisition , 2006 .

[8]  Krzysztof Okarma,et al.  Combined image similarity index , 2012 .

[9]  Henk J. A. M. Heijmans,et al.  A new quality metric for image fusion , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[10]  D. Amir.  Characterizations of Inner Product Spaces , 1986 .

[11]  Zhou Wang,et al.  Complex Wavelet Structural Similarity: A New Image Similarity Index , 2009, IEEE Transactions on Image Processing.

[12]  Nikolay N. Ponomarenko,et al.  Color image database TID2013: Peculiarities and preliminary results , 2013, European Workshop on Visual Information Processing (EUVIP).

[13]  J. Benedetto,et al.  Modern Sampling Theory , 2012 .

[14]  Zhou Wang,et al.  Image distortion analysis based on normalized perceptual information distance , 2013, Signal Image Video Process..

[15]  Zhou Wang,et al.  Structural Similarity-Based Approximation of Signals and Images Using Orthogonal Bases , 2010, ICIAR.

[16]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[17]  Gian Luca Foresti,et al.  A multi-camera approach to sensor evaluation in video surveillance , 2005, IEEE International Conference on Image Processing 2005.

[18]  Nikolay N. Ponomarenko,et al.  Image database TID2013: Peculiarities, results and perspectives , 2015, Signal Process. Image Commun..

[19]  Stphane Mallat,et al.  A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way , 2008 .

[20]  Honghua Chang,et al.  New metrics for clutter affecting human target acquisition , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[21]  Peter Alexander Hst,et al.  A New Weighted Metric: the Relative Metric I , 2001 .

[22]  Zhou Wang,et al.  Multiscale structural similarity for image quality assessment , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.

[23]  Chun-Shien Lu,et al.  Geometric distortion-resilient image hashing system and its application scalability , 2004, MM&Sec '04.

[24]  T. Apostol.  Ptolemy's Inequality and the Chordal Metric , 1967 .

[25]  Jorge E. Pezoa,et al.  An Enhancement to the Constant Range Method for Nonuniformity Correction of Infrared Image Sequences , 2004, CIARP.

[26]  Peter Hästö,et al.  A new weighted metric: the relative metric II , 2001 .

[27]  Hore,et al.  [IEEE 2010 20th International Conference on Pattern Recognition (ICPR) - Istanbul, Turkey (2010.08.23-2010.08.26)] 2010 20th International Conference on Pattern Recognition - Image Quality Metrics: PSNR vs. SSIM , 2010 .

[28]  Nikolay N. Ponomarenko,et al.  METRICS PERFORMANCE COMPARISON FOR COLOR IMAGE DATABASE , 2008 .

[29]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[30]  Djemel Ziou,et al.  Image Quality Metrics: PSNR vs. SSIM , 2010, 2010 20th International Conference on Pattern Recognition.

[31]  Alan C. Bovik,et al.  Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures , 2009, IEEE Signal Processing Magazine.

[32]  Nikolay N. Ponomarenko,et al.  TID2008 – A database for evaluation of full-reference visual quality assessment metrics , 2004 .

[33]  David L. Neuhoff,et al.  Structural Texture Similarity Metrics for Image Analysis and Retrieval , 2013, IEEE Transactions on Image Processing.

[34]  Martin O Leach,et al.  A complete distortion correction for MR images: II. Rectification of static-field inhomogeneities by similarity-based profile mapping , 2005, Physics in medicine and biology.

[35]  Tom Fawcett,et al.  An introduction to ROC analysis , 2006, Pattern Recognit. Lett..

[36]  D H HUBEL,et al.  RECEPTIVE FIELDS AND FUNCTIONAL ARCHITECTURE IN TWO NONSTRIATE VISUAL AREAS (18 AND 19) OF THE CAT. , 1965, Journal of neurophysiology.

[37]  Ingmar Lissner,et al.  Image-Difference Prediction: From Grayscale to Color , 2013, IEEE Transactions on Image Processing.

[38]  Edward H. Adelson,et al.  Shiftable multiscale transforms , 1992, IEEE Trans. Inf. Theory.

[39]  Zhou Wang,et al.  Spatial Pooling Strategies for Perceptual Image Quality Assessment , 2006, 2006 International Conference on Image Processing.