The above block diagram represents our proposed scheme for image authentication.  The candidate image to be authenticated is presented as an input and it first goes through a randomized feature extractor based on a secret key K.  We approximate geometric distortions based on the structure matching scheme in [1], [2].  Here T(∙) is an affine transformation defined as follows:

The transformation of N, feature points from the candidate image, is compared with a reference set of feature points and based on structure matching scheme, we lock onto the minimum distance between the the data points.   We use a modified Hausdorff distance used extensively in computer vision for shape matching [3], [4].  Based on the minimum distance, d_min, we make our conclusions about the image.

From extensive testing, we find that a good value of ε = 0.15 and δ = 0.20.  Results obtained on some images are shown below.

BRIDGE

   
                    Reference Image                                                             Rotation                                                            JPEG  QF = 20

HOUSE

   
                      Reference Image                                               Shearing                                                           Stirmark

TOYS

   
                      Reference Image                                        JPEG QF = 20                                                    Shearing

PEPPERS

                                     
                      Reference Image                                                        Scaling                                                                   print-scan               

CONTENT CHANGING

                   
           Reference Image                                                        Candidate Image                                            Image is tampered

                  
        Reference Image                                                    Candidate Image                                                  Image is tampered

References

[1] D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge, "Comparing images using the hausdorff distance," IEEE Trans. on Pattern Analysis and Machine Int., pp. 850-863, 1993.

[2] W.J. Rucklidge, "Locating objects using the hausdorff distance," IEEE Int. Conf. on Computer Vision, 1995

[3] M.P. Dubuisson and A.K. Jain, "A modified Hausdorff distance for object matching," IEEE Int. Conf. Pattern Recognition, pp. 566-568, Jerusalem, Israel, 1994.

[4] V. Monga, D. Vats and B. L. Evans, "Image Authentication Under Geometric Attacks Via Structure Matching", IEEE Int. Conf. on Multimedia and Expo, 2005 submitted