On fingerprint theorems

Fingerprint theorems, i.e. under what conditions the primal sketch can determine the image uniquely, are discussed. The weakness of A.L. Yuille and T. Poggio's fingerprint theorem (1986) is pointed out and two novel 1-D fingerprint theorems are presented. Then a practical algorithm based on one of these theorems is given for reconstructing the image from its primal sketch. From the given examples, it is shown that the fingerprint theorems are a substantial improvement over Yuille and Poggio's conjecture that Gaussian function is the only filter which can be used as the basis of a fingerprint theorem. The 1-D fingerprint theorems are generalized to 2-D ones.<<ETX>>

[1]  Alan L. Yuille,et al.  Scaling Theorems for Zero Crossings , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Andrew P. Witkin,et al.  Uniqueness of the Gaussian Kernel for Scale-Space Filtering , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[4]  T. Poggio,et al.  Fingerprints theorems for zero crossings , 1985 .

[5]  Tomaso A. Poggio,et al.  On Edge Detection , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[7]  Andrew P. Witkin,et al.  Scale-space filtering: A new approach to multi-scale description , 1984, ICASSP.