Image Representation Via a Finite Radon Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A Fast Number Theoretic Finite Radon Transform
DICTA '09 Proceedings of the 2009 Digital Image Computing: Techniques and Applications
An exact, non-iterative Mojette inversion technique utilising ghosts
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
On Constructing Minimal Ghosts
DICTA '10 Proceedings of the 2010 International Conference on Digital Image Computing: Techniques and Applications
Exact, scaled image rotations in finite Radon transform space
Pattern Recognition Letters
Growth of discrete projection ghosts created by iteration
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Growth of discrete projection ghosts created by iteration
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
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A ghost image is an array of signed pixel values so positioned as to create zero-sums in all discrete projections taken across that image for a pre-defined set of angles. The discrete projection scheme used here is the finite Radon transform. Minimal ghosts employ just 2N pixels to generate zero-sum projections at N projection angles. We describe efficient methods to construct Nth order minimal ghost images on primesized 2D arrays. Ghost images or switching components are important in discrete image reconstruction. Ghosts usually grow larger as they are constrained by more projection angles. When ghosts become too large to be added to an image, image reconstruction from projections becomes unique and exact. Ghosts can be used to synthesize image/anti-image data that will also exhibit zero-sum projections at N pre-defined angles. We examine the remarkable symmetry, cross- and auto-correlation properties of minimal ghosts. The geometric properties of minimal ghost images may make them suitable to embed in data as watermarks.