Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multidimensional signal representation by zero crossings and algebraic study
SIAM Journal on Applied Mathematics
On Photometric Issues in 3D Visual Recognition from aSingle 2D Image
International Journal of Computer Vision
Image reconstruction from multiscale critical points
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
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Image representation by sign data in its most general context is considered for the case when f is a two-dimensional signal. The authors study conditions under which f is determined by its sign or, in other words, by its quantization to 1 bit of information. This study is carried out in two different directions. First, theoretical results are presented that set an algebraic condition under which real zero-crossings uniquely specify a band-limited image. An interesting paradigm arising in theoretical computer vision is then posed: are the zero-crossing of f convolved with a Laplacian-of-a-Gaussian at a single channel enough for unambiguously representing f? Second, the problem of the completeness of the representation when the position of the zero-crossings is known only approximately is addressed. It is shown that when sign(f) is sampled, significant ambiguities are introduced in the representation. Experimental results are presented which were obtained from an iterative algorithm devised to reconstruct real images from multiscale sign information.