Image representation by sign information

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