A stabilized zero-crossing representation in the wavelet transform domain and its extension to image representation for early vision

We present a new stabilized zero-crossing representation with a salient feature that the signal reconstruction problem reduces to a typical minimum-norm optimization problem, the solution of which is formulated as a linear simultaneous equation, and develop an iterative algorithm for signal reconstruction. Moreover, we extend them to the two-dimensional case. With the extended two-dimensional reconstruction algorithm we can almost perfectly reconstruct an original image from the stabilized two-dimensional zero-crossing representation, and after some dozens of iterations the algorithm provides a reconstructed image with subjectively high picture quality. Furthermore, we introduce a threshold operation based on edge intensity to reduce the amount of information in the stabilized zero-crossing representation, and experimentally demonstrate that the threshold operation works well.