Efficient contour extraction from noisy digitized images

Abstract

The successful application of the ZJ algorithm to a problem radically different from the decoding of convolutional codes seems to suggest that sequential decoding algorithms may belong to a broader class of optimization algorithms. This conjecture has been made fact by showing that sequential decoding algorithms indeed form a special class of branch and bound algorithms. The new insights provided by this mathematical programming formulation of sequential decoding strategies are then presented.

A new approach is presented here, where the contour extraction problem is posed as a heuristic tree search problem. More specifically, the Zigangirov-Jelinek (ZJ) sequential decoding algorithm is adapted from the field of communications to perform the contour extraction task. Extensive results demonstrate the reliability, robustness and flexibility of this approach, in the sense that a wide variety of contours can be extracted by simple modification of a few key parameters.

The contour extraction problem arises quite often in the field of digital image processing and involves the determination of the boundaries of certain objects or regions in a given image. While many solutions to this problem have been suggested in the literature with claims of flexibility and reliability, the fact remains that most approaches taken so far are either restricted in their application or require appreciable changes before they can be applied to different problems.

Finally, it is of some interest to estimate the number of computations required by the ZJ algorithm in a given application. In an effort to resolve this difficult problem, the ZJ algorithm is modelled as an age-dependent branching process which provides expressions for the quit probability associated with ZJ decoding as well as a nonlinear difference equation for the probability generating function of the number of computations. Morevoer, it is shown that the Fano algorithm can also be modelled as an age-dependent branching process. The model is then extended in order to handle communication over fading channels.