The necessary and sufficient condition and the efficient algorithms for gradually varied fill (Q749234)

Filling is an important part in pattern recognition and computer vision. In the discrete plane (grid of plane) \(\Sigma_ 2\), fill means ``determination of the region D enclosed by the simple closed curve J which is given beforehand''. In other words, if the valuation of the points on the contour J is 1, we want to do a valuation for \(\Sigma_ 2\) to make the valuation of a point p be 1 iff p belongs to D. But in reality, values of the contour J are variable. In most cases, values of the contour J are varying gradually. That is to say, not only the region D should be determined but also the value of each point in D should be determined and such values should be proved to be gradually varied. In the present note, only the second part will be examined. As for the first part, it may be seen [\textit{T. Pavlidis}, Algorithms for graphics and image processing (1982; Zbl 0482.68087)].