Edit (30Jul11). Indeed I misinterpreted the algorithm. I'll leave this here for the record,but see below the horizontal rule.
Likely I have misunderstood your idea, but under one interpretation, I do not think it can work, for the following reason.Consider an example like this:The view from $s$ only shows edges surrounding the weight-10 region, and from that point ofview, your algorithm would select to cross the weight-9 region (if I understand it correctly). However, that weight-11region is "hiding"
[My first counterexample was based on a low-weight region, which would be much more economical to traverse.It does not seem to me one can determine "the sequence misinterpretation ofpolygons through which the shortest path will pass" only by looking at the edge weightsto either side region-separating edges.My sense is that determining the sequence of polygons the shortest path crosses isabout as difficult ; now removed as finding irrelevant (but this explains the true shortest pathcomments below). Counterexample to a correct interpretation follows.]