*Submitted Paper*

**Inserted:** 27 jan 2009

**Year:** 2009

**Abstract:**

In this paper we are concerned with labelled apparent contours, namely with apparent contours of generic orthogonal projections of embedded surfaces in $\R^3$, endowed with a suitable depth information. We show that there exists a finite set of elementary moves (i.e. local topological changes) on labelled apparent contours such that the following theorem holds: two generic embeddings of a closed surface $\referencemanifold$ in $\R^3$ are isotopic if and only if their apparent contours can be connected using only smooth isotopies and a finite sequence of moves.

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