Recovering a Polygon from Noisy Data

Many classes of scenes contain objects that are (approximately) two-dimensional polygons-for example, buildings in an aerial photograph, or flat mechanical parts on a tabletop. This paper deals with the problem of recovering (an approximation to) an unknown polygon from noisy digital data, obtained by digitizing either an image of the (solid) polygon or a sequence of points on its boundary. Note that our goal is to obtain an approximation to the original polygon, not an approximation to the noisy data. We derive constraints on the polygon and on the noisy digitization process under which (approximate) recovery of the polygon is possible. We show that if these constraints are satisfied, the desired approximation can be recovered by selecting a subset of the data points as vertices. We define a vertex elimination process that accomplishes this recovery and give examples of successful recovery of both synthetic and real noisy polygons.