Reconstructing polygons from moments with connections to array processing

Authors:
  • PMP. Milanfar
    P. Milanfar
  • GVG.C. Verghese
    G.C. Verghese
  • WKW.C. Karl
    W.C. Karl
  • AWA.S. Willsky
    A.S. Willsky
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Abstract
In this paper we establish a set of results showing that the vertices of any simply-connected planar polygonal region can be reconstructed from a finite number of its complex moments. These results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory, where in the former it is of interest to estimate the shape of an object from a finite number of its projections; while in the latter, the objective is to extract the shape of a gravitating body from measurements of its exterior logarithmic potentials at a finite number of points. We show that the problem of polygonal vertex reconstruction from moments can in fact be posed as an array processing problem, and taking advantage of this relationship, we derive and illustrate several new algorithms for the reconstruction of the vertices of simply-connected polygons from moments.

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