Building Better Formlet Codes for Planar Shape

Abstract

The GRID/formlet representation of planar shape has a number of nice properties [4], [10], [3], but there are also limitations: it is slow to converge for shapes with elongated parts, and it can be sensitive to parameterization as well as grossly ill-conditioned. Here we describe a number of innovations on the GRID/formlet model that address these problems: 1) By generalizing the formlet basis to include oriented deformations we achieve faster convergence for elongated parts. 2) By introducing a modest regularizing term that penalizes the total energy of each deformation we limit redundancy in formlet parameters and improve identifiability of the model. 3) By applying a recent contour remapping method [9] we eliminate problems due to drift of the model parameterization during matching pursuit. These innovations are shown to both speed convergence and to improve performance on a shape completion task.