An automatic method of measuring foot girths for custom footwear using local RBF implicit surfaces

Scanned 3D point cloud data of a foot and a last are used in the manufacture of custom footwear. But, automatic and accurate measurement of dimensions, especially girths, is an issue of concern to many designers and footwear developers. Existing methods for measuring girths are primarily based on points or generated triangles, but their accuracy is heavily dependent on the density of the point cloud data. In this paper we present the use of the Radial Basis Function (RBF) surface modeling technique for measuring girths as it has the advantage of being able to operate on unorganized 3D points, allowing the surface that is produced to go through every scanned point, while repairing incomplete meshes. To overcome the high computational expense of the RBF method, local surface recovery, octree division and combination, inverse power method and improved Cholesky factorization are also used. The girth measurements obtained from these approaches are compared against those using purely scan points, and other methods. Experimental results demonstrate that the local RBF implicit surface can provide more stable and accurate measurements, using relatively less time, proving its value in custom footwear manufacture.