3DDIR: The distance interior ratio of volumetric models for object recognition

We extend a novel 2D shape descriptor called Distance Interior Ratio (DIR) [4] to describe a 3D shape represented by a volumetric model, called 3DDIR. The 3DDIR is defined as follow: Given a segment ab between two points a and b on the surface of an object O, the DIR of ab is the ratio of the total length of its fragments O ∩ ab to the length |ab|. To find the fragments O ∩ ab, we apply a simple ray triangle intersection to analyze the location of ab. The experimental result shows that the DIR descriptor perform 13% better than D2 descriptor when comparing using the first match object of each query.