Three-dimensional intrinsic shape

Abstract

In this paper, we define the intrinsic shape of an object in three-dimensional (3D) space as the shape invariant, to affine-permutation geometric shape distortions. We present an algorithm that blindly recovers from an arbitrarily affine-permutation distorted shape its intrinsic shape. This algorithm referred to us 3D BLAlSER (blind algorithm for intrinsic shape recovery) executes as one of its steps 3D PRA (point-based reorientation algorithm). 3D PRA reorients (blindly) rotated versions of the same object so that they become exactly aligned. 3D PRA extends 2D PRA to 3D space, but is much more complicated due to the multiple axes of rotation and the associated fold numbers. We describe the algorithms of 3D BLAISER and 3D PRA in detail.