Three-dimensional intrinsic shape

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 axbitrarily affine-permutation distorted shape its intrinsic shape. This algorithm referred to as 3D BLAISER. (BLind Algorithm for Intrinsic ShapE Recovery) executes as one of its steps 3DPRA (Point-based Reorientation Algorithm). 3D PRA re-orients (blindly) rotated versions of the same object so Chat 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.