The most commonly used type of shape analysis is designed to compare shapes under the invariants of scale, translation, rotation, and in certain methods re-parameterization. These methods are not invariant to affine or projective transformations, which apply certain types of perspective distortion to the shape, skewing it in a manner that differs greatly from rigid motion and global scaling. Recent research efforts have focused on developing a framework to compare discrete point sets or pre-determined landmarks in 2-dimensional affine or projective shape spaces, but we treat shapes as fully elastic, continuous curves, allowing for a more accurate and robust shape matching procedure. The goal of this research is to properly define affine shape space and projective shape space in the context of continuous curves and formulate an elastic distance measure on each space. From these distance measures, we can then build geodesics and shape statistics in these spaces.

Each row represents an equivalence class under the action of projective transformation.