Manifold Pursuit (MP) extends Principal Component Analysis to be invariant to a desired group of image-plane transformations of an ensemble of un-aligned images.

We derive a simple technique for projecting a misaligned target image onto the linear subspace defined by the superpositions of a collection of model images. We show that it is possible to generate a fixed projection matrix which would separate the projected image into the aligned projected target and a residual image which accounts for the misalignment. An iterative procedure is then introduced for eliminating the residual image and leaving the correct aligned projected target image.

Taken together, we demonstrate a simple and effective technique for obtaining invariance to image-plane transformations within a linear dimensionality reduction approach.