We present an image coding technique based on linear superposition of basis images we call 'Manifold Pursuit'. The objective of the coding paradigm is to represent an object class, say human faces, under invariance to a desired group of transformations. In other words, we wish to use the widely applicable technique of Principle Component Analysis for dimensionality reduction of the image ensemble, yet avoid the predicament of having the objects properly aligned and scaled.

We derive a simple technique for projecting a mis-aligned 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 mis-alignment. 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.