Separating desired image and signal invariant components from extraneous variations

Images and signals can be characterized by representations invariant to time shifts, spatial shifts, frequency shifts, and scale changes as the situation dictates. Advances in time-frequency analysis and scale transform techniques have made this possible. The next step is to distinguish between invariant forms representing different classes of image or signal. Unfortunately, additional factors such as noise contamination and `style' differences complicate this. A ready example is found in text, where letters and words may vary in size and position within the image segment being examined. Examples of complicating variations include font used, corruption during fax transmission, and printer characteristics. The solution advanced in this paper is to cast the desired invariants into separate subspaces for each extraneous factor or group of factors. The first goal is to have minimal overlap between these subspaces and the second goal is to be able to identify each subspace accurately. Concepts borrowed from high-resolution spectral analysis, but adapted uniquely to this problem have been found to be useful in this context. Once the pertinent subspace is identified, the recognition of a particular invariant form within this subspace is relatively simple using well-known singular value decomposition techniques.