Detecting the presence of an inhomogeneous region in a homogeneous background: Taking advantages of the underlying geometry via manifolds

Detection of inhomogeneous regions in a homogeneous background (e.g. textures) is considered. The underlying assumption is that samples from the homogeneous background reside on an underlying manifold, while samples that intersect with the embedded object (i.e. the inhomogencous region) are 'away' from this manifold. The empirical distance from each sample (which will be specified in the paper) to the manifold is a quantity to determine the likelihood of a sample's overlapping with an embedded object. This result can consequently be integrated with the 'Significant Runs Algorithms', to predict the presence of embedded structures. A 'local projection' algorithm is designed to estimate the distances between samples and the manifold. Simulation results for features embedded in textural imageries show promises. This work can be extended to a formal theoretical framework for underlying feature detection. It is particularly suitable for textural images.