Brownian Images: A Generic Background Model

The local structure of a suitably differentiable function can be described through it’s truncated Taylor series. Gaussian scale space theory is a sensible framework for calculating image derivatives or the coefficients of the Taylor series up to any order using the corresponding derivatives of the Gaussian kernel. Zero-crossings of invariant combinations of such regularised derivatives have successfully been used as feature detectors. Recent work shows that feature detection can be stated as a simple problem of classification into the feature types of interest (edges, blobs, etc.). The information used in the classification is the mapping of Taylor series coefficients, i.e. image derivatives, into jet space. The conjecture is that features form classes or clusters in jet space. We introduce the classification framework and present feature detection results based on empirical edge and blob models. These models are augmented with a theoretical parametric model of a background feature type, namely the Brownian image model. The background feature type is not to be considered as the class of all non-modelled feature types, but as a new feature type in itself. The quality of the Brownian image background model is further investigated. The background model leads to classification of images into areas which are plausible featureless background areas. From an intuitive point of view the image structure is more complex in areas classified as features as opposed to the simpler background region. We verify this using a reconstruction scheme with spatially uniform constraints and a simple Gaussian assumption of prior pixel distributions. We are, however, also able to show that reconstructions using a Brownian prior results in a significant gain in reconstruction quality for the Brownian like background areas.