Abstract

In this paper, we study a family of analytical probability models for images within the spectral representation framework. First the input image is decomposed using a bank of filters, and probability models are imposed on the filter outputs (or spectral components). A two-parameter analytical form, called a Bessel K form, derived based on a generator model, is used to model the marginal probabilities of these spectral components. The Bessel K parameters can be estimated eficiently from the filtered images and extensive simulations using video, infrared, and range images have demonstrated Bessel K form’s fit to the observed histograms. The efiectiveness of Bessel K forms is also demonstrated through texture modeling and synthesis. In contrast to numeric-based dimension reduction representations, which are derived purely based on numerical methods, the Bessel K representations are derived based on ob ject representations and this enables us to establish relationships between the Bessel parameters and certain characteristics of the imaged ob jects. We have derived a pseudo- metric on the image space to quantify image similarities/difierences using an analytical expression for L2 -metric on the set of Bessel K forms. We have applied the Bessel K representation to texture modeling and synthesis, clutter classification, pruning of hypotheses for ob ject recognition, and ob ject classification. Results show that Bessel K representation captures important image features, suggesting its role in building e?cient image understanding paradigms and systems.