Covariant Derivatives and Vision

Abstract. We describe a new theoretical approach to Image Processing and Vision. Expressed in mathemetical terminology, in our formalism image space is a fibre bundle, and the image itself is the graph of a section on it. This mathematical model has advantages to the conventional view of the image as a function on the plane: Based on the new method we are able to do image processing of the image as viewed by the human visual system, which includes adaptation and perceptual correctness of the results. Our formalism is invariant to relighting and handles seamlessly illumination change. It also explains simultaneous contrast visual illusions, which are intrinsically related to the new covariant approach. Examples include Poisson image editing, Inpainting, gradient domain HDR compression, and others.

• Type: Conference
• Year: 2006
• Where: ECCV
• Authors: Todor Georgiev
• Keywords: Computer Vision, Contrast Visual Illusions, ECCV 2006, Formalism Image Space, Handles Seamlessly Illumination, Image Processing, Poisson Image