Image analysis method for overcoming source distortion using algebraic invariant methods

For multispectral sensory and geospatial data to be properly integrated they must be co-registered with known data which is a difficult and time consuming process. A persistent problem with new unregistered data is geometric image distortion. This paper deals with distortion due to disproportional transformation. Images can be disproportionally transformed because of a specific angle of data acquisition, sensor and lens distortions, atmospheric effects, and others factors. This research is focused on developing a method to overcome such distortion effects and to provide computational tools to automate a large portion of the process without relying on the sensor geometry and model that may not be known. Current methods of image analysis and feature recognition rely heavily on geometric shapes and/or the topological nature of data contained within the image. In addition to geometric shapes and topological data, features and images can also be compared algebraically. Algebraic structures have been defined with which comparisons can be made between geometric components such as relative angles, and lengths. Invariant point placement and feature comparison methods are developed here that can overcome the effect of distortion and disproportional scaling. Deriving a method that is invariant to disproportional scaling that is based on an algebraic invariant method is a new approach to solving this problem and represents a new mathematical language for the processing of image data.