William Q. Sumner

Algebraic relational approach to conflating images

An approach to conflation/registration of images that does not depend on identifying common points is being developed. It uses the method of algebraic invariants to provide a common set of coordinates to images using continuous chains of line segments formally described as polylines. It is shown the invariant algebraic properties of the polylines provide sufficient information to automate conflation. When there are discrepancies between the image data sets, robust measures of the possibility and quality of match (measures of correctness) are necessary. Decision making and the usability of the resulting conflation depends on such quality control measures. These measures may also be used to mitigate the effects of sensor and observational artifacts. This paper describes the theory of algebraic invariants and presents a conflation/registration method and measures of correctness of feature matching.

Matching image feature structures using shoulder analysis method

The problems of imagery registration, conflation, fusion and search require sophisticated and robust methods. An algebraic approach is a promising new option for developing such methods. It is based on algebraic analysis of features represented as polylines. The problem of choosing points when attempting to prepare a linear feature for comparison with other linear features is a significant challenge when orientation and scale is unknown. Previously we developed an invariant method known as Binary Structural Division (BSD). It is shown to be effective in comparing feature structure for specific cases. In cases where a bias of structure variability exists however, this method performs less well. A new method of Shoulder Analysis (SA) has been found which enhances point selection, and improves the BSD method. This paper describes the use of shoulder values, which compares the actual distance traveled along a feature to the linear distance from the start to finish of the segment. We show that shoulder values can be utilized within the BSD method, and lead to improved point selection in many cases. This improvement allows images of unknown scale and orientation to be correlated more effectively.

Image conflation and change detection using area ratios

The problem of imagery registration/conflation and change detection requires sophisticated and robust methods to produce better image fusion, target recognition, and tracking. Ideally these methods should be invariant to arbitrary image affine transformations. A new abstract algebraic structural invariant approach with area ratios can be used to identify corresponding features in two images and use them for registration/conflation. Area ratios of specific features do not change when an image is rescaled or skewed by an arbitrary affine transformation. Variations in area ratios can also be used to identify features that have moved and to provide measures of image registration/conflation quality. Under more general transformations, area ratios are not preserved exactly, but in practice can often still be effectively used. The theory of area ratios is described and three examples of registration/conflation and change detection are described.