Digital surface analysis: A completely new approach using differential geometry

Abstract

After more than a decade of research and development our Eureka Moment is presented discussing a new differential geometry solution applied to the problem of digital surface analysis. The solution applies a completely different approach in mathematics without the use of existing techniques or algorithms. The process entails the calculation of a complete set of morphometric properties for the surface as it is defined by Differential Geometry. All processing of the data is automated, fast and accurately locates objects within the surface without the introduction of high frequency artefacts commonly associated with existing approaches. A number of objective evaluation methods are demonstrated offering comparative analysis with other published technologies on known mathematical models (with noise). Real data examples are provided showing the application of this technology on the analysis of data surfaces from seismic and potential fields surveys The queryable database of accurate and high quality elements becomes and essential aspect to highly simplify and speed up the data mining process. While this new approach and philosophy is demonstrated here on specific types of surface data, it has application to problems related to the analysis of any digital signals, images, surfaces and volumes.