This invention relates to methods and apparatus for determining the multi-dimensional topology of a substance (system) within a volume (space). A method according to a preferred embodiment of the invention comprises the steps of: acquiring a set of relative values for the density (scalar properties) of the volume, each value for a given location (point) within the volume; interpolating a set of functions to generate a continuous relative density for the volume; identifying critical points of the continuous relative density by using an eigenvector following method; and associating critical points with one another by following a gradient path of the continuous relative density between the critical points, The method is applicable to a wide range of data relating to fields such as crystallography, fluid dynamics, edge detection, and financial markets, to determine the topology of structures contained therein.
| Publication number | US6345235 B1 |
| Publication type | Grant |
| Application number | US 09/086,593 |
| Publication date | Feb 5, 2002 |
| Filing date | May 29, 1998 |
| Priority date | May 30, 1997 |
| Fee status | Lapsed |
| Also published as | CA2239146A1, CA2239146C, US6516277, US20020111761 |
| Inventors | Kenneth E. Edgecombe, Alan D. Ableson |
| Original Assignee | Queen’s University At Kingston |