Method for determining multi-dimensional topology

• US 6,516,277 B2
• Filed: 02/04/2002
• Issued: 02/04/2003
• Est. Priority Date: 05/30/1997
• Status: Expired due to Fees

• Current Assignee: Kenneth E. Edgecombe
• Original Assignee: Queen's University At Kingston
• Inventors: Edgecombe, Kenneth E., Ableson, Alan D.
• Primary Examiner(s): Hoff, Marc S.
• Assistant Examiner(s): Tsai, Carol S. W.
• Application Number:
  US10/061,257
• Publication Number:
  US 20020111761A1
• Time in Patent Office: 365 Days
• Field of Search: 702/27, 702/21, 702/28, 702/32, 702/179, 702/180, 703/1, 703/7, 703/11, 703/12, 703/2
• US Class Current: 702/27
• CPC Class Codes: G16B 15/00 ICT specially adapted for analysing two-dimensional or three-dimensional molecular structures, e.g. structural or functional relations or structure alignment
• CPC Class Codes: G16B 15/20 Protein or domain folding
• CPC Class Codes: G16C 20/30 Prediction of properties of chemical compounds, compositions or mixtures

Abstract

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.

Claims

1. A method of determining the multi-dimensional topology of a system within a space from a set of relative values for scalar properties of the space, each value for a given point within the space, the method comprising the steps of:

a) interpolating a set of functions to generate continuous relative values for the scalar properties;

b) identifying critical points of the continuous relative values by using an eigenvector following method;

c) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

d) generating a representation of the topology according to the associated critical points,

wherein the system is the flow of a fluid over a surface.

2. A method of determining the multi-dimensional topology of a system within a space from a set of relative values for scalar properties of the space, each value for a given point within the space, the method comprising the steps of:

a) interpolating a set of functions to generate continuous relative values for the scalar properties;

b) identifying critical points of the continuous relative values by using an eigenvector following method;

c) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

d) generating a representation of the topology according to the associated critical points,

wherein the system is the reaction and/or folding of a protein or protein complex.

3. A method of determining the multi-dimensional topology of a system within a space from a set of relative values for scalar properties of the space, each value for a given point within the space, the method comprising the steps of:

a) interpolating a set of functions to generate continuous relative values for the scalar properties;

b) identifying critical points of the continuous relative values by using an eigenvector following method;

c) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

d) generating a representation of the topology according to the associated critical points,

wherein the system is an edge portion of a graphical image.

4. A method of determining the multi-dimensional topology of a system within a space from a set of relative values for scalar properties of the space, each value for a given point within the space, the method comprising the steps of:

a) interpolating a set of functions to generate continuous relative values for the scalar properties;

b) identifying critical points of the continuous relative values by using an eigenvector following method;

c) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

d) generating a representation of the topology according to the associated critical points,

wherein the system is one or more extremal points within a scalar field.

5. A method of determining the multi-dimensional topology of a system within a space from a set of relative values for scalar properties of the space, each value for a given point within the space, the method comprising the steps of:

a) interpolating a set of functions to generate continuous relative values for the scalar properties;

b) identifying critical points of the continuous relative values by using an eigenvector following method;

c) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

d) generating a representation of the topology according to the associated critical points,

wherein the system is a trend or energy surface within a set of data.

6. A method of determining the multi-dimensional topology of a system within a space, having continuous relative values of scalar properties for the space generated from a set of functions interpolating a set of acquired relative values of the scalar properties, each value for a given location within the space, the method comprising the steps of:

a) identifying critical points of the continuous relative values by using an eigenvector following method;

b) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

c) generating a representation of the topology according to the associated critical points,

wherein the system is the flow of a fluid over a surface.

7. A method of determining the multi-dimensional topology of a system within a space, having continuous relative values of scalar properties for the space generated from a set of functions interpolating a set of acquired relative values of the scalar properties, each value for a given location within the space, the method comprising the steps of:

a) identifying critical points of the continuous relative values by using an eigenvector following method;

b) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

c) generating a representation of the topology according to the associated critical points,

wherein the system is the reaction and/or folding of a protein or protein complex.

8. A method of determining the multi-dimensional topology of a system within a space, having continuous relative values of scalar properties for the space generated from a set of functions interpolating a set of acquired relative values of the scalar properties, each value for a given location within the space, the method comprising the steps of:

a) identifying critical points of the continuous relative values by using an eigenvector following method;

b) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

c) generating a representation of the topology according to the associated critical points,

wherein the system is an edge portion of a graphical image.

9. A method of determining the multi-dimensional topology of a system within a space, having continuous relative values of scalar properties for the space generated from a set of functions interpolating a set of acquired relative values of the scalar properties, each value for a given location within the space, the method comprising the steps of:

a) identifying critical points of the continuous relative values by using an eigenvector following method;

b) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

c) generating a representation of the topology according to the associated critical points,

wherein the system is one or more extremal points within a scalar field.

10. A method of determining the multi-dimensional topology of a system within a space, having continuous relative values of scalar properties for the space generated from a set of functions interpolating a set of acquired relative values of the scalar properties, each value for a given location within the space, the method comprising the steps of:

a) identifying critical points of the continuous relative values by using an eigenvector following method;

b) associating critical points with one another by following a gradient path of the continuous relative values between the critical points; and

c) generating a representation of the topology according to the associated critical points,

wherein the system is a trend or energy surface within a set of data.