Patent US5920319A successfully refreshed from Google Patents.
US5920319A
Expired / Lapsed
US
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Automatic analysis in virtual endoscopy
Assignee: Wake Forest Baptist Medical Center
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Filing: 1997-02-25
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Granted: 1999-07-06
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Expires: 2017-02-25
Abstract
Abstract A computer system and a computer-implemented method are provided for interactively displaying a three-dimensional rendering of a structure having a lumen and for indicating regions of abnormal wall structure. A three-dimensional volume of data is formed from a series of two-dimensional images representing at least one physical property associated with the three-dimensional structure. An isosurface of a selected region of interest is created by a computer from the volume of data based on a selected value or values of a physical property representing the selected region of interest. A wireframe model of the isosurface is generated by the computer wherein the wireframe model includes a plurality of vertices. The vertices of the wireframe model are then grouped into populations of contiguous vertices having a characteristic indicating abnormal wall structure by the computer. The wireframe model is then rendered by the computer in an interactive three-dimensional display to indicate the populations of abnormal wall structure.
Inventors
- 👤 David J. Vining
- 👤 Gordon W. Hunt
- 👤 David K. Ahn
- 👤 David R. Stelts
- 👤 Yaorong Ge
- 👤 Paul F. Hemler
- 👤 Tiffany W. Salido
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-04 18:26
CPC Classifications
G; G06; G06T; G06T7/00; G06T7/0002; G06T7/0012; A; A61; A61B; A61B5/00; A61B5/103; A61B5/107; A61B5/1076; G06T15/00; G06T15/08; G06T17/00; G06T17/20; G06T7/10; G06T7/11; G06T7/155; G09; G09B; G09B23/00; G09B23/28; G09B23/285; G06T2207/00; G06T2207/10; G06T2207/10072; G06T2207/10081; G06T2207/20; G06T2207/20004; G06T2207/20012; G06T2207/30; G06T2207/30004; G06T2207/30028; G06T2207/30032; G06T2207/30061; G06T2207/30064; Y; Y02; Y02A; Y02A90/00; Y02A90/10; Y10; Y10S; Y10S128/00; Y10S128/92
Claims Analysis
Total Claims: 65
Claim 1
Independent Claim
129 words
A computer-implemented method for interactively displaying a three-dimensional rendering of a structure having a lumen and indicating regions of abnormal wall thickness comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with the three-dimensional structure; b. creating an isosurface of a selected region of interest from the three-dimensional volume of data based on a selected value of the physical property representing the selected region of interest; c. generating a wireframe model of the isosurface, the wireframe model comprising a plurality of vertices; d. grouping the vertices of the wireframe model into populations having a characteristic indicating abnormal wall structure; and e. rendering the wireframe model in an interactive three-dimensional display to indicate the populations.
Claim 2
Dependent Claim
129 words
A computer-implemented method for interactively displaying a three-dimensional rendering of a structure having a lumen and indicating regions of abnormal wall thickness comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with the three-dimensional structure; b. creating an isosurface of a selected region of interest from the three-dimensional volume of data based on a selected value of the physical property representing the selected region of interest; c. generating a wireframe model of the isosurface, the wireframe model comprising a plurality of vertices; d. grouping the vertices of the wireframe model into populations having a characteristic indicating abnormal wall structure; and e. rendering the wireframe model in an interactive three-dimensional display to indicate the populations.
Claim 3
Dependent Claim
71 words
The method as recited in claim 1 wherein the step of grouping the vertices into populations comprises the steps of: a. determining a normal vector for each vertex position; b. determining a wall thickness value associated with each normal vector for each vertex; c. determining a connectivity matrix of contiguous vertices for each vertex; and d. grouping contiguous vertices having a characteristic indicating abnormal thicknesses into separate populations of abnormal thickness.
Claim 4
Dependent Claim
28 words
The method as recited in claim 2 wherein the step of determining the connectivity matrix comprises the step of re-ordering the connectivity matrix using local geometry connectivity information.
Claim 5
Dependent Claim
20 words
The method as recited in claim 1 further comprising the step of analyzing each population according to selected shape characteristics.
Claim 6
Dependent Claim
36 words
The method as recited in claim 4 wherein the step of analyzing each population according to shape characteristics comprises the step of determining a convexity value for each population representing an amount and direction of curvature.
Claim 7
Dependent Claim
27 words
The method as recited in claim 4 wherein the step of analyzing each population according to shape comprises the step of determining a curvature for each population.
Claim 8
Independent Claim
125 words
A method for interactively displaying a three-dimensional rendering of a structure having a lumen comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with the three-dimensional structure; b. segmenting a selected region of interest from the three-dimensional volume of data based on a threshold value of the physical property, wherein the threshold value is adaptively adjusted in the region of interest; c. creating an isosurface of a selected region of interest from the three-dimensional volume of data based on selected values of the physical property representing the selected region of interest; d. generating a wireframe model of the isosurface; and e. rendering the wireframe model in an interactive three-dimensional display.
Claim 9
Independent Claim
125 words
A method for interactively displaying a three-dimensional rendering of a structure having a lumen comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with the three-dimensional structure; b. segmenting a selected region of interest from the three-dimensional volume of data based on a threshold value of the physical property, wherein the threshold value is adaptively adjusted in the region of interest; c. creating an isosurface of a selected region of interest from the three-dimensional volume of data based on selected values of the physical property representing the selected region of interest; d. generating a wireframe model of the isosurface; and e. rendering the wireframe model in an interactive three-dimensional display.
Claim 10
Independent Claim
137 words
A system for interactively displaying a three-dimensional rendering of a structure having a lumen and indicating regions of abnormal wall thickness comprising: a. volume formation means for forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with the three-dimensional structure; b. isosurface creation means for creating an isosurface of a selected region of interest from the three-dimensional volume of data based on a selected value of the physical property representing the selected region of interest; c. wireframe generation means for generating a wireframe model of the isosurface, the wireframe model comprising a plurality of vertices; d. vertex grouping means for grouping the vertices of the wireframe model into populations having abnormal wall structure; and e. rendering means for rendering the wireframe model in an interactive three-dimensional display.
Claim 11
Independent Claim
137 words
A system for interactively displaying a three-dimensional rendering of a structure having a lumen and indicating regions of abnormal wall thickness comprising: a. volume formation means for forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with the three-dimensional structure; b. isosurface creation means for creating an isosurface of a selected region of interest from the three-dimensional volume of data based on a selected value of the physical property representing the selected region of interest; c. wireframe generation means for generating a wireframe model of the isosurface, the wireframe model comprising a plurality of vertices; d. vertex grouping means for grouping the vertices of the wireframe model into populations having abnormal wall structure; and e. rendering means for rendering the wireframe model in an interactive three-dimensional display.
Claim 12
Independent Claim
149 words
A system for interactively displaying a three-dimensional rendering of a structure having a lumen and indicating regions of abnormal wall thickness comprising: a. formation means for forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with the three-dimensional structure; b. segmentation means for segmenting a selected region of interest from the three-dimensional volume of data based on a threshold value of the physical property, wherein the threshold value is adaptively adjusted; c. isosurface creation means for creating an isosurface of a selected region of interest from the three-dimensional volume of data based on selected values of the physical property representing the selected region of interest; d. wireframe generation means for generating a wireframe model of the isosurface, the wireframe model comprising a plurality of vertices; and e. rendering means for rendering the wireframe model in an interactive three-dimensional display.
Claim 13
Independent Claim
149 words
A system for interactively displaying a three-dimensional rendering of a structure having a lumen and indicating regions of abnormal wall thickness comprising: a. formation means for forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with the three-dimensional structure; b. segmentation means for segmenting a selected region of interest from the three-dimensional volume of data based on a threshold value of the physical property, wherein the threshold value is adaptively adjusted; c. isosurface creation means for creating an isosurface of a selected region of interest from the three-dimensional volume of data based on selected values of the physical property representing the selected region of interest; d. wireframe generation means for generating a wireframe model of the isosurface, the wireframe model comprising a plurality of vertices; and e. rendering means for rendering the wireframe model in an interactive three-dimensional display.
Claim 14
Dependent Claim
36 words
The method as recited in claim 1 wherein the rendering step comprises splitting the structure open in lengthwise sections and displaying the split open structure so that inner surfaces of the split open structure are visible.
Claim 15
Dependent Claim
36 words
The method as recited in claim 7 wherein the rendering step comprises splitting the structure open in lengthwise sections and displaying the split open structure so that inner surfaces of the split open structure are visible.
Claim 16
Dependent Claim
38 words
The system as recited in claim 8 wherein the rendering means comprises means for splitting the structure open in lengthwise sections and displaying the split open structure so that inner surfaces of the split open structure are visible.
Claim 17
Dependent Claim
38 words
The system as recited in claim 9 wherein the rendering means comprises means for splitting the structure open in lengthwise sections and displaying the split open structure so that inner surfaces of the split open structure are visible.
Claim 18
Dependent Claim
28 words
The method as recited in claim 1 wherein the rendering step comprises simulating movement along a line which passes along the center of the lumen of the structure.
Claim 19
Dependent Claim
28 words
The method as recited in claim 7 wherein the rendering step comprises simulating movement along a line which passes along the center of the lumen of the structure.
Claim 20
Dependent Claim
30 words
The system as recited in claim 8 wherein the rendering means comprises means for simulating movement along a line which passes along the center of the lumen of the structure.
Claim 21
Dependent Claim
30 words
The system as recited in claim 9 wherein the rendering means comprises means for simulating movement along a line which passes along the center of the lumen of the structure.
Claim 22
Dependent Claim
34 words
The method as recited in claim 1 comprising the step of displaying a volume-rendered image of the interactive three-dimensional display centered on a point located within a surface-rendered image of the interactive three-dimensional display.
Claim 23
Dependent Claim
40 words
The method as recited in claim 18 wherein the step of displaying the interactive three-dimensional display comprises the step of displaying at least one planar image through a second point located within the surface-rendered image of the interactive three-dimensional display.
Claim 24
Dependent Claim
34 words
The method as recited in claim 7 comprising the step of displaying a volume-rendered image of the interactive three-dimensional display centered on a point located within a surface-rendered image of the interactive three-dimensional display.
Claim 25
Dependent Claim
40 words
The method as recited in claim 20 wherein the step of displaying the interactive three-dimensional display comprises the step of displaying at least one planar image through a second point located within the surface-rendered image of the interactive three-dimensional display.
Claim 26
Dependent Claim
33 words
The system as recited in claim 8 comprising means for displaying a volume-rendered image of the interactive three-dimensional display centered on a point located within a surface-rendered image of the interactive three-dimensional display.
Claim 27
Dependent Claim
34 words
The system as recited in claim 22 wherein the display means comprises means for displaying at least one planar image through a second point located within the surface-rendered image of the interactive three-dimensional display.
Claim 28
Dependent Claim
33 words
The system as recited in claim 9 comprising means for displaying a volume-rendered image of the interactive three-dimensional display centered on a point located within a surface-rendered image of the interactive three-dimensional display.
Claim 29
Dependent Claim
34 words
The system as recited in claim 24 wherein the display means comprises means for displaying at least one planar image through a second point located within the surface-rendered image of the interactive three-dimensional display.
Claim 30
Independent Claim
101 words
A method for interactively displaying three dimensional structures comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with a three dimensional body; b. segmenting a selected region of interest from the volume of data based on selected values of the physical property representing the selected region of interest; c. rendering the segmented region of interest as a surface rendered image in an interactive three-dimensional display, therein producing a virtual three-dimensional environment; and d. displaying a volume-rendered image of the interactive three-dimensional display adjoining the surface-rendered image.
Claim 31
Independent Claim
101 words
A method for interactively displaying three dimensional structures comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with a three dimensional body; b. segmenting a selected region of interest from the volume of data based on selected values of the physical property representing the selected region of interest; c. rendering the segmented region of interest as a surface rendered image in an interactive three-dimensional display, therein producing a virtual three-dimensional environment; and d. displaying a volume-rendered image of the interactive three-dimensional display adjoining the surface-rendered image.
Claim 32
Dependent Claim
35 words
The method as recited in claim 26 wherein the step of displaying the interactive three-dimensional display comprises the step of displaying at least one planar image through the surface-rendered image of the interactive three-dimensional display.
Claim 33
Independent Claim
95 words
A method for interactively displaying three dimensional structures comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with a three dimensional body; b. segmenting a selected region of interest from the volume of data based on selected values of the physical property representing the selected region of interest; c. determining an arbitrarily oriented cross-sectional area of the selected region of interest; and d. rendering the segmented region of interest in an interactive three-dimensional display, therein producing a virtual three-dimensional environment.
Claim 34
Independent Claim
95 words
A method for interactively displaying three dimensional structures comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with a three dimensional body; b. segmenting a selected region of interest from the volume of data based on selected values of the physical property representing the selected region of interest; c. determining an arbitrarily oriented cross-sectional area of the selected region of interest; and d. rendering the segmented region of interest in an interactive three-dimensional display, therein producing a virtual three-dimensional environment.
Claim 35
Independent Claim
122 words
A method for interactively displaying three dimensional structures comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with a three dimensional body; b. segmenting a selected region of interest from the volume of data based on selected values of the physical property representing the selected region of interest; c. generating a wireframe model of the segmented region of interest, wherein the wireframe model comprises a plurality of vertices and information regarding the connectivity of the plurality of vertices is provided by connectivity matrices; d. re-ordering the connectivity matrices; and e. rendering the segmented region of interest in an interactive three-dimensional display, therein producing a virtual three-dimensional environment.
Claim 36
Independent Claim
122 words
A method for interactively displaying three dimensional structures comprising the steps of: a. forming a three-dimensional volume of data from a series of two-dimensional images representing at least one physical property associated with a three dimensional body; b. segmenting a selected region of interest from the volume of data based on selected values of the physical property representing the selected region of interest; c. generating a wireframe model of the segmented region of interest, wherein the wireframe model comprises a plurality of vertices and information regarding the connectivity of the plurality of vertices is provided by connectivity matrices; d. re-ordering the connectivity matrices; and e. rendering the segmented region of interest in an interactive three-dimensional display, therein producing a virtual three-dimensional environment.
Claim 37
Dependent Claim
23 words
The method as recited in claim 29 comprising the step of determining an arbitrarily oriented cross-sectional area of the selected region of interest.
Claim 38
Independent Claim
73 words
A method for indicating regions of a three-dimensional structure having an abnormal wall characteristic comprising: a. forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure, the three-dimensional volume of data comprising a three-dimensional matrix of voxels wherein each voxel has an associated voxel value; and b. grouping the voxels, as a selected function of voxel value, into populations having a characteristic indicating abnormal wall structure.
Claim 39
Independent Claim
73 words
A method for indicating regions of a three-dimensional structure having an abnormal wall characteristic comprising: a. forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure, the three-dimensional volume of data comprising a three-dimensional matrix of voxels wherein each voxel has an associated voxel value; and b. grouping the voxels, as a selected function of voxel value, into populations having a characteristic indicating abnormal wall structure.
Claim 40
Dependent Claim
36 words
The method as recited in claim 31 wherein the step of grouping the voxels into populations comprises the step of grouping contiguous voxels having a characteristic indicating abnormal wall thickness into separate populations of abnormal thickness.
Claim 41
Independent Claim
89 words
A method for interactively displaying a three-dimensional rendering of a three-dimensional structure having a lumen comprising the steps of: a. forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure; b. segmenting a selected region of interest from the three-dimensional volume of data; c. creating a surface of the selected region of interest based on selected values of the physical property representing the selected region of interest; and d. grouping regions of the surface into populations having a characteristic indicating abnormal structure.
Claim 42
Independent Claim
89 words
A method for interactively displaying a three-dimensional rendering of a three-dimensional structure having a lumen comprising the steps of: a. forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure; b. segmenting a selected region of interest from the three-dimensional volume of data; c. creating a surface of the selected region of interest based on selected values of the physical property representing the selected region of interest; and d. grouping regions of the surface into populations having a characteristic indicating abnormal structure.
Claim 43
Dependent Claim
40 words
The method as recited in claim 33 wherein the step of grouping regions of the isosurface into populations comprises the step of grouping contiguous regions of the isosurface having a characteristic indicating abnormal thicknesses into separate populations of abnormal thickness.
Claim 44
Independent Claim
64 words
A method for indicating regions of a three-dimensional structure having an abnormal wall characteristic comprising: a. forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure; b. constructing a three-dimensional model of the three-dimensional structure from the three-dimensional volume of data; and c. grouping regions of the three-dimensional model into populations having a characteristic indicating abnormal structure.
Claim 45
Independent Claim
64 words
A method for indicating regions of a three-dimensional structure having an abnormal wall characteristic comprising: a. forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure; b. constructing a three-dimensional model of the three-dimensional structure from the three-dimensional volume of data; and c. grouping regions of the three-dimensional model into populations having a characteristic indicating abnormal structure.
Claim 46
Dependent Claim
42 words
The method as recited in claim 35 wherein the step of grouping regions of the three-dimensional model into populations comprises the step of grouping contiguous regions of the three-dimensional model having a characteristic indicating abnormal thicknesses into separate populations of abnormal thickness.
Claim 47
Independent Claim
81 words
A system for indicating regions of a three-dimensional structure having an abnormal wall characteristic comprising: a. volume formation means for forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure, the three-dimensional volume of data comprising a three-dimensional matrix of voxels wherein each voxel has an associated voxel value; and b. voxel grouping means for grouping the voxels, as a selected function of voxel value, into populations having a characteristic indicating abnormal wall structure.
Claim 48
Independent Claim
81 words
A system for indicating regions of a three-dimensional structure having an abnormal wall characteristic comprising: a. volume formation means for forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure, the three-dimensional volume of data comprising a three-dimensional matrix of voxels wherein each voxel has an associated voxel value; and b. voxel grouping means for grouping the voxels, as a selected function of voxel value, into populations having a characteristic indicating abnormal wall structure.
Claim 49
Dependent Claim
31 words
The system as recited in claim 37 wherein the voxel grouping means comprises means for grouping contiguous voxels having a characteristic indicating abnormal wall thickness into separate populations of abnormal thickness.
Claim 50
Independent Claim
101 words
A system for interactively displaying a three-dimensional rendering of a three-dimensional structure having a lumen comprising: a. formation means for forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure; b. segmentation means for segmenting a selected region of interest from the three-dimensional volume of data; c. surface creation means for creating a surface of the selected region of interest based on selected values of the physical property representing the selected region of interest; and d. surface grouping means for grouping regions of the surface into populations having a characteristic indicating abnormal wall structure.
Claim 51
Independent Claim
101 words
A system for interactively displaying a three-dimensional rendering of a three-dimensional structure having a lumen comprising: a. formation means for forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure; b. segmentation means for segmenting a selected region of interest from the three-dimensional volume of data; c. surface creation means for creating a surface of the selected region of interest based on selected values of the physical property representing the selected region of interest; and d. surface grouping means for grouping regions of the surface into populations having a characteristic indicating abnormal wall structure.
Claim 52
Dependent Claim
33 words
The system as recited in claim 39 wherein the surface grouping means comprises means for grouping contiguous regions of the surface having a characteristic indicating abnormal thicknesses into separate populations of abnormal thickness.
Claim 53
Independent Claim
73 words
A system for indicating regions of a three-dimensional structure having an abnormal wall characteristic comprising: a. formation means for forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure; b. modeling means for constructing a three-dimensional model of the three-dimensional structure from the three-dimensional volume of data; and c. grouping means for grouping regions of the three-dimensional model into populations having a characteristic indicating abnormal structure.
Claim 54
Independent Claim
73 words
A system for indicating regions of a three-dimensional structure having an abnormal wall characteristic comprising: a. formation means for forming a three-dimensional volume of data representing at least one physical property associated with the three-dimensional structure; b. modeling means for constructing a three-dimensional model of the three-dimensional structure from the three-dimensional volume of data; and c. grouping means for grouping regions of the three-dimensional model into populations having a characteristic indicating abnormal structure.
Claim 55
Dependent Claim
33 words
The system as recited in claim 41 wherein the grouping means comprises means for grouping contiguous regions of the three-dimensional model having a characteristic indicating abnormal thicknesses into separate populations of abnormal thickness.
Claim 56
Independent Claim
77 words
A method for indicating regions of a colon having an abnormal wall characteristic comprising: b. inflating the colon with gas; c. forming a three-dimensional volume of data representing at least one physical property associated with the colon, the three-dimensional volume of data comprising a three-dimensional matrix of voxels wherein each voxel has an associated voxel value; and d. grouping the voxels, as a selected function of voxel value, into populations having a characteristic indicating abnormal wall structure.
Claim 57
Independent Claim
77 words
A method for indicating regions of a colon having an abnormal wall characteristic comprising: b. inflating the colon with gas; c. forming a three-dimensional volume of data representing at least one physical property associated with the colon, the three-dimensional volume of data comprising a three-dimensional matrix of voxels wherein each voxel has an associated voxel value; and d. grouping the voxels, as a selected function of voxel value, into populations having a characteristic indicating abnormal wall structure.
Claim 58
Independent Claim
89 words
A system for indicating regions of a colon having an abnormal wall characteristic comprising: a. colon preparation means for inflating the colon with gas; b. volume formation means for forming a three-dimensional volume of data representing at least one physical property associated with the colon, the three-dimensional volume of data comprising a three-dimensional matrix of voxels wherein each voxel has an associated voxel value; and c. voxel grouping means for grouping the voxels, as a selected function of voxel value, into populations having a characteristic indicating abnormal wall structure.
Claim 59
Independent Claim
89 words
A system for indicating regions of a colon having an abnormal wall characteristic comprising: a. colon preparation means for inflating the colon with gas; b. volume formation means for forming a three-dimensional volume of data representing at least one physical property associated with the colon, the three-dimensional volume of data comprising a three-dimensional matrix of voxels wherein each voxel has an associated voxel value; and c. voxel grouping means for grouping the voxels, as a selected function of voxel value, into populations having a characteristic indicating abnormal wall structure.
Claim 60
Independent Claim
23 words
The method as recited in claims 31, 33, or 35 further comprising the step of analyzing each population according to selected shape characteristics.
Claim 61
Dependent Claim
36 words
The method as recited in claim 45 wherein the step of analyzing each population according to shape characteristics comprises the step of determining a convexity value for each population representing an amount and direction of curvature.
Claim 62
Dependent Claim
28 words
The method as recited in claim 45 wherein the step of analyzing each population according to shape characteristics comprises the step of determining a curvature for each population.
Claim 63
Independent Claim
25 words
The system as recited in claims 37, 39, or 41 further comprising a population analyzing means for analyzing each population according to selected shape characteristics.
Claim 64
Dependent Claim
29 words
The system as recited in claim 48 wherein the population analyzing means comprises means for determining a convexity value for each population representing an amount and direction of curvature.
Claim 65
Dependent Claim
21 words
The system as recited in claim 48 wherein the population analyzing means comprises means for determining a curvature for each population.
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USPTO Annuity & Maintenance Windows
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| 7.5 Years (Year 8) | 2006-07-05 | 2007-01-04 | 2007-07-06 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2010-07-05 | 2011-01-04 | 2011-07-06 | $7700.00 | Window Closed / Lapsed |