System and method for simulated linearization of curved surface

• US 8,417,004 B2
• Filed: 04/07/2011
• Issued: 04/09/2013
• Est. Priority Date: 04/07/2011
• Status: Active Grant

• Current Assignee: Dolpin Imaging Systems LLC
• Original Assignee: Dolpin Imaging Systems LLC
• Inventors: Liao, Swanwa
• Primary Examiner(s): Allison, Andrae S
• Application Number:
  US13/081,895
• Publication Number:
  US 20120257841A1
• Time in Patent Office: 733 Days
• Field of Search: 382128-132, 382/154, 382/285, 379/9, 379168-171, 433/2, 433/6, 433/4, 433/213, 345/419, 600/410
• US Class Current: 382/128
• CPC Class Codes: G06T 19/00 Manipulating 3D models or images for computer graphics
• CPC Class Codes: G06T 2219/021 Flattening
• CPC Class Codes: G06T 3/06 Topological mapping of higher dimensional structures onto lower dimensional surfaces

Abstract

In accordance with embodiments of the present disclosure, a method may include mapping an ellipse with its center at the origin of an xy-coordinate plane to a circle with its center at the origin of the xy-coordinate plane. The method may also include transforming a three-dimensional subject image including a curved profile in the xy-coordinate plane to an intermediate image based at least on the mapping of the ellipse to a base circle. The method may further include transforming the intermediate image to a transformed image having a linear profile by distorting each of one or more points of interest of the intermediate image based at least on a dimension of the circle and a coordinate of such point.

Claims

1. A method comprising:

mapping an ellipse with its center at the origin of an xy-coordinate plane to a circle with its center at the origin of the xy-coordinate plane;

transforming a three-dimensional subject image including a curved profile in the xy-coordinate plane to an intermediate image based at least on the mapping of the ellipse to the circle; and

transforming the intermediate image to a transformed image having a linear profile by distorting each of one or more points of interest of the intermediate image based at least on a dimension of the circle and a coordinate of such point.

2. A method according to claim 1, wherein a radius of the circle is equal to one of a major radius of the ellipse or a minor radius of the ellipse.

3. A method according to claim 1, wherein transforming the subject image to the intermediate image is in accordance with the following equations:

P_x′

=P_x×

b/a

P_y′

=P_y

P_z′

=P_z

where P_x, P_y, and P_z are respectively the x, y, and z coordinates of each point P_i in the subject image, P_x′

, P_y′

, and P_z′

are respectively the x, y, and z coordinates of each corresponding point P_i′

in the intermediate image, a is a minor radius of the ellipse, and b is a major radius of the ellipse.

4. A method according to claim 1, wherein transforming the intermediate image to the transformed image is in accordance with the following equations:

P_x″

=b×

arctan(P_x′

/P_y′

)

P_y″

=√

(P_x′

²+P_y′

²)

P_z″

=P_z′

where P_x″

, P_y″

, and P_z″

are respectively the x, y, and z coordinates of each point of interest in the transformed image, P_x′

, P_y′

, and P_z′

are respectively the x, y, and z coordinates of each corresponding point of interest in the intermediate image, and b is the radius of the circle.

5. A method according to claim 1, wherein each of the subject image and the transformed image is a segmented surface image.

6. A method according to claim 1, in which the subject image is a graphical representation of one of a mandible and a maxilla.

7. An article of manufacture comprising:

a non-transitory computer-readable medium; and

computer-executable instructions carried on the computer-readable medium, the instructions executable by one or more processors and configured to cause the one or more processors to;

map an ellipse with its center at the origin of an xy-coordinate plane to a circle with its center at the origin of the xy-coordinate plane;

transform a three-dimensional subject image including a curved profile in the xy-coordinate plane to an intermediate image based at least on the mapping of the ellipse to the circle; and

transform the intermediate image to a transformed image having a linear profile by distorting each of one or more points of interest of the intermediate image based at least on a dimension of the circle and a coordinate of such point.

8. An article of manufacture according to claim 7, wherein a radius of the circle is equal to one of a major radius of the ellipse or a minor radius of the ellipse.

9. An article of manufacture according to claim 7, wherein transforming the subject image to the intermediate image is in accordance with the following equations:

P_x′

=P_x×

b/a

P_y′

=P_y

P_z′

=P_z

where P_x, P_y, and P_z are respectively the x, y, and z coordinates of each point P_i in the subject image, P_x′

, P_y′

, and P_z′

are respectively the x, y, and z coordinates of each corresponding point P_i′

in the intermediate image, a is a minor radius of the ellipse, and b is a major radius of the ellipse.

10. An article of manufacture according to claim 7, wherein transforming the intermediate image to the transformed image is in accordance with the following equations:

P_x″

=b×

arctan(P_x′

/P_y′

)

P_y″

=√

(P_x′

²+P_y′

²)

P_z″

=P_z′

where P_x″

, P_y″

, and P_z″

are respectively the x, y, and z coordinates of each point of interest in the transformed image, P_x′

, P_y′

, and P_z′

are respectively the x, y, and z coordinates of each corresponding point of interest in the intermediate image, and b is the radius of the circle.

11. An article of manufacture according to claim 7, wherein each of the subject image and the transformed image is a segmented surface image.

12. An article of manufacture according to claim 7, in which the subject image is a graphical representation of one of a mandible and a maxilla.

13. A computing system, comprising:

a processor; and

a memory communicatively coupled to the processor and having stored thereon a program of instructions configured to, when executed by the processor;

map an ellipse with its center at the origin of an xy-coordinate plane to a circle with its center at the origin of the xy-coordinate plane;

transform a three-dimensional subject image including a curved profile in the xy-coordinate plane to an intermediate image based at least on the mapping of the ellipse to the circle; and

transform the intermediate image to a transformed image having a linear profile by distorting each of one or more points of interest of the intermediate image based at least on a dimension of the circle and a coordinate of such point.

14. A computing system according to claim 13, wherein a radius of the circle is equal to one of a major radius of the ellipse or a minor radius of the ellipse.

15. A computing system according to claim 13, wherein transforming the subject image to the intermediate image is in accordance with the following equations:

P_x′

=P_x×

b/a

P_y′

=P_y

P_z′

=P_z

where P_x, P_y, and P_z are respectively the x, y, and z coordinates of each point P_i in the subject image, P_x′

, P_y′

, and P_z′

are respectively the x, y, and z coordinates of each corresponding point P_i′

in the intermediate image, a is a minor radius of the ellipse, and b is a major radius of the ellipse.

16. A computing system according to claim 13, wherein transforming the intermediate image to the transformed image is in accordance with the following equations:

P_x″

=b×

arctan(P_x′

/P_y′

)

P_y″

=√

(P_x′

²+P_y′

²)

P_z″

=P_z′

where P_x″

, P_y″

, and P_z″

are respectively the x, y, and z coordinates of each point of interest in the transformed image, P_x′

, P_y′

, and P_z′

are respectively the x, y, and z coordinates of each corresponding point of interest in the intermediate image, and b is the radius of the circle.

17. A computing system according to claim 13, wherein each of the subject image and the transformed image is a segmented surface image.

18. A computing system according to claim 13, in which the subject image is a graphical representation of one of a mandible and a maxilla.