Monoscopic radiographic image and three-dimensional model registration methods and systems

1. A method of determining the actual position and pose of a known three-dimensional construct of an orthopedic fixation device utilizing at least four discrete shapes formed by fiducials of the construct shown in a two-dimensional (2D) image of the construct, comprising:

identifying at least four fiducial shadows in the 2D image that correspond to the fiducials of the construct;

correlating the identified at least four fiducial shadows with their respective locations on the construct; and

determining a spatial relationship between the 2D image and the construct, comprising:

determining a focal point of a source of the 2D image relative to the 2D image via the identified at least four fiducial shadows and pre-determined mutual separation distances between the fiducials of the construct corresponding thereto;

locating actual fiducial locations along vectors from the focal point to the fiducial shadow location;

converting the actual fiducial locations into three-dimensional (3D) image coordinates;

defining actual fiducial location vectors between the fiducial locations via the 3D image coordinates; and

constructing a first orthogonal coordinate system for a collection of three discrete fiducials in terms of the 2D image via determining vector cross products between appropriate pairs of the location vectors.

2. The method of claim 1 , wherein correlating the identified at least four fiducial shadows with their respective locations on the construct comprises:

identifying the identified at least four fiducial shadows as upper or lower fiducial shadows;

determining the foreground or background order of the identified at least four fiducial shadows based on their respective sizes;

determining the left-to-right or right-to-left order of the identified at least four fiducial; and

annotating the identified at least four fiducial to correlate with respective annotated fiducial locations on the construct.

3. The method of claim 1 , wherein determining a spatial relationship between the 2D image and the construct further comprises:

inverting the first constructed orthogonal coordinate system or a second constructed orthogonal coordinate system determined via the first constructed orthogonal coordinate system to develop a coordinate transformation for the 2D image with respect to any coordinate system representing the construct.

4. A computer program product comprising:

a non-transitory computer readable storage medium readable by one or more processing circuit and storing instructions for execution by one or more processor for performing a method according to any one of claims 1-3 .

5. A system comprising:

a memory;

at least one processor in communication with memory; and

program instructions executable by one or more processor via the memory to perform a method according to any one of claims 1-3 .

6. A method of determining the actual position and pose of a known collection of spherical objects from an orthopedic fixation device in a projected three-dimensional space lying above a two-dimensional radiographic space, comprising:

obtaining two or more digital radiographic images of the known collection of spherical objects in the projected three-dimensional space lying above the two-dimensional radiographic space; and

utilizing a measurement of at least one of a minor diameter, an average diameter, or an area of elliptical shadows from the spherical objects of the known collection of spherical objects in the two-dimensional radiographic space in the two or more digital radiographic images to determine the actual position and pose of the known collection of spherical objects in the projected three-dimensional space lying above the two-dimensional radiographic space.

7. The method of claim 6 , further comprising constructing a three-dimensional model of the actual position and pose of the known collection of spherical objects in the projected three-dimensional space.

8. The method of claim 6 , wherein the utilizing elliptical shadows of the known collection of spherical objects in the two-dimensional radiographic space in the two or more digital radiographic images to determine the actual position and pose of the known collection of spherical objects comprises:

utilizing perspective distortion to determine of relative magnifications of the images to reconstruct the projected three-dimensional space;

determining the relationship between the two or more digital radiographic images via comparison of a common spherical object of the known collection of spherical objects in the images; and

wherein the two or more digital radiographic images further comprise at least one anatomical structure in need of correction, and constructing a three-dimensional model of the actual position and pose of the at least one anatomical structure in the projected three-dimensional space.

9. The method of claim 6 , wherein the measurement of at least one of the minor diameter, an average diameter, or an area of the elliptical shadow, includes determining the minor diameter.

10. A computer program product comprising:

a non-transitory computer readable storage medium readable by one or more processing circuit and storing instructions for execution by one or more processor for performing a method of determining the actual position and pose of a known collection of objects of an orthopedic fixation device utilizing at least four discrete shapes formed by fiducials of the construct shown in a two-dimensional (2D) image of the construct, comprising:

identifying at least four fiducial shadows in the 2D image that correspond to the fiducials of the construct;

correlating the identified at least four fiducial shadows with their respective locations on the construct; and

determining a spatial relationship between the 2D image and the construct, comprising:

determining a focal point of a source of the 2D image relative to the 2D image via the identified at least four fiducial shadows and pre-determined mutual separation distances between the fiducials of the construct corresponding thereto;

establishing an orthogonal coordinate system utilizing the 2D image as one of the three planes of the coordinate system;

determining the location along the focal point ray that each of the at least four fiducials must lie; and

constraining a model of the at least four fiducials based on known characteristics of the construct via a cost function, the known characteristics not including one ray and four fiducial-fiducial distances, wherein the constraining forms a tripod model that trace out a planar curve that lies in a plane that is normal to the image plane.

11. The method of claim 10 , wherein determining the spatial relationship between the 2D image and the construct by determining the focal point of the source of the image relative to the 2D image via the identified at least four fiducial shadows and pre-determined mutual separation distances between the fiducials of the construct corresponding thereto further comprises:

reconfiguring the tripod model such that a first plane formed by a first group of three fiducials of the at least four fiducials lies along an image plane;

determining a first equation for a first line which depicts the intersection of the image plane and the first plane;

reconfiguring the tripod model such that a second plane formed by a second group of three fiducials of the at least four fiducials lies along the image plane;

determining a second equation for a first line which depicts the intersection of the image plane and the second plane;

determining x and y coordinates of the focal point via at least the first and second lines;

and determining a z coordinate of the focal point via the x and y coordinates and a cost function.

12. A system comprising:

a memory;

at least one processor in communication with memory; and

program instructions executable by one or more processor via the memory to perform a method of determining the actual position and pose of a known collection of objects from an orthopedic fixation device in a projected three-dimensional space lying above a two-dimensional radiographic space, comprising:

obtaining a digital radiographic image of the known collection of objects in the projected three-dimensional space lying above the two-dimensional radiographic space; and

utilizing shadows of the known collection of objects in the two-dimensional radiographic space in the digital radiographic image to determine the actual position and pose of the known collection of objects in the projected three-dimensional space lying above the two-dimensional radiographic space by:

determining a focal point and locating actual locations of the known collection of objects along vectors from the focal point to locations of the shadows;

converting the actual location of the known collection of objects into three-dimensional image coordinates; and

defining actual location vectors between the actual location of the known collection of objects via the 3D image coordinates.

13. The system of claim 12 , wherein determining the actual position and pose of the known collection of objects in the projected three-dimensional space lying above the two-dimensional radiographic space further includes:

constructing a first orthogonal coordinate system for a collection of three of the known collection of objects in terms of the digital radiographic image via determining vector cross products between appropriate pairs of location vectors; and

inverting the first constructed orthogonal coordinate system to develop a coordinate transformation for the digital radiographic image with respect to any coordinate system representing the construct.