Hybrid Fiducial System for Tuned-Aperture Computed

Tomography

R.L. Webber, S.B. Robinson, and R.L. Webber, S.B. Robinson, and F.H. FaheyF.H. Fahey

Wake Forest UniversityWake Forest University

Supported in part by NIH RO1 DE12227, DAMD 17-98-1-8349, and Instrumentarium Imaging

Objectives:

Simplify extraction of essential fiducial Simplify extraction of essential fiducial informationinformation

Eliminate obscuration of desired Eliminate obscuration of desired information by superposition of fiducial information by superposition of fiducial shadowsshadows

Facilitate quantitative 3D radiography with Facilitate quantitative 3D radiography with conventional (2D) imaging systemsconventional (2D) imaging systems

Methods:

Use digital camera to isolate radiolucent Use digital camera to isolate radiolucent fiducials from underlying tissues as seen from fiducials from underlying tissues as seen from a variety of projection anglesa variety of projection angles

Geometrically couple resulting photographic Geometrically couple resulting photographic image with respective simultaneously exposed image with respective simultaneously exposed x-ray projection imagesx-ray projection images

Use photographic data to infer the associated Use photographic data to infer the associated x-ray projection geometry required for 3D x-ray projection geometry required for 3D reconstructionreconstruction

Compute 3D radiograph using TACT Compute 3D radiograph using TACT algorithm algorithm

Projection Schematic:

Mathematical Justification: P(P1,P2,…,Pn) are x-ray source positionsP(P1,P2,…,Pn) are x-ray source positions P*(P*1,P*2,…,P*n) are corresponding P*(P*1,P*2,…,P*n) are corresponding

camera positionscamera positions x is point in object projected by x-ray beamx is point in object projected by x-ray beam x* is point in object seen by ‘coupled’ x* is point in object seen by ‘coupled’

cameracamera Theorem: Whenever an image of a point xTheorem: Whenever an image of a point xi i

is created using pis created using pii,, then thethen the backprojection backprojection using p*using p*ii yields an unambiguous point x*, yields an unambiguous point x*, i.e. the homologous projection lines i.e. the homologous projection lines intersect at x*. intersect at x*.

This geometry can be realized with This geometry can be realized with reasonable ‘coupling’ constraints reasonable ‘coupling’ constraints

Methods (cont’d):

Expose isolated tooth from 12 arbitrary angles

Methods (cont’d):

Photograph coupled fiducials from 12 homologous angles

Results:

Reconstruct arbitrary slices from optically registered x-ray projections

Results (cont’d):

Reconstruct arbitrary 3D projections from same data

Conclusions:

Hybrid photographic/radiographic system can Hybrid photographic/radiographic system can produce accurately registered 3D reconstructions produce accurately registered 3D reconstructions using TACT algorithmsusing TACT algorithms

Potential obscuration of information caused by Potential obscuration of information caused by overlying fiducial shadows can be eliminated overlying fiducial shadows can be eliminated completely from TACT 3D reconstructionscompletely from TACT 3D reconstructions

Hybrid method facilitates automated 3D analysis Hybrid method facilitates automated 3D analysis by simplifying isolation of essential fiducial by simplifying isolation of essential fiducial registration data from radiographic informationregistration data from radiographic information