Abstract
Ray tracing (RT) and perspective projection (PP) using fiducial-based registration can be used to determine points of interest in biplanar X-ray imaging. We sought to investigate the implementation of these techniques as they pertain to X-ray imaging geometry. The mathematical solutions are presented and then implemented in a phantom and actual case with numerical tables and imaging. The X-ray imaging is treated like a Cartesian system in millimeters (mm) with a standard frame-based stereotactic system. In this space, the point source is the X-ray emitter (focal spot), the plane is the X-ray detector, and fiducials are in between the source and plane. In a phantom case, RT was able to predict locations of fiducials after moving the point source. Also, a scaled PP matrix could be used to determine imaging geometry, which could then be used in RT. Automated identification of spherical fiducials in 3D was possible using a center of mass computation with average Euclidean error relative to manual measurement of 0.23 mm. For PP, RT projection or a combinatorial approach could be used to facilitate matching 3D to 2D points. Despite being used herein for deep brain stimulation (DBS), utilization of this kind of imaging analysis has wide medical and non-medical applications.
Highlights
In 1895, Wilhelm Roentgen discovered X-rays, which subsequently had an important impact in medicine for over 100 years [1]
Background mathematical solutions In Ray tracing (RT), the geometry of the point source (P 0) to a fiducial (P1 or P2) forms a ray that intersects a detector (Pp1 or Pp2) plane, which is seen on a display (Puv1 or Puv2) plane (Figure 1) [6]
Computing the ray-plane intersections for all the relevant objects reveals the AP dimension to be constant at -515 (COA), which allows the use of the LAT and VERT coordinates to be translated directly to image (Table 2)
Summary
In 1895, Wilhelm Roentgen discovered X-rays, which subsequently had an important impact in medicine for over 100 years [1]. RT requires knowledge of the entire imaging geometry, whereas PP requires knowledge of the 3D points and their associated projection points in 2D (two dimension) Using these techniques, RT and PP represent important tools that offer critical analysis of X-rays. Frame-based coordinate systems typically use an N-localizer apparatus calibrated on a CT or MRI [3,4,5]. We implement mathematical solutions for point-based registration from 3D (x, y, z) to 2D (U, V) using RT and PP These techniques assume that there are no geometrical distortions (scattering or diffraction), that the focal spot of the X-ray emitter is a point source, that the X-ray detector. Many of the solutions provided assume biplanar imaging (two views or poses), but the same mathematical solutions can allow many more
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