Automatic calibration for radiological tomographic imaging using fiducials with unknown placement

Abstract

Techniques for radiological tomographic imaging using a first target, where the first target is three dimensional, and where a plurality of fiducials are positioned relative to the first target, are presented. The techniques include: obtaining an initial fiducial localization of at least some of the plurality of fiducials using a radiological imaging machine; labeling, based on the initial fiducial localization, fiducial coordinates of at least some of the plurality of fiducials, where the labeling is based on a plurality of long traces; refining the fiducial coordinates based on the labeling the fiducial coordinates; determining, based on the fiducial coordinates, a geometry of the radiological imaging machine; and acquiring, using the radiological imaging machine and based on the geometry of the radiological imaging machine, a tomographic image of a second target.

Description

AUTOMATIC CALIBRATION FOR RADIOLOGICAL TOMOGRAPHIC IMAGING USING FIDUCIALS WITH UNKNOWN PLACEMENTRelated Application

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 549,103, entitled, “Automatic Calibration for Radiological Tomographic Imaging Using Fiducials with Unknown Placement,” and filed February 2, 2024.Government Support

[0002] This invention was made with government support under grant EB027127 awarded by the National Institutes of Health. The government has certain rights in the invention.Field

[0003] This disclosure relates generally to radiological tomographic imaging, such as cone beam computer tomography.Background

[0004] Cone-beam CT (CBCT) with noncircular scanning orbits can improve image quality for 3D intraoperative image guidance. However, geometric calibration of such scans, which may include adjusting parameters such as angles, distances, and / or positions to ensure accurate conversion of radiological projections to 3D images, can be challenging. Existing methods typically require a prior image, specialized phantoms, presumed repeatable orbits, or long computation time.

[0005] In general, CBCT is widely used for interventional imaging. It can provide valuable intraoperative image guidance in many clinical applications. In recent years, noncircular scan orbits have been increasingly investigated for potential benefits such as increased field of view (FOV), improved image quality and / or dose reduction, collision avoidance, accommodating upright patient positions, and reduced metal artifacts. While studies have demonstrated sufficient reproducibility for standard circular scanning orbits, current implementations of non-circular orbits often result in aless predictable geometry due to factors such as gantry vibration, sagging, and manual data acquisition, etc. However, an accurate CBCT geometry is critical for the image quality of 3D reconstructions.

[0006] While geometric calibration methods exist that involve auxiliary instruments such as laser interferometers and optical cameras, other direct approaches do not require hardware augmentation. Methods for different intended applications typically have different sets of advantages and disadvantages. A brief summary of commonly employed features and the associated advantages and disadvantages is presented here, focusing on methods that may be extended to noncircular orbits.

[0007] Offline methods perform the calibration for a given scanning protocol during system servicing and save the geometry data for subsequent use. Offline methods thus assume that the scanning orbit for the calibrated protocol is highly reproducible. Online methods treat each scan as a new calibration task and therefore are suitable for irreproducible scanning orbits. Image-based methods find the geometry by optimizing image quality-related metrics, such as sharpness in the 3D reconstruction and similarity between the projection images and simulated forward projections from a known model of the imaging target. These 2D and 3D image operations tend to be computationally intensive and time consuming. Fiducial-based methods localize the 2D coordinates of fiducial markers from the projection images and perform calibration-related calculations only on the coordinates. These operations are typically less computationally intensive than image-based methods, but the fiducials may be difficult to localize when the background is complex. Methods using a known target assume that the 3D structure of the imaging target is precisely known a priori, for example, from a digital model or prior scans, as is the case with aforementioned dedicated calibration phantoms and 3D-2D registration methods. Conversely, methods using an unknown target are suitable for fiducials placed in an unknown configuration and for cases where a patient has not previously been scanned or presents major anatomical changes from prior scans, but these methods typically require precisely fiducial localization in projection images or optimization of 3D image metrics. Some newer methods are addressing some of these intrinsic limitations. For example, Ji et al. proposed a 2D-2D registration-based method to address the high computation cost in 3D-2D registration-based methods. See X. Ji, Y. Lu, X. Zhuo, Y.Zhang, S. Zhu, and Y. Chen, A Geometrical Calibration Method for C-arm CT based on a Non-Linear Registration Model, IEEE Transactions on Instrumentation and Measurement , 1-1 (2023). Li et al. proposed a method that alleviates the need for precisely manufactured calibration phantoms. See G. Li, S. Luo, C. You, M. Getzin, L. Zheng, G. Wang, and N. Gu, A novel calibration method incorporating nonlinear optimization and ball-bearing markers for conebeam CT with a parameterized trajectory, Medical Physics, mp.13278 (2018).

[0008] Some previous investigations of practical implementation of non-circular orbits tested an imaged-based 3D-2D registration method and a fiducial-based method. See S. Ouadah, J. W. Stayman, G. J. Gang, T. Ehtiati, and J. H. Siewerdsen, Self-calibration of cone-beam CT geometry using 3D-2D image registration, Physics in Medicine & Biology 61 , 2613 (2016), IOP Publishing; Y. Q. Ma, G. J. Gang, T. Reynolds, T. Ehitiati, J. Li, O. Dillon, T. Russ, W. Wang, C. Weiss, N. Theodore, K. Hong, R. O’Brien, J. Siewerdsen, and J. W. Stayman, Practical workflow for arbitrary non-circular orbits for CT with clinical robotic C-arms, in 7th International Conference on Image Formation in X-Ray Computed Tomography, volume 12304, pages 551- 558, SPIE, 2022; and G. Li, S. Luo, C. You, M. Getzin, L. Zheng, G. Wang, and N. Gu, A novel calibration method incorporating nonlinear optimization and ball-bearing markers for conebeam CT with a parameterized trajectory, Medical Physics, mp.13278 (2018). The 3D-2D registration method required no fiducials, but it required a prior scan of the imaging target and high computation time. The fiducial-based method used radiopaque beads placed directly on the imaging target with an unknown configuration and was fast. However, the fiducial localization was challenging due to the complex anatomical background of the imaging target and therefore required manual intervention, which is not desirable for clinical scenarios.Summary

[0009] According to various method embodiments, a method of radiological tomographic imaging using a first target, wherein the first target is three dimensional, and wherein a plurality of fiducials are positioned relative to the first target, is presented. The method includes: obtaining an initial fiducial localization of at least some of the plurality of fiducials using a radiological imaging machine; labeling, based on the initial fiducial localization, fiducial coordinates of at least some of the pluralityof fiducials, wherein the labeling is based on a plurality of long traces; refining the fiducial coordinates based on the labeling the fiducial coordinates; determining, based on the fiducial coordinates, a geometry of the radiological imaging machine; and acquiring, using the radiological imaging machine and based on the geometry of the radiological imaging machine, a tomographic image of a second target.

[0010] Various optional features of the above method embodiments include the following. The method may include: combining at least two disjoint long traces of the plurality of long traces, wherein the at least two disjoint long traces correspond to a same fiducial. The refining may include: updating three dimensional centroid location estimates for the fiducials; predicting two dimensional fiducial locations in images; and designating regions of interest as the predicted two dimensional centroid locations. The method may include iterating the updating, the predicting, and the designating. The obtaining the initial fiducial localization may include: performing background subtraction; performing edge detection; and performing circle detection. The radiological imaging machine may include a radiation source and a detector, and the geometry may include an orientation of the detector and at least one of a location of the detector or a location of the radiation source. The first target may include the second target. The radiological imaging machine may include a radiation source and a detector, and positions of the source and the detector during the acquiring may not be reproducible. The first target may be different from the second target, and the determining may include calibrating the radiological imaging machine. Each of the plurality of long traces may include at least 20 images.

[0011] According to various system embodiments, a system for radiological tomographic imaging using a first target, wherein the first target is three dimensional, and wherein a plurality of fiducials are positioned relative to the first target, is presented. The system includes a non-transitory computer readable medium comprising instructions, and at least one electronic processor that executes the instructions, to perform operations comprising: obtaining an initial fiducial localization of at least some of the plurality of fiducials using a radiological imaging machine; labeling, based on the initial fiducial localization, fiducial coordinates of at least some of the plurality of fiducials, wherein the labeling is based on a plurality of long traces; refining the fiducial coordinates based on the labeling the fiducial coordinates; determining, based on the fiducial coordinates, a geometry of the radiological imagingmachine; and acquiring, using the radiological imaging machine and based on the geometry of the radiological imaging machine, a tomographic image of a second target.

[0012] Various optional features of the above system embodiments include the following. The operations may further include: combining at least two disjoint long traces of the plurality of long traces, wherein the at least two disjoint long traces correspond to a same fiducial. The refining may include: updating three dimensional centroid location estimates for the fiducials; predicting two dimensional fiducial locations in images; and designating regions of interest as the predicted two dimensional centroid locations. The operations may further include iterating the updating, the predicting, and the designating. The obtaining the initial fiducial localization may include: performing background subtraction; performing edge detection; and performing circle detection. The radiological imaging machine may include a radiation source and a detector, and the geometry may include an orientation of the detector and at least one of a location of the detector or a location of the radiation source. The first target may include the second target. The radiological imaging machine may include a radiation source and a detector, and positions of the source and the detector during the acquiring may not be reproducible. The first target may be different from the second target, and the determining may include calibrating the radiological imaging machine. Each of the plurality of long traces may include at least 20 images.

[0013] Combinations, (including multiple dependent combinations) of the above-described elements and those within the specification have been contemplated by the inventors and may be made, except where otherwise indicated or where contradictory.Brief Description of the Drawings

[0014] Various features of the examples can be more fully appreciated, as the same become better understood with reference to the following detailed description of the examples when considered in connection with the accompanying figures, in which:

[0015] Fig. 1 is a flowchart of a method for radiological tomographic imaging according to various non-limiting example embodiments;

[0016] Fig. 2 depicts a diagram of backprojections of fiducial centroids under accurate geometry and a diagram of backprojections of fiducial centroids under inaccurate geometry, as well as illustrating the concepts of virtual intersection and reprojection error (RPE), according to various non-limiting example embodiments;

[0017] Figs. 3A and 3B illustrate phantom design used to assess resolution performance on an X-ray test bench, according to an non-limiting example embodiment;

[0018] Figs. 4A, 4B, 4C, and 4D illustrate an X-ray test bench and associated data used to assess the resolution performance of an non-limiting example embodiment;

[0019] Figs. 5A and 5B illustrate a robotic C-arm and associated data used to assess the resolution performance of a non-limiting example embodiment;

[0020] Figs. 6A and 6B illustrate an anthropomorphic phantom and associated data used to assess the resolution performance of a non-limiting example embodiment with a robotic C-arm;

[0021] Figs. 7A, 7B, and 7C show an example RPE plot and reconstructions from a sinusoidal orbit scan with 1x nominal motion errors and the spiral fiducial configuration, according to an example non-limiting embodiment;

[0022] Figs. 8A and 8B show MTF and F20 results from an assessment of a nonlimiting example embodiment.

[0023] Figs. 9A, 9B, 9C, and 9D present the results of the resolution performance assessment using a robotic C-arm and cylindrical phantom design, according to a non-limiting example embodiment;

[0024] Fig. 10 presents the results of the resolution performance assessment using a robotic C-arm and anthropomorphic phantom for a circular scan, according to a non-limiting example embodiment; and

[0025] Fig. 11 presents the results of the resolution performance assessment using a robotic C-arm and anthropomorphic phantom for a multi-arc scan, according to a non-limiting example embodiment.Description of the Examples

[0026] Reference will now be made in detail to example implementations, illustrated in the accompanying drawings. Wherever convenient, the same referencenumbers will be used throughout the drawings to refer to the same or like parts. In the following description, reference is made to the accompanying drawings that form a part thereof, and in which is shown by way of illustration specific exemplary examples in which the invention may be practiced. These examples are described in sufficient detail to enable those skilled in the art to practice the invention and it is to be understood that other examples may be utilized and that changes may be made without departing from the scope of the invention. The following description is, therefore, merely exemplary.

[0027] Some embodiments provide fully automatic fiducial-based online geometric calibration that does not require prior knowledge of the fiducial configuration. Some embodiments are fast, accurate, and can accommodate arbitrary scanning orbits and fiducial configurations. Some embodiments can perform geometric calibration for radiological tomographic imaging devices having unpredictable geometries due to, for example, gantry vibration, sagging, manual positioning, etc. Some embodiments can perform geometric calibration for radiological tomographic imaging devices in the presence of rigid motion of an imaged patient, or other target, with respect to the fiducials. For example, the usage of fiducials, even without prior knowledge of fiducial placement, allows some embodiments to perform geometric calibration when imaging a breathing patient. Thus, some embodiments provide a geometric calibration system and method that is suitable both for unpredictable geometries and for the intraoperative workflow.

[0028] Some embodiments utilize long traces, which track 2D coordinates of fiducials across multiple neighboring projection angles. The use of long traces solves the prior art problem of requiring the use of fiducials with known placement and / or difficult and time consuming processing for geometric calibration of radiological tomographic imaging devices. Some embodiments combine multiple disjoint long traces that correspond to the same fiducial, which solves the prior art problem of handling disappearing fiducials during radiological scanning.

[0029] Further features and advantages are shown and described herein in reference to the accompanying figures. In particular, a detailed description of an implementation on a research test bench and a clinical robotic CBCT scanner for noncircular orbits is presented herein. The effectiveness and robustness are demonstrated through physical experiments with realistic setups.

[0030] Fig. 1 is a flowchart of a method 100 for radiological tomographic imaging according to various non-limiting example embodiments. The method 100 is described in reference to an example implementation using a non-limiting example experimental setup. Further by way of non-limiting example, and for clarity of explanation, the method is organized into three major processes: initial fiducial localization, fiducial coordinate labeling, and iterative refinement of fiducial coordinates and geometry. Details of implementation for these processes are described in reference to subsequent figures.

[0031] The setup for the method 100 places spherical fiducials directly on the imaging target. Their precise configuration is not measured or known a priori. In general, the CBCT system geometry of a robotic C-arm system may be defined by nine parameters that describe the position and orientation of the detector and the position of the x-ray source. Some embodiments make use of an additional assumption that the position of the x-ray source is fixed with respect to the detector, thus reducing the degrees of freedom (DoF) to be estimated from nine parameters to six parameters. For example, a CBCT system includes radiation source and a detector, and the system geometry may be characterized by an orientation of the detector together with either a location of the detector or a location of the radiation source. The gantry motion is assumed to be predominantly continuous and smooth.

[0032] The first major process, fiducial localization, automatically generates rough fiducial localization results to initialize the calibration process. The inputs are: (1 ) inaccurate initial estimates of the geometry, typically from the headers of projection frames from a robotic C-arm, (2) line integral images, and (3) an estimate of the maximum number of fiducials visible in any line integral image. Theoretically, only (3) may make use of manual input from the operator. The processing chain for each line integral image may include the following steps:

[0033] (1 ) Run wavelet-based background and noise subtraction (WBNS) to isolate the most prominent fiducials. Remaining features that are too small or too large compared to the expected fiducial size range are removed via connected component analysis and morphological operations.

[0034] (2) Make a binary mask from the background-subtracted image.

[0035] (3) Apply the mask on the Gaussian-filtered line integral image.

[0036] (4) Apply Canny edge detection on the full masked image.

[0037] (5) Run Hough transform -based circle detection on the edge image.

[0038] For the open source WBNS package (step 1 ), non-limiting example empirically chosen parameters may include: “point spread function (PSF) width” = 5 pixels, and “level of discrete wavelet transform decomposition” = 2. For Canny edge detection (step 4), the default settings from the MATLAB built-in function edge (MATLAB and Image Processing Toolbox Release 2022b, The MathWorks, Inc., Natick, Massachusetts, United States) may be used. For circle detection (step 5), a range of expected circle diameters in pixels may be estimated based on the fiducial size, detector pixel size, and magnification factor. The open source circle detection tool detects circles up to the user provided maximum number of fiducials in each projection. All steps utilized the MATLAB built-in parallel processing capability (MATLAB and Parallel Computing Toolbox Release 2022b, The MathWorks, Inc., Natick, Massachusetts, United States). The outputs of this processing are integervalued 2D coordinates for the centroids of the most prominent fiducials in each line integral image.

[0039] The second major process, fiducial coordinate labeling, includes roughly estimating the 3D locations of the fiducials and labeling the 2D centroid coordinates by their 3D counterpart. The estimation of the 3D location of a fiducial is based on the following premise: given accurate geometry (Q), lines (L(Q)) connecting the 3D world coordinates of the 2D centroids on the detector to the locations of the x-ray source (centroid rays) intersect in 3D at an infinitesimal point (p) (Fig. 2, reference 202). In other words, the point-to-line Euclidean distances d(p, L) = 0. From this premise, given the incorrect geometry initialization and the incomplete and inaccurate fiducial localization the first process, the initial fiducial localization, the 3D fiducial location can be estimated in the following steps (see Fig. 2, reference 204):

[0040] (1 ) Discard nearly overlapping centroids within a distance of 1.5x diameter from each other in the same frame.

[0041] (2) Form long traces by grouping 2D fiducial coordinates that are within a specified distance (by way of non-limiting example, within 30 pixels) in neighboring frames and that maintain this proximity continuously for at least a specified number of frames (by way of non-limiting example, at least 20 frames). A long trace keeps track of the 2D coordinates of a single fiducial across a series of neighboring projectionangles. A total of S long traces may be formed. Discard short traces spanning less than, for example, 20 frames.

[0042] (3) For each long trace and for each projection angle, calculate the centroid ray ( / _) using the initial geometry estimate (fi). The set of all centroid rays for the sthlong trace spanning frame numbers m to n is denoted Ls(fim...n).

[0043] (4) For each long trace and for all possible pairs of centroid rays Ls(fi / ) and Ls(n / ), where m < ij < n, calculate their virtual intersections: the point at the shortest distance to a pair of skew 3D lines. The mean of all virtual intersections is the estimated fiducial location (ps) corresponding to the sthlong trace.

[0044] (5) Of the S long traces, combine long traces whose mean virtual intersections p are within, for example, 25 mm of each other.

[0045] The parameters presented herein were chosen empirically and are disclosed solely for purposes of illustration rather than limitation. Step (1 ) reduces the chance of labeling errors caused by nearly overlapping fiducials. In step (2), different long traces may track the same fiducial in different frame ranges due to the fiducial disappearing and reappearing in different frames. The short traces are discarded to reduce the chance of incorporating false positive localization results. In step (5), long traces with mean virtual intersections within 25 mm of each other are assumed to track the same fiducials because the fiducials were placed more than 30 mm apart in the experiments with the example implementation. Combining these long traces results in a total of K combined long traces, each corresponding to a distinct fiducial pk. If true positives are discarded in step (2), they are highly likely recovered in the subsequent processing introduced below. No parallelization was applied to these operations, however, embodiments may include parallelization. The outputs of this processing are the integer-valued 2D centroid coordinates in the outputs from the above, labeled with a fiducial index from 1 to K, minus the discarded fiducials in steps (1 ) and (2).

[0046] The goal of the third major process, iterative refinement of fiducial coordinates and geometry, is to iteratively refine the 2D fiducial localization, system geometry, and the 3D fiducial coordinates (Figure 1 c). The steps are as follows, by way of non-limiting example:

[0047] (1 ) From the line integral images, extract square regions of interest(ROIs) centered at the 2D centroids. The centroids are provided either by thecombined long traces from step 5 of the second major process (for the first iteration) or by the centroids predicted in step 6 below (for subsequent iterations).

[0048] (2) Run sub-pixel level Hough transform based circle detection in theROIs.

[0049] (3) Calculate confidence weights for the fiducial localization in each ROI using Weber contrast. Normalize the fiducial weights in the same frame to a mean of 1.

[0050] (4) For each fiducial, calculate centroid rays using the current geometry estimate and update the estimated 3D location p using the mean virtual intersection.

[0051] (5) For each frame, minimize the reprojection error (RPE) with respect to the system geometry parameters for the n-th frame (£ln) (see Fig. 2):

[0053] where k is the fiducial index, and wk nis a scalar confidence weight for fiducial k in frame n.

[0054] (6) Repeat steps 4 and 5 three times.

[0055] (7) Predict 2D centroid locations using current estimatesand p.

[0056] (8) Return to step 1 for a total of three iterations unless a target RPE is met.

[0057] The parameters disclosed herein by way of non-limiting example were chosen empirically. In step (2), for the circle detection tool, the “gradient threshold” is, for example, 0.5. In step (3), the contrast-based confidence down-weights fiducials with a low contrast against the background due to high background attenuation. In the example implementation, step (5) used the MATLAB builtin constrained nonlinear optimizer fmincon with the Active Set algorithm (MATLAB and Optimization Toolbox Release 2022b, The MathWorks, Inc., Natick, Massachusetts, United States). Constraints were set based on estimates of motion error amplitudes. The system geometry is hence optimized by:

[0059] where / is the iteration number. The 2D centroid prediction (step (7)) is based on the 3D to 2D projection operation. By way of non-limiting example, the physical experiments described herein ran three iterations of both the inner (step 6)and outer (step 8) loops, as additional iterations did not substantially change estimates. While possible, the per-frame optimization (step 5) was not parallelized. The outputs of this processing are the calibrated geometry (fl), the estimated fiducial locations (px K), and the locations and diameters of the projected 2D fiducial images. The fiducial diameters are used to inpaint the fiducial images prior to reconstruction to reduce the metal artifacts from the fiducials.

[0060] Fig. 2 depicts a diagram 202 of backprojections of fiducial centroids under accurate geometry and a diagram 204 of backprojections of fiducial centroids under inaccurate geometry, as well as illustrating the concepts of virtual intersection and reprojection error (RPE). The x-ray source travels on the surface of an imaginary sphere with a fixed isocenter at the center of the mesh spheres.

[0061] Regarding the physical experiment setups, physical phantom studies were performed on an x-ray CBCT test bench and a clinical robotic C-arm scanner (Siemens Artis Zeego, Siemens Healthineers, Forchheim, Germany) to test the calibration performance of the algorithm in realistic settings. Both circular and noncircular orbits were tested. Two different phantoms were used to produce quantitative and qualitative results. The setup of three physical experiments and the design and implementation of the orbits are presented. The techniques and orbit parameters are summarized in Table I.Table

[0062] Table I summarizes various parameters in the experimental setups. The double horizontal lines mark the parameter categories: phantom setup, x-ray technique, orbit design, 3D reconstruction, and configuration robustness. The parameters apply to all circular and non-circular scans within each experiment unless otherwise noted. A short dash (-) indicates the parameter is unavailable or the test is not performed.

[0063] Figs. 3A and 3B illustrate phantom design used to assess resolution performance on an X-ray test bench, according to a non-limiting example embodiment. In particular, Figs. 3A and 3B show a constructed test phantom featuring a 3D printed cervical spine section with anatomical structures, a 0.127 mm diameter tungsten wireto measure the modulation transfer function (MTF), and plastic spheres of various sizes as background clutter. The spine was placed in a 9 cm diameter plastic cylindrical container. The tungsten wire was cast in epoxy resin and fixed in the spinal canal (side view of wire in resin: Fig. 3A, 302; top view of spinal canal: Fig. 3A, 304). The container was filled with plastic spheres of and water (side views: Fig. 3A, 306, 308). Twelve 2.5 mm diameter spherical stainless steel skin markers (Spee-D-Mark, PDC Healthcare, Valencia, California) were manually affixed to the side of the container. Two widely used fiducial configurations were adopted: spiral and double rings. In Fig. 3B, the fiducials are numbered and connected by lines to help visualize the spiral and ring configuration styles. The spiral configuration wrapped around the cylinder twice (Fig. 3A, 306 and Fig. 3B, 312). The double ring configuration included 5 fiducials per ring and 2 fiducials near the center and on the opposite sides of the phantom (Fig. 3A, 308 and Fig. 3B, 314). The locations of the fiducials were not measured a priori.

[0064] Figs. 4A, 4B, 4C, and 4D illustrate an X-ray test bench and associated data used to assess the resolution performance of a non-limiting example embodiment.

[0065] For non-circular orbit designs and implementation, two types of noncircular orbits that were previously investigated for eliminating metal artifacts, namely sinusoid and multi-arc orbits, were applied, as shown in Fig. 4B. Both types of orbits were designed with a fixed isocenter. The LAO / RAO gantry rotation angle and CRAN / CAUD gantry tilt angle were the parameters in non-circular actuation. In the sinusoidal orbit, the gantry oscillated between ±25° in tilt for two full cycles while rotating 360°. The multi-arc orbit consisted of two tilted full 360° circular scans (essentially long arcs) at +25° and -20° tilt angles, plus a short arc connecting the tilted circles, where the gantry tilted from +25° to -20°, with the rotation angle fixed.

[0066] The test bench included an x-ray tube (Varex Rad-94), a flat-panel detector (Varex PaxScan 4343CB) with 0.278 mm square pixels (2x2 binned), a 6 DoF hexapod robot (PI H-900K Series) and rotation stage (PI PRS-200), as shown in Fig. 4A. The noncircular orbits were performed using the hexapod robot and the rotation stage by articulating the mounted phantom, which was equivalent to gantry motion on a robotic C-arm. Both non-circular orbits were tested and circular scans were acquired as a benchmark, as shown in Fig. 4B.

[0067] Inaccuracies in the positioning of a Siemens Artis Zeego robotic C-arm have previously been identified during manual fluoroscopy-based non-circular acquisitions. These inaccuracies in the encoder-reported geometry parameters may follow a sinusoidal pattern with respect to the gantry angles (likely caused mostly by gravity-induced sagging) with some jitter (likely due to vibrations and encoder inaccuracies). The bench test performance assessment emulated such geometry deviations by adding motion errors composed of a sinusoidal bias plus random jitter to the designed non-circular orbits. The motion error amplitude was also exaggerated by a factor of three to stress test the proposed algorithm. Figs. 4C and 4D illustrate the translational and rotational errors, respectively, in each parameter added to each frame of the error-free sinusoidal scan. The motion errors added to the multi-arc scans were the same and not shown. Motion errors were not added to the circular scans. The ideal error-free orbit parameters were used as the input to initialize the geometric calibration process, as described herein in reference to the initial fiducial localization major process of Fig. 1 .

[0068] For all test bench scans, 360 frames were acquired. For the circular and sinusoidal scans, frames were acquired with equal 1° increments in LAO / RAO rotation. For the multi-arc orbit, the 360 frames were divided into 320 tilted circular (long arc) frames and 40 short arc frames. The long arc frames were acquired with 2.25° increments in LAO / RAO rotation at each tilt angle. Also, for better sampling coverage, the two titled circles were offset by 1.125° from each other (i.e., frames in the +25° circle were acquired at [0° , 2.25° , 4.5° , ...], and frames in the -20° circle were acquired at [1.125° , 3.375° , 5.625° , ...]). The short arc frames were acquired with 1.125° increments in CRAN / CAUD tilt.

[0069] Figs. 5A and 5B illustrate a robotic C-arm and associated data used to assess the resolution performance of a non-limiting example embodiment. In particular, the same resolution phantom shown and described herein in reference to Figs. 3A and 3B was imaged on a robotic C-arm to test and quantify the resolution performance of a non-limiting example embodiment on a robotic C-arm. Fig. 5A illustrates the physical setup of robotic C-arm with a diagram of the axes, according to the non-limiting example embodiment. In particular, an unmodified clinical Siemens Artis Zeego robotic C-arm system at the Johns Hopkins Hospital was used for theassessment, as shown in Fig. 5A. The multi-arc orbit and a traditional circular orbit were tested, as shown in Fig. 5B. The orbit parameters and acquisition techniques are provided in Table I.

[0070] The bedside joystick and built-in 2D fluoroscopy mode were used to manually drive the multi-arc orbit while acquiring images at 7.5 frames per second (fps). The nominal dose setting was reduced to 0.1 pGy / frame for both 2D fluoroscopy and 3D circular scan protocols to reduce radiation exposure to the operator at the bedside and to match dose levels between 2D and 3D protocols (Table I). Due to automatic exposure control (AEC), there was some dose variability, but the average was close to the nominal dose. For the double-ring and spiral fiducial configurations, 787 and 544 frames were initially acquired, respectively. Frames were discarded during preprocessing so that both noncircular scans had 496 frames to match the total dose of the standard circular scan, and both had 56 short arc frames and 440 tilted circle frames. The discarded frames were chosen so that the remaining frames retained the designed shape of the orbit and were approximately uniformly distributed. The (inaccurate) encoded geometry information recorded from the header of each frame was used to initialize the geometric calibration algorithms (per the initial fiducial localization major process, as shown and described herein in reference to Fig. 1 ). The detector pixels were 2x2 binned into 0.308 mm square pixels. The acquisition process required no modifications to the system. Raw images were extracted with a custom software tool.

[0071] Figs. 6A and 6B illustrate an anthropomorphic phantom and associated data used to assess the resolution performance of a non-limiting example embodiment with a robotic C-arm.

[0072] As shown in Fig. 6A, the anthropomorphic head and thorax phantom was used to test the algorithm in a clinically realistic setting. The head and thorax were two separate modules with a gap just below the C4 vertebra. Ten 2.5 mm spherical stainless steel ball bearings were manually affixed to the exterior of the phantom. The fiducial configuration did not follow any particular patterns such as the aforementioned spiral and double-ring configurations. Rather, the fiducials were placed not too close to each other so that their 2D projections covered a large area of the FOV of the flatpanel detector, a general guideline for fiducial placement for registration and calibration tasks.

[0073] This phantom presented two additional challenges to the algorithm: (1 ) Due to the size of the phantom and the scanning orbits, some fiducials exited and reentered the FOV throughout the scan; and (2) The shoulders were highly attenuating, so at projection angles where some fiducials aligned with both shoulders, the fiducials became difficult or impossible to identify and localize. As a result, the non-limiting example embodiment needed to localize, track, and correctly label a varying and unpredictable number of fiducials.

[0074] For a non-circular orbit implementation using the phantom of Fig. 6A, the same robotic C-arm shown and described in reference to Fig. 5A was used. The orbit parameters are provided in Table I. The circular and multi-arc orbits were performed. Due to the size of the setup, the tilted circle at -20.2° tilt could only cover approximately 200° in LAO / RAO rotation without collision with the table or the phantom. The final orbits as recorded in the projection image headers are shown in Fig. 6B. That is, Fig. 6B illustrates the orbits when performed on the robotic C-arm, as recorded from projection headers, including circular and non-circular orbits. Initially, 569 frames were acquired. In preprocessing, nearly equivalent frames (e.g. frames acquired when the gantry was stationary) and frames outside of the designed range (e.g. short arc frames beyond the designed tilt angles) were discarded, leaving 513 frames for reconstruction, including 63 short arc frames and 450 long arc frames. Nominal dose was reduced for the non-circular acquisitions, no attempt was made to match total dose between the non-circular and circular scans (see Table I).

[0075] Using the targets and setups shown and described in reference to Figs. 3A, 3B, 4A, 4B, 4C, 4D, 5A, 5B, 6A, and 6B, the robustness and resolution performance of the non-limiting example embodiment was evaluated and compared with a benchmark geometric calibration method. Quantitative and qualitative evaluations of spatial resolution were performed on 3D reconstructions.

[0076] To accommodate non-circular orbits and provide high resolution reconstructions of targets (e.g. the tungsten wire) without truncation artifacts (e.g. due to the table and shoulders of the anthropomorphic phantom), a multiresolution modelbased iterative reconstruction (MR-MBIR) algorithm that utilized the penalized weighted least-squares framework with a quadratic regularizer and a separable paraboloidal surrogates optimizer with ordered subsets was applied. The reconstruction parameters are reported in Table I.

[0077] The proposed geometric calibration algorithm does not relate the optimized fiducial locations to common world coordinates. Therefore, to compare different calibration methods, 3D-3D registration using 6 DoF rigid transformation was performed for each reconstruction volume to a common volume, and the transformation was used to re-reconstruct the registered volumes in a common reference frame.

[0078] To reduce the metal artifacts from the steel fiducials in 3D reconstructions, a projection inpainting-based metal artifact reduction algorithm simplified from Kalender et al. was used. 2D masks for the fiducial projections were created using the final predicted 2D fiducial centroids and diameters. With the masks, the fiducials were inpainted using the MATLAB built-in regionfill function (MATLAB and Image Processing Toolbox Release 2022b, The MathWorks, Inc., Natick, Massachusetts, United States). The inpainted projections were used for 3D reconstruction. The fiducial-based geometric calibration and 3D reconstruction were run on a desktop computer with an AMD Ryzen 9 5950x CPU and one NVIDIA RTX 3090 Ti GPU.

[0079] To benchmark the geometric calibration, the geometric calibration of the non-limiting example embodiment was compared to a 3D-2D registration-based method, which had previously been used as a benchmark for calibrating non-circular orbits. The method used a prior reconstruction (e.g. from a calibrated circular scan) as the registration target. An algorithm optimized the system geometry by maximizing the similarity between simulated forward projections from the registration target and measured projections. The 3D-2D registration process was performed on a GPU cluster with seven NVIDIA GTX TITAN X units.

[0080] For spatial resolution, a Modulation Transfer Function (MTF) was used to quantify spatial resolution performance in tests with the resolution phantom. For each scan, a high-resolution wire image was reconstructed around the tungsten wire. The pose of the reconstructed volume was adjusted before the reconstruction so that the wire was nearly vertical in the volume. For each wire image, a 2D point spread function (PSF) image and an MTF curve were calculated after averaging 70 axial slices near the center of the wire, following the method described by Jaffray and Siewerdsen. See D. A. Jaffray and J. H. Siewerdsen, Conebeam computed tomography with a flatpanel imager: Initial performance characterization, Medical Physics 27, 1311-1323(2000), eprint: onlinelibrary.wiley.com / doi / pdf / 10.1118 / 1.599009. Additionally, the frequency response at 20% modulation (F20) was calculated for each MTF curve (higher F20 is better).

[0081] The assessment takes into account different configurations of fiducial subsets. As described above in reference to Fig. 6A, realistic constraints may result in only a subset of the fiducials placed around a phantom / patient being successfully imaged. To address this, the performance was tested using different subsets of four fiducials to emulate different fiducial configurations with a small number of fiducials. Based on empirical evidence, the assessment focused on the effect of different 4- fiducial configurations on the final geometry optimization (steps (3)-(6) of the iterative refinement of fiducial coordinates and geometry major process), assuming the fiducial localization and refinement were sufficiently reliable with 4-fiducial configurations. The input to step (3) was a 4-fiducial subset of the final 2D fiducial localization results from the full 12- or 10-f iducial setups. An exhaustive evaluation of all possible permutations of 4-fiducial configurations was performed.

[0082] Because an evaluation of 3D reconstructions of all permutations was impractical, the assessment compared the predicted 2D centroids using the estimated geometry from 4-fiducial configurations (Q.subset) against those from the full fiducial configurations (ftMn) following steps 4 and 7 of the iterative refinement of fiducial coordinates and geometry major process. The mean Euclidean distance (c ) between predictions using Q.subsetandfuUacross all frames was calculated as a surrogate for calibration performance (lower d2D is better). The assessment only compared predicted 2D centroids of the unchosen fiducials (e.g. the other eight fiducials of a 12 -fiducial phantom). Evaluating the unchosen fiducials, rather than the four chosen ones, mitigated biases in configurations with only closely clustered fiducials, whose RPE values did not truly represent overall performance across the full FOV. 3D reconstructions were created for the best case (cfeo, min), worst case (d2D, max), and median case (comedian). Permutation numbers of configurations are reported in Table I and explained below.

[0083] It is hypothesized that a predictor of a suitable 4-fiducial configuration for geometric calibration was the volume of the tetrahedron ( oltet) formed with the four fiducials as vertices (covering a large area of the detector FOV). The relationship between voltet and d2D was evaluated.

[0084] For the resolution phantom scans, 495 permutations of 4-fiducial configurations were performed from the spiral and double-ring configurations, yielding a total of 990 cases. In a few cases, roughly 1 % of all frames contained one fiducial obscured by metallic screws in the patient table, leaving three of four fiducials visible. This effect was negligible and did not include applying special treatment to these frames. The tests were only run on the multi-arc scans. The voltet - d2D relationship was plotted. Quantitative MTF analysis and visual quality comparisons were performed on the reconstructions of the best, worst, and median cases.

[0085] Regarding the anthropomorphic phantom on the C-arm, due to the size of the anthropomorphic phantom, different numbers of fiducials were visible depending on the orbit used. In the circular scan, three fiducials placed near the top of the skull never entered the FOV. Of the remaining seven, only six appeared in over half of the frames. So, the exhaustive evaluation of 4-fiducial configurations from six available fiducials contained 15 different permutations. In the multi-arc scan, eight fiducials appeared in at least half of all projections, and configurations were chosen that contained at least three visible fiducials in at least half of all frames, which accounted for 17 different permutations. Visual quality comparisons were performed on high- resolution 3D reconstructions of the C4 vertebra for the best, worst, and median cases.

[0086] Results of the assessment are summarized in Tables II and III and shown and described in reference to Figs. 7, 8A, and 8B.Table

[0087] Table II provides a summary of the RPEs of the non-limiting example embodiment and the speed performance. Columns 2-4 correspond to the respective experimental setups shown and described in reference to Figs. 3A, 3B, 4A, 4B, 4C, 4D, 5A, 5C, 6A, and 6B. Frame size refers to cropped frames for reducing processing time. The speed from each of the three major processes shown and described in reference to Fig. 1 is reported separately. The test bench results are grouped by different motion error amplitudes to illustrate a notable trend. The 3D-2D registration speed refers to the processing time on a single GPU without parallelization. Table II shows that an increase in the motion error amplitude corresponds to an increase in the Mean RPEs and the processing time for the iterative refinement major process. The processing time per frame using the non-limiting example embodiment is substantially lower than the benchmark method.

[0088] Figs. 7A, 7B, and 7C show an example RPE plot and reconstructions from a sinusoidal orbit scan with 1x nominal motion errors and the spiral fiducial configuration, according to an example non-limiting embodiment. Fig. 7A depicts a violin plot showing the RPEn from the geometric calibration process. Each dot represents the RPEn for a frame. The horizontal blue line indicates the mean. The white dot indicates the median. Fig. 7B shows an axial slice near the center of the phantom. The display window is [ u min u max] = [0 0.04], Fig. 7C shows an axial slice using MR-MBIR with 0.02 mm isotropic voxels centered at the tungsten wire with overlaying contour map. The display window is [ u min u max] = [0 0.3],

[0089] In Fig. 7A, the RPE plot contains several outliers, but the image quality does not show noticeable deterioration. In Figs. 7B and 7C, the example reconstructed phantom looks clearly resolved, and the PSF appears circular. All other reconstructions are visually indistinguishable and therefore not shown.

[0090] Figs. 8A and 8B show MTF and F20 results from the assessment of the non-limiting example embodiment. Fig. 8A shows MTF curves from all orbits, fiducial configurations, motion error levels, and calibration methods. Fig. 8B shows plots F20 values at different amplitudes of motion error. Experiments are encoded using acombination of line style and marker style. The circular scans are plotted as horizontal dotted lines to serve as a baseline with no motion error.

[0091] In Fig. 8A, all MTF plots appear similar and almost overlap. In Fig. 8B, across all nominal motion error amplitudes, the F20 values are within a small range of 1 .5-1 .6 cycles / mm with a slight decrease with exaggerated motion errors.Table III

[0092] Table III summarizes key comparisons of F F20 values. Except for the comparison of the proposed fiducial-based method against the benchmark 3D-2D registration method, all other comparisons are within the fiducial-based method to best evaluate factors affecting the proposed method. All comparisons result in a mean difference of < 1 %.

[0093] Figs. 9A, 9B, 9C, and 9D present the results of the resolution performance assessment using a robotic C-arm and cylindrical phantom design, according to a non-limiting example embodiment. That is, the results of using both 12-fiducial configurations and 4-fiducial robustness experiments are summarized in Figs. 9A, 9B, 9C, and 9D. The RPE and speed performance for the 12-fiducial configurations are summarized in Table II.

[0094] Fig. 9A presents diagrams of the 3 selected representative 4-fiducial configurations. The 4 selected fiducials are marked as solid black disks and connected to form tetrahedrons.

[0095] Fig. 9B shows PSFs and contours with their respective F20. Experiments are differentiated by underlined labels to the rows and columns.

[0096] Fig. 9C shows a plot of d2D vs voltet values from all 4-fiducial configurations.

[0097] Fig. 9D presents example axial and sagittal slices of reconstructions of using the calibration from the worst 4-fiducial configuration and the reference calibration. In Fig. 9D, references 952 and 954 correspond to PSF 910, and references 962 and 964 correspond to PSF 922. 3 axial slices are averaged to reduce noise.

[0098] Due to the non-circularity of the PSFs in Fig. 9B, their mean MTFs, defined as the mean of the MTFs in the x- and y-directions, were calculated. The corresponding F20 values were calculated via linear interpolation and are reported in Fig. 9B. In Fig. 9B, except for the worst 4-fiducial configuration, all other calibration settings and methods performed similarly, with F20 values between 1.93 cycles / mm and 2.04 cycles / mm. Phantom reconstructions of the similarly performing cases are visually indiscernible from the reference images in 962 and 964 (Fig. 9D) and are therefore not shown. Figs. 9A, 9B (910, 912, and 914), 9C, and 9D (952 and 954) and summarize the results from the 4-fiducial configuration robustness experiments. In Fig. 9A, the worst configuration clustered the fiducials in a small area on the side wall of the cylinder; the median configuration placed the fiducials roughly in a slanted plane close to the axial plane; and the best configuration distributed the fiducials throughout the phantom, forming a large tetrahedron. The corresponding F20, d2D, and voltet values are marked in and under Fig. 9B (910, 912, and 914). The worst and median configurations have small voltet values of 10.01 cm3and 4.23 cm3, respectively. The best configuration has a much larger voltet value of 173.75 cm3. Between Fig. 9D references 952 and 962, the worst 4-fiducial configuration is slightly blurrier in the horizontal direction, which is consistent with the shape of the PSF in Fig. 9B, reference 910. Between Fig. 9D, references 954 and 964, reference 954 presents more streaking artifacts near the top and bottom of the FOV. Fig. 9C shows a clear trend of decreasing d2D with increasing voltet. Low-voltet configurations (< 50 cm3, for example) can result in a wide range of d2D values, but all high-vo / fef configurations (> 150 cm3) have d2D values below 0.5 pixels.

[0099] Figs. 10 and 11 present the results of the resolution performance assessment using a robotic C-arm, according to a non-limiting example embodiment. In particular, for the anthropomorphic experiments on the robotic C-arm, Figs. 10 and 11 show the reconstructions from the circular scan and multi-arc scan, respectively. The RPE and speed performance for the 10-fiducial configurations are summarized in Table II.

[0100] References 10A, 10B, 10C depict tetrahedron diagrams of selected 4- fiducial configurations. Brighter and darker spheres indicate fiducials on the ventral and dorsal surfaces of the phantom, respectively. Reference 10D is a plot showing the tracked fiducials in each frame. Un-tracked fiducials are shown as discontinuitiesin the horizontal lines. References 10E-10X show axial and sagittal slices of the C4 vertebra from MR-MBIR using different calibration results. The voxel sizes for lower- resolution and higher-resolution images are 0.5 mm and 0.1 mm, respectively. The ROIs of the higher-resolution images are marked as dark blue rectangles in the lower- resolution images. The d2D, voltet, and number of frames with only 3 fiducials tracked are marked under references 10T, 10U, and 10V. No slice averaging was applied.

[0101] In the circular scan represented in Fig. 10, fiducials #6 and #7 were intermittently tracked due to disappearing and reappearing the FOV (reference 10D). Fiducials #8 - 10 never entered the FOV. The algorithm was initialized to search for 10 fiducials and automatically and correctly concluded with 7 fiducials without false positives. The left three columns of Fig. 10 (references 10E, 10F, 10G, 10J, 10J, 10L, 10O, 10P, 10Q, 10T, 10U, 10V) show reducing streaking and blurring around anatomical structures from the worst to the best 4-fiducial configurations in low- and high-resolution images. The worst configuration has the lowest voltet with the fiducials almost placed co-planar and closely around the back of the head and shoulder (reference 10A). Despite all 4 fiducials being visible in all frames, this placement underperforms the median case, which contains 104 frames with only 3 fiducials visible. The best configuration has a lower voltet than the median configuration but all frames contain 4 visible fiducials. The right three columns (references 10H, 101, 10M, 10N, 10R, 10S, 10W, 10X) show visually comparable image quality, clearly resolving the same fine features such as the trabecular bone.

[0102] Regarding Fig. 11 , references 11 A, 11 B, and 11 C depict tetrahedron diagrams of selected 4-fiducial configurations. Brighter and darker spheres indicate fiducials on the ventral and dorsal surfaces of the phantom, respectively. Reference 11 D depicts a plot showing the tracked fiducials in each frame. Un-tracked fiducials are shown as discontinuities in the horizontal lines. References 11 E-11X show axial and sagittal slices of the C4 vertebra from MR-MBIR using different calibration results. The voxel sizes for lower-resolution and higher-resolution images are 0.5 mm and 0.1 mm, respectively. The ROIs of the higher-resolution images are marked as rectangles in the lower-resolution images. The d2D, voltet, and number of frames with only 3 fiducials tracked are shown in references 11T, 11 U, and 11V. To reduce image noise, 3 and 7 slices were averaged for the lower- and higher-resolution images, respectively.

[0103] In the multi-arc scan represented in Fig. 11 , all 10 fiducials entered the FOV and were tracked (references 11 D). Fiducials #1 , #2, #5, and #6 were continuously tracked throughout the scan; the rest were tracked intermittently due to limited FOV and blockage. Note that of the 10 fiducials, only 6 - 8 fiducials were in the FOV simultaneously in any frame, and the algorithm automatically and correctly tracked and labeled them as 10 distinct fiducials. The left three columns of Fig. 11 (references 11 E, 11 F, 11 G, 11 J, 11 K, 11 L, 110, 11 P, 11 Q, 11T, 11 U, 11V) show reducing blurring near fine bony features from the worst to the best 4-fiducial configurations. Compared to the circular scans in Fig. 10, the difference in spatial resolution between the median and the best configurations is less pronounced and is better observed in the high-resolution images (references 11 K, 11 L, 11 U, 11V). The worst configuration uses a small tetrahedron near the left cheek and shoulder and contains 178 frames with only 3 fiducials. The median and best configurations have comparable voltet, but the median configuration contains 197 frames with only 3 fiducials, while the best configuration contained none. The right three columns (references 11 H, 111, 11 M, 11 N, 11 R, 11 S, 11W, 11X) show visually comparable image quality.

[0104] As presented here, the non-limiting example embodiment demonstrated fast, accurate, and robust performance in a number of physical experiments. Full automation made use of integration of automatic initial fiducial localization, robust fiducial coordinate labeling, and iterative refinement of fiducial localization and geometry (all shown and described in reference to Fig. 1 ). The fiducial labeling process allowed initial localization of fiducials in any order; and the iterative refinement recovered lower-contrast fiducials that may be missed by the initial localization. Together, the processes enabled the use of an imprecise but automatic initial fiducial localization. The non-limiting example embodiment therefore preserved the advantages of the previously implemented fiducial-based method while addressing the challenge of human-assisted fiducial localization and coordinate labeling in many existing methods. The only input obtained from the operator was an estimate of the number of fiducials available in the FOV, minimizing the burden to the clinicians.

[0105] The non-limiting example embodiment was designed to be modular, using available packages and MATLAB built-in functions where possible; therefore, implementation and customization are relatively easy. While it is possible to potentiallyreduce processing time and assist in fiducial labeling by defining small, moving ROIs for fiducial searching based on neighboring frames and initializing geometry, doing so may risk missing a large number of fiducials, particularly after an ROI reaches the edge of the FOV or when heavy attenuation occurs (obscuring some fiducials at certain angles). Instead, the non-limiting example embodiment performed localization on full images to maximize the number of identified fiducials. Because each frame is processed independently, the initialization can be parallelized and / or run concurrently with data acquisition.

[0106] The speed performance in Table II shows that the non-limiting example embodiment was substantially faster than the benchmark 3D-2D registration method. Additionally, the initial fiducial localization process in all experiments was faster than the 7.5 fps (-0.133 s / frame) acquisition frame rate on the robotic C-arm, indicating that this process may be performed during acquisition without contributing to the overall processing time for geometric calibration. The fiducial coordinate label process only took less than 1 second to process all localized centroids. While the iterative refinement process took several minutes, the process was not parallelized in these studies, which leaves room for further reducing processing time according to other embodiments. In applications where fiducials are easily localized and labeled during initialization, such as offline calibration and imaging of low-attenuation targets, the outer loop of the iterative refinement may not require repetitions, which can further reduce processing time.

[0107] The spatial resolution experiments on the test bench demonstrated the performance of the non-limiting example embodiment with exaggerated amounts of motion errors and different fiducial configurations. While Table II shows a notable increase in RPE with increasing motion error amplitude, the reconstructed images and MTF calculations show minimal changes in spatial resolution. This suggests that the image blur in the system was dominated by other factors than the accuracy of geometric calibration. The increase in processing time in the iterative refinement process may be explained by the larger deviations that needed to be recovered through optimization. There is a small difference in performance between the sinusoidal orbit and the multi-arc orbit, but the reconstructed images do not visually reflect the differences. These results suggest that the non-limiting exampleembodiment is highly accurate and robust for systems with varying levels of mechanical stability.

[0108] The spatial resolution experiments on the Zeego C-arm demonstrated that the non-limiting example embodiment remained highly accurate and robust on a real clinical robotic C-arm system. Moreover, the 4-fiducial configuration experiments offer insights into optimal fiducial configuration for the geometric calibration task. Although some configurations with closely clustered fiducials can produce good calibration results, maximizing the volume of the convex polyhedron formed by the fiducials is more likely to guarantee a higher quality geometric calibration. Also, using more than 4 fiducials enhances robustness against cases with disappearing fiducials in the FOV. These insights agree with the guideline that high fiducial separation and more fiducials should benefit calibration tasks. Another finding is that as d2D decreases below a certain threshold, the image blur caused by geometric inaccuracies may become negligible, which may be relevant for task-based imaging. A certain imaging task may be less sensitive to geometric inaccuracies if it use a sufficiently large voxel size, or if other sources of blur become dominant. In this case, the operator may choose a more convenient fiducial configuration, even if it may not be theoretically optimal for geometric calibration.

[0109] The anthropomorphic experiments on the Zeego C-arm added realistic constraints and challenges. The large and highly attenuating phantom introduced the additional challenges that (1 ) fiducials may be intermittently visible in the FOV due to limited FOV size and / or photon starvation, and that (2) the number of fiducials available in the FOV may be different from the number of fiducials placed by the operator. The non-limiting example embodiment demonstrated robustness against these challenges by automatically and correctly tracking and labeling only the available fiducials in the projections. In the 4-fiducial configuration studies, a good 4- fiducial configuration could perform as well as the reference methods in high-resolution imaging. Using a higher number of fiducials (e.g., 10 fiducials) provided configuration redundancy and hence reduced the need to optimize fiducial configurations. These findings suggest that in a clinical workflow, the operator may place fiducials liberally around the patient without knowing the exact number of fiducials in the FOV, and an embodiment can automatically track the fiducials available for calibration, reducing the burden to the operator.

[0110] While the presented physical experiments were based on a 6 DoF assumption, one may easily add or further reduce dimensions based on the orbit and system design. Prior knowledge of the sensitivity of a system to geometric misalignments in different dimensions may aid the optimization process.

[0111] Embodiments may be useful in applications other than intraoperative image guidance. For example, for offline geometric calibration, a precisely manufactured calibration phantom is typically required, which may be unavailable. Because the proposed algorithm also estimates the 3D fiducial locations, one may use an inaccurately-manufactured fiducials phantom and simultaneously calibrate a scanner and estimate the precise configuration of the fiducials. The phantom then becomes a known model and can be subsequently used for both offline and online calibration tasks. Robotic arms-based industrial CBCT using arbitrary orbits may also benefit from various embodiments for non-destructive testing.

[0112] Thus, a method for fully automatic online geometric calibration of arbitrary CBCT orbits using fiducials with unknown placement is disclosed. The nonlimiting example implementation proved via physical experiments to be fast, accurate, easy to operate, easily adaptable to different imaging systems, and robust against several practical challenges. Embodiments may be easily implementable and adaptable to different CBCT systems and imaging tasks. Embodiments may allow for novel non-circular 3D scanning orbits for intraoperative image guidance. Potentially, an embodiment can help improve existing offline geometric calibration, as it does not require a precisely manufactured calibration phantom. It may also be adapted for industrial CBCT using robotic arms.

[0113] Certain examples can be performed using a computer program or set of programs. The computer programs can exist in a variety of forms both active and inactive. For example, the computer programs can exist as software program (s) comprised of program instructions in source code, object code, executable code or other formats; firmware program(s), or hardware description language (HDL) files. Any of the above can be embodied on a transitory or non-transitory computer readable medium, which include storage devices and signals, in compressed or uncompressed form. Exemplary computer readable storage devices include conventional computer system RAM (random access memory), ROM (read-only memory), EPROM (erasable,programmable ROM), EEPROM (electrically erasable, programmable ROM), flash memory, and magnetic or optical disks or tapes.

[0114] Aspects of the present disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented using computer readable program instructions that are executed by an electronic processor.

[0115] These computer readable program instructions may be provided to a processor of a general-purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the electronic processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function / act specified in the flowchart and / or block diagram block or blocks.

[0116] In embodiments, the computer readable program instructions may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, statesetting data, configuration data for integrated circuitry, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the C programming language or similar programming languages. The computer readable program instructions may execute entirely on a user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server.

[0117] As used herein, the terms “A or B” and “A and / or B” are intended to encompass A, B, or {A and B}. Further, the terms “A, B, or C” and “A, B, and / or C” are intended to encompass single items, pairs of items, or all items, that is, all of: A, B, C, {A and B}, {A and C}, {B and C}, and {A and B and C}. The term “or” as used herein means “and / or.”

[0118] As used herein, language such as “at least one of X, Y, and Z,” “at least one of X, Y, or Z,” “at least one or more of X, Y, and Z,” “at least one or more of X, Y, or Z,” “at least one or more of X, Y, and / or Z,” or “at least one of X, Y, and / or Z,” is intended to be inclusive of both a single item (e.g., just X, or just Y, or just Z) and multiple items (e.g., {X and Y}, {X and Z}, {Y and Z}, or {X, Y, and Z}). The phrase “at least one of” and similar phrases are not intended to convey a requirement that each possible item must be present, although each possible item may be present.

[0119] The techniques presented and claimed herein are referenced and applied to material objects and concrete examples of a practical nature that demonstrably improve the present technical field and, as such, are not abstract, intangible or purely theoretical. Further, if any claims appended to the end of this specification contain one or more elements designated as “means for [perform]ing [a function]...” or “step for [performing [a function]...”, it is intended that such elements are to be interpreted under 35 U.S.C. § 112(f). However, for any claims containing elements designated in any other manner, it is intended that such elements are not to be interpreted under 35 U.S.C. § 112(f).

[0120] While the invention has been described with reference to the exemplary examples thereof, those skilled in the art will be able to make various modifications to the described examples without departing from the true spirit and scope. The terms and descriptions used herein are set forth by way of illustration only and are not meant as limitations. In particular, although the method has been described by examples, the steps of the method can be performed in a different order than illustrated or simultaneously. Those skilled in the art will recognize that these and other variations are possible within the spirit and scope as defined in the following claims and their equivalents.

Claims

What is claimed is:1 . A method of radiological tomographic imaging using a first target, wherein the first target is three dimensional, and wherein a plurality of fiducials are positioned relative to the first target, the method comprising: obtaining an initial fiducial localization of at least some of the plurality of fiducials using a radiological imaging machine; labeling, based on the initial fiducial localization, fiducial coordinates of at least some of the plurality of fiducials, wherein the labeling is based on a plurality of long traces; refining the fiducial coordinates based on the labeling the fiducial coordinates; determining, based on the fiducial coordinates, a geometry of the radiological imaging machine; and acquiring, using the radiological imaging machine and based on the geometry of the radiological imaging machine, a tomographic image of a second target.

2. The method of claim 1 , further comprising: combining at least two disjoint long traces of the plurality of long traces, wherein the at least two disjoint long traces correspond to a same fiducial.

3. The method of claim 1 , wherein the refining comprises: updating three dimensional centroid location estimates for the fiducials; predicting two dimensional fiducial locations in images; and designating regions of interest as the predicted two dimensional centroid locations.

4. The method of claim 3, further comprising iterating the updating, the predicting, and the designating.

5. The method of claim 1 , wherein the obtaining the initial fiducial localization comprises: performing background subtraction; performing edge detection; andperforming circle detection.

6. The method of claim 1 , wherein the radiological imaging machine comprises a radiation source and a detector, wherein the geometry comprises an orientation of the detector and at least one of a location of the detector or a location of the radiation source.

7. The method of claim 1 , wherein the first target comprises the second target.

8. The method of claim 7, wherein the radiological imaging machine comprises a radiation source and a detector, and wherein positions of the source and the detector during the acquiring are not reproducible.

9. The method of claim 1 , wherein the first target is different from the second target, and wherein the determining comprises calibrating the radiological imaging machine.

10. The method of claim 1 , wherein each of the plurality of long traces comprise at least 20 images.

11. A system for radiological tomographic imaging using a first target, wherein the first target is three dimensional, and wherein a plurality of fiducials are positioned relative to the first target, the system comprising a non-transitory computer readable medium comprising instructions, and at least one electronic processor that executes the instructions, to perform operations comprising: obtaining an initial fiducial localization of at least some of the plurality of fiducials using a radiological imaging machine; labeling, based on the initial fiducial localization, fiducial coordinates of at least some of the plurality of fiducials, wherein the labeling is based on a plurality of long traces; refining the fiducial coordinates based on the labeling the fiducial coordinates;determining, based on the fiducial coordinates, a geometry of the radiological imaging machine; and acquiring, using the radiological imaging machine and based on the geometry of the radiological imaging machine, a tomographic image of a second target.

12. The system of claim 11 , wherein the operations further comprise: combining at least two disjoint long traces of the plurality of long traces, wherein the at least two disjoint long traces correspond to a same fiducial.

13. The system of claim 11 , wherein the refining comprises: updating three dimensional centroid location estimates for the fiducials; predicting two dimensional fiducial locations in images; and designating regions of interest as the predicted two dimensional centroid locations.

14. The system of claim 13, wherein the operations further comprise iterating the updating, the predicting, and the designating.

15. The system of claim 11 , wherein the obtaining the initial fiducial localization comprises: performing background subtraction; performing edge detection; and performing circle detection.

16. The system of claim 11 , wherein the radiological imaging machine comprises a radiation source and a detector, wherein the geometry comprises an orientation of the detector and at least one of a location of the detector or a location of the radiation source.

17. The system of claim 11 , wherein the first target comprises the second target.

18. The system of claim 17, wherein the radiological imaging machine comprises a radiation source and a detector, and wherein positions of the source and the detector during the acquiring are not reproducible.

19. The system of claim 11 , wherein the first target is different from the second target, and wherein the determining comprises calibrating the radiological imaging machine.

20. The system of claim 11 , wherein each of the plurality of long traces comprise at least 20 images.

Images