Patent Publication Number: US-2021166424-A1

Title: Methods and systems of registering a radiographic image and a 3d model of an external fixation device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority benefit from International Application No. PCT/US2019/043326 filed on Jul. 24, 2019, which claimed priority from U.S. Provisional Application No. 62/702,378 filed Jul. 24, 2018, each of which is incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present disclosure generally relates to systems and methods for registration of a two-dimensional image (e.g., a radiographic image) and a three-dimensional model of a fixation device (e.g., an external fixation device) for deformity and/or orthopedic analysis and/or correction. The systems and methods determine the relative position and orientation/pose of an image of anatomical structure of interest (e.g., two or more bone segments) and a known fixation device (e.g., an external fixation device, such as a hexapod) secured to the anatomical structure of interest relative to the fixation device. In some embodiments, the systems and methods determine the focal point of the image and account for perspective distortion in the image, and create a coordinate transformation matrix) 
     The methods and systems of the disclosure enable generation of a three-dimensional computer model of bone segments and a fixation device (e.g., an external fixation device) for the planning of movement of the bone segments into desired locations via the fixation device. For example, through operations on the model, desired position and orientation/pose of the bone segments and adjustments of the fixation device to achieve such desired placement can be determined quickly and accurately regardless of the initial configuration of the fixation device. The operations required to create the desired position and orientation/pose of the bone segments may then be enacted on the corresponding fixation device and bone segments to achieve the desired position and orientation/pose. However, other devices other than external fixation device may be utilized with the system and methods. 
     BACKGROUND 
     The correction of orthopedic deformities usually involves at a minimum a pair of x-ray radiographs. Typically, these radiographs of the patient are attempted to be taken along the conventional lines of an anterior to posterior (AP) direction as well as a medial to lateral (ML) direction, or along other orthogonal or known vantage points (or known difference between vantage points). In accordance with convention, the AP and ML radiographs are taken or assumed to be orthogonal to each other in patient space (the patient space being defined as having the X axis aligned from right to left, the Y axis aligned from anterior to posterior, and the Z axis aligned with inferior to superior). Measurements are made, and deformity axes and points are annotated, within the pair of radiographs. These measurements and annotations within the pair of radiographs are then compared or otherwise used to reconstruct a  3 -dimensional representation of the deformity in order that the deformity can be manipulated by some means to correct the condition. 
     However, inaccuracy in the vantage points of the pair of radiographs, and their spatial relationship to each other, results in an inaccurate representation of the patient and objects coupled thereto contained in the images (i.e., artifacts shown in the images). Radiographs and other patient imaging techniques do not produce perfect images of the artifacts contained within those images. The relationship between the artifacts shown in an image and the actual objects being imaged is one of perspective such that those objects that lie closer to the image have a smaller amount of magnification than those that lie further away. In addition, the vantage points of the images are not perfectly aligned with conventional lines/vantage points (and thereby a pair of images are not truly orthogonal) as the arrangement of the patient with respect to the focal point of the imager is a manual operation. By not accounting for these aspects/inaccuracies of the images, 3D reconstructions of the patient and/or objects coupled thereto contained in the images are not true representations thereof. 
     As a result, systems and methods that account for the uncertainties/inaccuracies of images of a portion of patient and objects coupled thereto, and construct a true 3D model thereof, are needed. Further, systems and methods that determine the position and pose/orientation of an image of a portion of patient and objects coupled thereto with respect to the objects, on a per-image basis, are needed. 
     While certain aspects of conventional technologies have been discussed to facilitate disclosure of Applicant&#39;s inventions, the Applicant in no way disclaims these technical aspects, and it is contemplated that their inventions may encompass one or more conventional technical aspects. 
     In this specification, where a document, act or item of knowledge is referred to or discussed, this reference or discussion is not an admission that the document, act or item of knowledge or any combination thereof was, at the priority date, publicly available, known to the public, part of common general knowledge, or otherwise constitutes prior art under the applicable statutory provisions; or is known to be relevant to an attempt to solve any problem with which this specification is concerned. 
     SUMMARY OF THE INVENTION 
     The present invention may address one or more of the problems and deficiencies of the art discussed above. However, it is contemplated that the invention may prove useful in addressing other problems and deficiencies in a number of technical areas. Therefore, the claimed invention should not necessarily be construed as limited to addressing any of the particular problems or deficiencies discussed herein. 
     In some embodiments, a radiographic or other image of a portion of a patient and objects coupled thereto contains the shadows of the three-dimensional objects that were posed and positioned/located above/below that image (e.g., the film in a radiographic image) when taken. The apparent source location and orientation of the image source (e.g., x-ray source) with respect to the image that is casting that shadow is unknown. 
     In an ideal world, the focal point of the imager would be a point source placed at an infinite distance above and centered on the image itself. An ideal representation would result in the shadow in the image being a true two-dimensional projection of the actual three-dimensional object. If two such ideal images/representations are obtained, and it is known the images/representations are orthogonal to each other about a common axis, the two sets of two-dimensional data can be directly utilized to accurately reconstruct a three-dimensional model of the object and its position and pose in space. 
     However, this is not generally possible given that the current state of the art in patient imagery (e.g., radiographic technology involving plain film radiographs) results in perspective distortion, as discussed above. Additionally, the likelihood that the images (e.g., radiographs) are taken truly orthogonal to both the trajectory of the image source and orthogonal to each other about a common axis, is also quite unlikely given all the variables involved in acquiring those images on the actual imaging machine (e.g., an x-ray machine) with an actual patient being instructed to lie/pose in prescribe ways, for example. 
     The system and methods of the present disclosure utilize the two main sources of error, focal point position and pose as well as patient orientation, to draw a number of conclusions to, ultimately, correct/account for the actual perspective/vantage point of an image and construct a true three-dimensional model of the objects within the image (and potentially the image itself). 
     The computer-based systems and methods may consider perspective distortion by determining portions (e.g., radiopaque portions) of an object coupled to the patient that are of a particular shape and potentially size (e.g., spherical elements) and the shadows they casted in a single image (e.g., a single radiographic image) (or on a per-image basis). For example, the system and methods may utilize a multitude of known portions of the object in the image, the shadows of which are present as artifacts in the image, and the known relative shape and size of the portions, and relationship of the portions to each other, to determine the apparent focal point location and pose of the image source (e.g., the x-ray source for a radiographic image). 
     The system and methods may determine the position and pose of the three-dimensional collection of known portions of the object in the image space using a plurality of closed vector loops through the shadow centers, the centers of the actual portions casting the shadows, and the focal point location of the imager. With the plurality of closed vector loops determined, the system and methods may construct a coordinate transform matrix for the collection of the known three-dimensional portions of the object in a shadow image space (i.e., determine a row dimension, a column dimension and a height dimension). 
     In a first aspect, this disclosure provides methods and systems that utilize known three-dimensional collection of objects, the shadows of which are cast in a 2-dimensional x-ray radiographic space, to determine the actual position and pose of that known collection of objects in a projected, and computer-modeled, three-dimensional space lying above the 2-dimensional radiographic space. 
     In some embodiments, the methods and systems may utilize perspective distortion to determine relative magnifications to aid in the reconstruction of the three-dimensional projected space. In some embodiments, the methods and systems may reconstruct a model of the actual three-dimensional conditional in a corrected relative spatial arrangement. 
     Certain embodiments of the presently-disclosed systems and methods may include several features, no single one of which is solely responsible for their desirable attributes. Without limiting the scope of the systems and methods, their more prominent features will now be discussed briefly. After considering this discussion, and particularly after reading the section of this specification entitled “Detailed Description of the Invention,” one will understand how the features of the various embodiments disclosed herein provide a number of advantages over the current state of the art. 
     These and other features and advantages of this invention will become apparent from the following detailed description of the various aspects of the invention taken in conjunction with the appended claims and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure will hereinafter be described in conjunction with the following drawing figures, which are not necessarily drawn to scale for ease of understanding, wherein the same reference numerals retain their designation and meaning for the same or like elements or aspects throughout the various drawings, and wherein: 
         FIG. 1  is a perspective view of an exemplary external fixation device coupled to exemplary bone segments; 
         FIG. 2  is a front view of a two-dimensional radiographic image depicting an exemplary external fixation device coupled to exemplary bone segments; 
         FIG. 3  is a perspective view of a constructed digital three-dimensional model including a digital two-dimensional radiographic image and a digital three-dimensional model of an external fixation device represented in the model in correct relative positions and poses with respect to a determined focal point of the radiographic image; 
         FIG. 4  is a flow diagram of an exemplary method of digitally registering a radiographic image and a three-dimensional model of an external fixation device depicted in the radiographic image; 
         FIG. 5  depicts an exemplary method for digitally constructing a coordinate transformation matrix that identifies the position and pose of a radiographic image relative to a three-dimensional model of an external fixation device depicted in the radiographic image; 
         FIG. 6  depicts an exemplary computer system that may be utilized to perform aspects of the present disclosure; and 
         FIG. 7  depicts an embodiment of a computer program product that may incorporate of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Aspects of the present inventions and certain features, advantages, and details thereof, are explained more fully below with reference to the non-limiting embodiments illustrated in the accompanying drawings. Descriptions of well-known materials, fabrication tools, processing techniques, etc., are omitted so as to not unnecessarily obscure the inventions in detail. It should be understood, however, that the detailed description and the specific example(s), while indicating embodiments of the inventions, are given by way of illustration only, and are not by way of limitation. Various substitutions, modifications, additions and/or arrangements within the spirit and/or scope of the underlying inventive concepts will be apparent to those skilled in the art from this disclosure. 
     Referring initially to  FIG. 1 , bodily tissues, for instance first and second bone segments  102 ,  104 , can be aligned and/or oriented to promote union or other healing between the bodily tissues. The alignment and/or orientation of the bodily tissues can be achieved by connecting the bodily tissues to an adjustable fixation apparatus, such as an orthopedic external fixation device or fixator  100 . The fixation device can comprise a plurality of discrete fixator platforms or members that remain external to the patient&#39;s body, but that are attached to respective discreet bodily tissues, for example with minimally invasive attachment members. By adjusting the spatial positioning of the platforms with respect to each other, the respective bodily tissues attached thereto can be reoriented and/or otherwise brought into alignment with each other, for example to promote union between the bodily tissues during a healing process. The use of external fixation devices in combination with the imagery analysis and positioning techniques described herein can be advantageous. 
     The fixator members can be connected to each other via adjustment struts or members, the adjustment struts configured to facilitate the spatial repositioning of the platforms with respect to each other. For example, in the illustrated embodiment shown in  FIG. 1 , the external fixation device  100  comprises a pair of platforms or fixator members in the form of at least one upper ring platform  106  and a lower ring platform  108 . The platform rings  106 ,  108  can be constructed the same or differently. For instance, the platform rings  106 ,  108  can have diameters that are the same or different. Similarly, the platform rings  106 ,  108  can be constructed with varying cross sectional diameters, thicknesses, etc. It should be appreciated that the fixator members of the fixation device  100  are not limited to the illustrated upper and lower platform rings  106 ,  108 , and that the fixation device  100  can be alternatively constructed. For example, additional fixator rings can be provided and interconnected with the upper ring platform  106  and/or the lower ring platform  108 . It should further be appreciated that the geometries of the platforms are not limited to rings, and that at least one, such as any or all of the platforms can be alternatively constructed using any other suitable geometry. 
     The first and second bone segments  102 ,  104  can be rigidly attached to the upper and lower platform rings  106 ,  108 , respectively, with attachment members (not shown) that can be mounted and/or coupled to the platform rings  106 ,  108 . For example, the external fixation device may include attachment rods and/or attachment wires (not shown) that are fixed or coupled to the upper and lower platform  106 ,  108  (e.g., directly or via a clamp or any other mounting mechanism configuration) and to the first and second bone segments  102 ,  104 , respectively. 
     The attachment members can be removably mounted to the platform rings  106 ,  108  at predefined points along the peripheries of the platform rings  106 ,  108 , for example by coupling them to apertures defined by the platforms  106 ,  108 . With respect to each platform  106 ,  108 , the attachment members and/or mounting mechanisms or members coupled therewith can be mounted to the upper surface of the platform, the lower surface of the platform, or any combination thereof. It should be appreciated that the configuration of the attachment members is not limited to the configurations discussed above. For example, any number of attachment members, such as any number of pins, wires or the like, can be used to secure the bone segments  102 ,  106  and to a respective platform  106 ,  108  as desired. It should further be appreciated that one or more of the attachment members can be configured to mount or couple directly to/with the platforms  106 ,  108  without utilizing an intermediary or additional mounting mechanism, or may be configured to mount indirectly to the platforms  106 ,  108  via a mounting mechanism or with the assistance or aid of a mounting mechanism. 
     The upper and lower platform  106 ,  108  of the external fixation device  100  are connected to each other by a plurality of adjustment struts or members  110 , as shown in  FIG. 1 . At least one, such as all, of the adjustment struts can be configured to be adjusted to adjust the spatial positioning and pose of the platforms  106 ,  108  with respect to each other. For example, in the illustrated embodiment, the upper and lower platform rings  106 ,  108  are connected to each other with six circumferentially-spaced length adjustable struts  110  that extend therebetween (at least partially). The external fixation device  100  may thereby comprise a hexapod or Stewart platform. It should be appreciated, however, that the construction of the fixation device  100  is not limited to the six struts  110  of the illustrated embodiment, and that more or fewer struts  110  can be utilized as desired. 
     As shown in  FIG. 1 , one or more of the length adjustable struts  110  can comprise an axially-elongate threaded rod portion  112  rotatably coupled to one of the first and second platforms  106 ,  108  via a joint  116 , and an axially-elongate barrel portion  114  rotatably coupled to the other of the first and second platforms  106 ,  108  via another joint  116 . The struts  110  are configured such that the threaded rod portion  112  extends within/through at least a portion of the barrel portion  114  in a telescoping manner. As shown in  FIG. 1 , in some embodiments the struts  110  may be arranged in pairs of oppositely oriented struts  110  coupled to the same portion of the first or second platforms  106 ,  108 . 
     The threaded rod portion  112  and the barrel portion  114  are threadably coupled such that rotation of at least a portion of the threaded rod portion  112  or the barrel portion  114  with respect to the other portion adjusts the relative axial position therebetween to adjust (i.e., shorten or lengthen) the overall or total axial length of the strut  110 . In this way, the struts  100  can be adjusted to change or alter the relative position and/or pose/orientation between the first and second platforms  106 ,  108 . In some embodiments, as shown in  FIG. 1 , the barrel portion  114  may include an adjustment knob that is rotatable about (and potentially translatable along) the (aligned) axes of the threaded rod portion  112  and the barrel portion  114  and is configured to rotate at least a portion of the threaded rod portion  112  or the barrel portion  114  that is threadably coupled to the other portion with respect to the other portion to adjust the total length of the strut assembly  110  (i.e., adjust the telescopic arrangement of the threaded rod portion  112  and the barrel portion  114 ). However, the threaded rod portion  112  and the barrel portion  114  may include any configuration or arrangement such that the telescopic axial arrangement of the threaded rod portion  112  and the barrel portion  114  can be adjusted to adjust the total length of the strut assembly  110 . It should further be appreciated that adjusting the positions of the first and second platforms  106 ,  108  is not limited to adjusting the lengths of the length adjustable struts  110 , and that the positioning of the first and second platforms  106 ,  108  with respect to each other can be alternatively adjusted, for example in accordance the type and/or number of adjustment members connected to the fixation device  100 . 
     The axial length of each strut assembly  110  can thus be independently adjusted. The adjustable length struts  110  and the universal joints  116  by which they are mounted to the platforms  106 ,  108 , allow the fixation device  100  to function like a Stewart platform, and more specifically like a distraction osteogenesis ring system, a hexapod, or a Taylor spatial frame. As such, by making length adjustments to the struts  110 , the spatial positioning of the platforms  106 ,  108 , and thus the spatial positioning of the bone segments  102 ,  104  coupled thereto, can be altered. For example, in one non-limiting embodiment, varying the length of one or more of the struts  110  may change the relative position and pose of the upper and lower platforms  106 ,  108 , and thus the bone segments  102 ,  104  coupled thereto, such that longitudinal axes of the bone segments  102 ,  104  are substantially aligned with each other (e.g., such that their respective ends abut each other, so as to promote union during a healing process for example). 
     Repositioning of the first and second platforms  106 ,  108  of the orthopedic external fixation device  100  can be used to correct displacements of angulation, translation, rotation, or any combination thereof, of the bodily tissues  102 ,  104 . The fixation device  100 , utilized with the techniques described herein, can correct a plurality of such displacement defects individually or simultaneously. 
     As shown in  FIG. 1 , the fixation device  100  may include a plurality of fiducial markers  118  coupled thereto. The fiducial markers  118  may be coupled to the first or second platforms  106 ,  108  in a fixed relationship to each other, the platforms  106 ,  108  and at least a portion of the strut assemblies  110 . For example, the fiducial markers  118  may be positioned at fixed three-dimensional spatial relationships with respect to at least a portion of one or more proximate strut assembly  110 , such as the joint  116  of one or a pair of proximate strut assemblies  110 . 
     The fiducial markers  118  may be of a particular shape and size that differs from that of any other component of the fixation device  100 . In this way, the shape and size of the fiducial markers  118  may be unique to the fiducial markers  118 . Further, at least one fiducial marker  118 ′ can differ from the other fiducial markers  118 . For example, as shown in  FIG. 1 , one fiducial marker  118 ′ may be of a smaller spherical shape as compared to the other fiducial markers  118 . The unique fiducial marker  118 ′ may thereby identify or distinguish the particular platforms  106 ,  108  that it is coupled to from the other platform  106 ,  108 . For example, the unique fiducial marker  118 ′ may be coupled to the first upper platform  106 , and thereby be utilized to identify or deduce the first upper platform  106  from the second lower platform  108 , such as in an image of the fixation device  100  (as described below). 
     As shown in  FIG. 1 , in some embodiments the fiducial markers  118  may comprise spherical portions that extend from, and/or are positioned proximate or adjacent to, one of the platforms  106 ,  108 . In some embodiments, the fiducial markers  118  may be circumferentially or angularly spaced about the platforms  106 ,  108 . For example, each fiducial markers  118  may be fixedly coupled to the same portion or general area of one of the platforms  106 ,  108  as a pair of struts  110 . As shown in  FIG. 1 , the fixation device  100  may thereby include three fiducial markers  118  coupled to the first upper platform  106 , each fiducial marker  118  position proximate to ends of a pair of strut assemblies  110  coupled to the first upper platform  106  via respective joints  116 . As shown in  FIG. 1 , the fixation device  100  may thereby also include three fiducial markers  118  coupled to the second lower platform  108 , each fiducial marker  118  position proximate to ends of a pair of strut assemblies  110  coupled to the second upper platform  108  via respective joints  116 . 
     The fiducial markers  118  are configured to be visible when the fixation device  100  is imaged, such x-rayed. For example, at least the (spherical) outer surface portion of the fiducial markers  118  may be radiopaque. The pre-determined or known locations of the fiducial markers  118  can thereby be used to identify or deduce the identification of the platforms  106 ,  108 , and/or the position and pose of the platforms  106 ,  108 , from an image (e.g., a radiograph/x-ray) of the fixation device  100  as explained further below. 
     The fiducial markers  118  can be mounted to specific pre-identified or known locations of components of the fixation device  100  prior to imaging thereof (e.g., radiographic imaging thereof), can be imbedded within components of the fixation device  100 , or any combination thereof. The marker elements can be configured for enhanced viewability of an image of the fixation device  100  when compared to the viewability of the other components of the fixation device  100 . For example, the fiducial markers  118  may be constructed of a different material, such as a radio-opaque material, or may be constructed with geometries that readily distinguish them from other components of the fiducial markers  118  in a radiographic image of the fixation device  100 . 
     Referring now to  FIGS. 2-4 , an exemplary method of digitally registering a digital radiographic image  201  depicting an external fixation device (and anatomical structure coupled thereto, such as bone segments or other tissue(s)) and a three-dimensional model  300  of the depicted external fixation device, is illustrated. More specially, a digital radiographic image  201  of patient with an external fixation device coupled to his/her anatomical structures is illustrated in  FIG. 2 . The digital radiographic image  201  thereby includes a depiction of an external fixation device  200  (corresponding to the external fixation device of the patient) and the anatomical structures (e.g., bone segment or other tissue segments)  202 ,  204  coupled to platforms  206 ,  208  of the external fixation device  200 . Aspects of a method  400  of digitally registering the radiographic image  201  of  FIG. 2  depicting the external fixation device  200  and a three-dimensional model  300  of the external fixation device of the patient (and therefore also the depicted external fixation device  200 ) is illustrated in the flow chart of  FIG. 4 . Further,  FIG. 3  illustrated a digitally constructed model  325  of the digital radiographic image  201  and a digital three-dimensional model  300  of the external fixation device of the patient and (and therefore also the depicted external fixation device  200  of the radiographic image  201 ) in a relative position and pose/orientation with respect to the three-dimensional modeled external fixation device  300  constructed via the method  400  of  FIG. 4 . 
     The external fixation device of the patient that is imaged, and thereby the external fixation device  200  depicted in the image  201  and the three-dimensionally modeled external fixation device  300  of the three-dimensional model  325 , may be an external fixation device that is the same or similar to the external fixation device  100  described above with respect to  FIG. 1 . For example, the external fixation device of the patient that is imaged, and thereby the external fixation device  200  depicted in the image  201  and the three-dimensionally modeled external fixation device  300  of the three-dimensional model  325 , may include one or more like component, aspect, process and/or function as compared to the external fixation device  100  of  FIG. 1 . Therefore, like reference numerals preceded with “2” with respect to the external fixation device  200  depicted in the image  201 , and like reference numerals preceded with “3” with respect to the three-dimensionally modeled external fixation device  300 , are used to indicate like components, aspects, processes and/or functions to the external fixation device  100  of  FIG. 1 , and the description above directed thereto equally applies, and is not repeated for brevity and clarity purposes. For example, the external fixation device that is coupled to a patient&#39;s anatomy and imaged, and thereby the external fixation device  200  depicted in the image  201  and the modeled external fixation device  300  (depicted in a three dimensional model  325  with the image  201  in a true or corrected relative position and pose, and with respect to a digitally modeled or identified focal point O of the image  201 ) may be configured as a hexapod including at least a pair of first upper and second lower platforms coupled to at least two bone or tissue segments, respectively, six length-adjustable struts extending between the platforms, and spherical fiducial markers proximate to the ends of pairs of struts on each platform (and one unique fiducial marker that identifies a particular platform, and thereby each platform). 
     As shown in  FIG. 4 , at aspect  402 , the method  400  may include inputting a first two-dimensional digital radiographic image, such as an image  201  of the patient depicting an external fixation device  200  coupled to first and second bone or tissue segments  202 ,  204  as shown in  FIG. 2 . As shown in  FIG. 2 , the image  201  may include an external fixation device depiction  200  (including fiducial marker depictions  218 ) and first and second bone or tissue segment depictions  202 ,  204 . The image  201  may be a digital radiographic image or any other two-dimensional image that includes perspective distortion and an unknown, inaccurate or mis-identified viewpoint/focal point. It is noted that the depictions of the fixation device  200  and the first and second bone or tissue segment  202 ,  204  may be equivalent or similar to shadows of the actual fixation device and bone or tissue segments that is imaged that are cast on the film or other image detection plane when the actual fixation device and bone or tissue segment is positioned between the image detection plane and the focal point. As such, the image  201  comprises inherent projectional distortion. 
     The image  201  may be digitally input by a user, or the image  201  may be obtained from an imager (not shown). For example, the digital image  201  can be acquired using x-ray imaging, computer tomography, magnetic resonance imaging, ultrasound, infrared imaging, photography, fluoroscopy, visual spectrum imaging, or any combination thereof. The image  201  can be captured from any position and/or orientation with respect to the actual fixation device and bone or tissue segments. 
     The method  400  may include inputting a plurality of images of the actual fixation device and bone or tissue segments, and thereby including an external fixation device depiction  200  (including fiducial marker depictions  218 ) and first and second bone or tissue segment depictions  202 ,  204 , that are taken from differing viewpoints or focal points. The method  400  may process each image separately or individually a per image basis, rather than comparing, contrasting or otherwise analyzing the images with respect to each other. 
     As shown in  FIG. 2 , an exemplary digitally input image  201  may depict first upper and second lower platforms  206 ,  208  coupled to at least two bone or tissue segments  202 ,  204 , respectively, six length-adjustable struts  110  extending between the platforms  206 ,  208 , and spherical fiducial markers  218  proximate to the ends of pairs of struts on each platform (and one unique fiducial marker  218 ′ that identifies a particular platform, and thereby each platform). 
     As shown in  FIG. 4 , at  404 , digital dimensions of the actual external device may be digitally input. For example, a user may enter one or more dimensions of the actual external device that are, or correspond to, the digital dimensions. For example, digital dimensions corresponding to the diameters of the actual fiducial markers, cord distances between the actual fiducial markers on each platform, and the axial lengths of the actual struts may be digitally input. The method  400  may calculate the distance between corresponding fiducial markers at the opposing ends of each strut via a known relationship between the distances and the axial lengths of the actual struts. 
     Referring to  FIG. 3 , the method  400  may digitally model or create a three-dimensional model  325  with a three-dimensional modeled external fixation device  300  corresponding to the actual external fixation device relative to the image  201  and an arbitrary focal point O. The three-dimensional modeled external fixation device  300  may consist of a the platforms  306 ,  308  disposed in space having attached to them the six spherical radiopaque fiducial markers  318  that serve as known shapes A, B, C, D, E, F (via the input digital dimensions), with known (via the input digital dimensions) cord distances AB, BC, CA and DE, EF, and FD therebetween. The fiducial marker shapes A, B, and C are also spaced from fiducial marker shapes D, E, and F at known lengths (via the input digital dimensions).  FIG. 3  thus depicts a three-by-three (3×3) fiducial marker configuration, which refers to the three coincident fiducial markers on each of the first and second platforms  306 ,  308 . In this example, the unique fiducial marker  318 ′ denoted by A is smaller than the rest of the fiducial markers  318  (which are all the same size). The unique fiducial marker  318 ′ A differentiates the first platform  306  from the second platform  308  and the rotation of the first platform  306  in image space. 
     When the fiducial markers of the actual external fixation device are spherical as shown in  FIG. 1 , the fiducial marker depictions  218  in the image  201  are spherical due to the position of the focal point O of the image  201  and the imaging plane relative to the fiducial markers, as shown in  FIG. 2 . The elliptical fiducial marker depictions  218  in the image  201  may include outer edges that are relatively sharp, as shown in  FIG. 2 . At  406 , the method  4000  may digitally locate the elliptical fiducial marker depictions  218  in the image  201 , as shown in  FIG. 4 . The method  400  may utilize the shape edges of the elliptical fiducial marker depictions  218 , and conclude that the respective fiducial markers that were the sources of the fiducial marker depictions  218  are in fact points located and posed somewhere above the shadows/depictions  218 . The method  400  can also conclude that each actual fiducial marker lies on a vector describing the line between the center of each elliptical fiducial marker depiction  218  and the focal point of the source of the image  201 , as shown in  FIG. 3 . 
     At  408 , the method  400  may further determine or relate (or define) the relative distance between the each elliptical fiducial marker depiction  218  and the actual respective fiducial marker and the distance between each elliptical fiducial marker depiction  218  and the image source or focal point O via the magnification factor of each elliptical fiducial marker depiction  218 , as shown in  FIG. 4 . In some embodiments, the method  400  located and evaluated the size and position of the elliptical fiducial marker depictions  218  within the image  201 . In some embodiments, the method  400  may utilize a digitally determined minor axis dimension of the fiducial marker depictions  218  in relation to the digitally input actual diameters of the elliptical fiducial marker depiction  218 , which may be related to the relative distance between the image  201  and the focal point O and the height along a vector extending therebetween where the actual fiducial marker lies. In some embodiments, the method  400  may utilize the image resolution to determine an initial image scale and relative size of the fiducial marker depictions  218  relative to their digitally input actual size. 
     For example, the method  400  may digitally identify or measure a diameter of each elliptical fiducial marker depiction  218  (e.g., identify or measure the minor diameter or an average diameter of each elliptical fiducial marker depiction  218 , for example) and compare the diameter of each elliptical fiducial marker depiction  218  with the actual diameter of the corresponding actual fiducial marker to digitally determine the magnification factor of the each elliptical fiducial marker depiction  218 , and utilize the magnification factor to relate or describe the relative distance between the fiducial marker depictions  218  in the image  201  and the actual fiducial markers and the distance between the fiducial marker depictions  218  and the image source or focal point O. The method  400  may thereby utilize the digitally determined diameters of each elliptical fiducial marker depiction  218  and the digitally input actual diameters of the respective fiducial markers of the actual fixation device to determine or describe the relative distances between the elliptical fiducial marker depictions  218  and the actual fiducial markers as functions of the distance between the fiducial marker depictions  218  and the image source or focal point O. The method may thereby determine an equation, expression or relationship of the distance (e.g., distance along a Z axis extending normally from the image  201 , for example) from the image  201  for each actual fiducial marker. 
     The distances between the each elliptical fiducial marker depiction  218  and the actual respective fiducial marker, by itself, does not indicate the position and pose of the image source or focal point O. The method  400  may utilize the input dimensions related to the distances between the actual fiducial markers to determine the apparent focal point location and pose of image source or focal point O. 
     The system and methods may determine the position and pose of the actual external fixation device corresponding to the depicted external fixation device  200  in the radiographic image  201  via the digitally modeled or created three-dimensional model  325  with the three-dimensional modeled external fixation device  300  corresponding to the actual external fixation device relative to the image  201  and the arbitrary focal point O, as shown in  FIG. 3 . As shown in  FIG. 3 , the focal point O is defined as an arbitrary point floating in space above the image  210 . 
     At  410 , the method  400  may define a plurality of constraints by construct a plurality of closed vector loops each extending or passing through at least two of a center of a fiducial marker depiction  218  of the image  201 , a center of a modeled fiducial marker  318  of the three-dimensional modeled external fixation device  300 , and the arbitrarily-chosen focal point location O, as shown in  FIGS. 3 and 4 . As a non-limiting example, the method  400  may construct a first closed vector loop  330  of P 1 A-O-P 2 A-P 1 A, a second closed vector loop  332  of B 2 A-C-E-P 1 A-B 2 A, and/or a third closed vector loop  334  of B 0 A-A-B-B 1 A-B 0 A, as shown in  FIG. 3 . 
     At  412 , the method  400  may solve the plurality of closed vector loops (e.g., such that they collapse on themselves and/or equal zero) to determine the nodal locations A, B, C, D, E, F of each of the actual fiducial markers of the external fixator (in X and Y and Z coordinates from the image  201 , for example), and the location of an actual, true or corrected focal point O of the image  201  (in X and Y and Z coordinates from the image  201 , for example), as shown in  FIG. 4 . It is noted that the nodal locations A, B, C, D, E, F of each of the actual fiducial markers of the external fixator and the location of the actual focal point O of the image  201  may be determined (i.e., the problem sufficiently constrained) utilizing a limited number of such closed vector loops. However, relatively more such closed vector loops can be used to statistically improve the results. 
     Having determined all of the nodal locations A, B, C, D, E, F, and O in image space, at  414 , the method  400  may construct a suitable first coordinate transformation matrix (or coordinate transform) for the known (via the input dimensions) actual external fixation device (depicted at least partially by the collection of spherical fiducial markers) relative to the image  201 , as shown in  FIG. 4 . The method  400  can then take the inverse of the coordinate transformation matrix, at  414 , to determine a second coordinate transformation matrix that defines or described the position (e.g., X, Y and Z location) and pose (i.e., orientation in X, Y and Z) of the image  201  with respect to the actual external fixation device, as shown in  FIG. 4 . 
     In some embodiments, the method  400  may construct a suitable first coordinate transform by determining the cross product of a pair of suitable vectors between the nodes of a common platform to determine a vector normal to both suitable vectors whose origin lies at a node common thereto. For example, the method  400  may take a cross product of AB×AC, and thereby determine a vector normal to both AB and AC whose origin lies at A. The method  400  may then cross the resultant vector with one of the previous suitable vectors to determine an orthogonal coordinate system (i.e., a coordinate transformation matrix) that depicts or describes, in this case, the platform in image space (defined by the respective chosen nodes, such as by ABC in the example above). With the plurality of closed vector loops determined, the method  400  may thereby define a coordinate transform for the collection of the known actual fiducial markers in a shadow image space (i.e., determine a row dimension, a column dimension and a height dimension). 
     The method  400  can utilize the second coordinate transformation matrix to create the digital three-dimensional model  325  of a three-dimensional model  300  of the actual external fixation and the image  201  in a relative position and pose/orientation with respect to the three-dimensional modeled external fixation device  300 , with the viewpoint or camera view of the image focal point O. The method may render the three-dimensional model  300  to display the three-dimensional model  300  to a user so that the user can qualitatively inspect or review the three-dimensional model  300  to ensure that the three-dimensional model  300  constructed via the method  400  is in the correct position and pose with respect to the image  201 . 
     An example of constructing the second coordinate transformation matrix, and a resultant coordinate transformation matrix, for the digitally modeled external fixator  300  and the image  201  of  FIG. 3  is depicted in  FIG. 5 . 
     With the coordinate system determined, the methods  400  can determine the coordinate transformation between any pair of images within the plurality of images utilizing the collection of known three-dimensional objects in each of the plurality of the radiographic images using a consistent approach in each image. The system and methods may correct for any non-orthogonal or otherwise rotated pairs of images when constructing the true three-dimensional location and pose of the three-dimensional objects, thus accurately describing whatever other annotations or measurements that are made within the radiographic images. 
     The methods and systems may use the method  400  for each of a plurality of images  201  on an image by image basis to determine a plurality of coordinate systems all describing the same known fiducial marker (external fixation device) in the greater patient space. 
     As would be evident to one of ordinary skill in the art, the inventions of this disclosure provide significant improvements in the field of external fixation device and anatomical structure computer modeling, including the field of hexapod and bone segment modeling. Further, the inventions of this disclosure provide significant improvements in the field of radiographic imaging, including the field of distortion correction of radiographic images. The inventions of this disclosure also provide significant improvements in the field of external fixation device adjustment prescription determination, including the field of hexapod adjustment prescriptions. 
     Those having ordinary skill in the art will recognize that aspects of the present invention may be embodied in system(s), method(s) and/or computer program product(s). In some embodiments, aspects of the present invention may be embodied entirely in hardware, entirely in software (for instance in firmware, resident software, micro-code, etc.), or in a combination of software and hardware aspects that may all generally be referred to herein as a “system” and include circuit(s) and/or module(s). 
       FIG. 6  depicts one example of a computer system to incorporate and use one or more aspects of the present invention. Computer system  500  may be a computer system of an article manufacturing and/or repair facility, such as a computer system used to additively manufacture articles, and/or a computer system for producing data used by an AM apparatus or device to fabricate articles. Computer system  500  of  FIG. 6  may be suitable for storing and/or executing program code, such as program code for performing processes described above and includes at least one processor  502  coupled directly or indirectly to memory  505  through, a bus  520 . In operation, processor(s)  502  may obtain from memory  505  instructions for execution by the processor(s). Memory  505  may include local memory employed during actual execution of the program code, bulk storage, and cache memories which provide temporary storage of at least some program code in order to reduce the number of times code must be retrieved from bulk storage during program code execution. A non-limiting list of examples of memory  505  includes a hard disk, a random-access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. Memory  505  may include an operating system  505  and one or more computer programs  506 , such as one or more programs for execution to perform aspects described herein, such as effecting adjustments to a digital layout of a circuit design. 
     Input/Output (I/O) devices  512 ,  515  (such as peripheral devices) may be coupled to the system either directly or through I/O controllers  510 . Network adapters  508  may also be coupled to the system to enable the computer system to become coupled to other computer systems through intervening private or public networks. Modems, cable modem and Ethernet cards are just a few of the currently available types of network adapters  508 . In one example, network adapters  508  facilitate obtaining data from remote sources to facilitate aspects of the present invention. 
     Computer system  500  may be coupled to storage  516  (e.g., a non-volatile storage area, such as magnetic disk drives, optical disk drives, a tape drive, etc.), having one or more databases. Storage  516  may include an internal storage device or an attached or network accessible storage. Computer programs in storage  516  may be loaded into memory  505  and executed by a processor  502 . 
     The computer system  500  may include fewer components than illustrated, additional components not illustrated herein, or some combination of the components illustrated and additional components. Computer system  500  may include any computing device, such as a mainframe, server, personal computer, workstation, laptop, handheld computer, smartphone, table, or other mobile device, telephony device, network appliance, virtualization device, storage controller, etc. 
     In addition, processes described above may be performed by multiple computer systems  500 , working in concert as part of a computing environment. 
     In some embodiments, aspects of the present invention may take the form of a computer program product embodied in computer readable medium(s). The computer readable medium(s) may have embodied thereon computer readable program code. Various computer readable medium(s) or combinations thereof may be utilized. For instance, the computer readable medium(s) may include a computer readable storage medium, examples of which include (but are not limited to) one or more electronic, magnetic, optical, or semiconductor systems, apparatuses, or devices, or any suitable combination of the foregoing. Example computer readable storage medium(s) include, for instance: an electrical connection having one or more wires, a portable computer diskette, a hard disk or mass-storage device, a random access memory (RAM), read-only memory (ROM), and/or erasable-programmable read-only memory such as EPROM or Flash memory, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device (including a tape device), or any suitable combination of the above. A computer readable storage medium is defined to include a tangible medium that can contain or store program code for use by or in connection with an instruction execution system, apparatus, or device, such as a processor. The program code stored in/on the computer readable medium therefore produces an article of manufacture (such as a “computer program product”) including program code. 
     Referring now to  FIG. 7 , in one example, a computer program product  600  includes, for instance, one or more computer readable media  602  to store computer readable program code means or logic  604  thereon to provide and facilitate one or more aspects of the present invention. 
     Program code contained or stored in/on a computer readable medium can be obtained and executed by a computer system (computer, computer system, etc. including a component thereof) and/or other devices to cause the computer system, component thereof, and/or other device to behave/function in a particular manner. The program code can be transmitted using any appropriate medium, including (but not limited to) wireless, wireline, optical fiber, and/or radio-frequency. Program code for carrying out operations to perform, achieve, or facilitate aspects of the present invention may be written in one or more programming languages. In some embodiments, the programming language(s) include object-oriented and/or procedural programming languages such as C, C++, C#, Java, etc. Program code may execute entirely on the user&#39;s computer, entirely remote from the user&#39;s computer, or a combination of partly on the user&#39;s computer and partly on a remote computer. In some embodiments, a user&#39;s computer and a remote computer are in communication via a network such as a local area network (LAN) or a wide area network (WAN), and/or via an external computer (for example, through the Internet using an Internet Service Provider). 
     In one example, program code includes one or more program instructions obtained for execution by one or more processors. Computer program instructions may be provided to one or more processors of, e.g., one or more computer system, to produce a machine, such that the program instructions, when executed by the one or more processors, perform, achieve, or facilitate aspects of the present invention, such as actions or functions described in flowcharts and/or block diagrams described herein. Thus, each block, or combinations of blocks, of the flowchart illustrations and/or block diagrams depicted and described herein can be implemented, in some embodiments, by computer program instructions. 
     The flowcharts and block diagrams depicted and described with reference to the figures illustrate the architecture, functionality, and operation of possible embodiments of systems, methods and/or computer program products according to aspects of the present invention. These flowchart illustrations and/or block diagrams could, therefore, be of methods, apparatuses (systems), and/or computer program products according to aspects of the present invention. 
     In some embodiments, as noted above, each block in a flowchart or block diagram may represent a module, segment, or portion of code, which includes one or more executable instructions for implementing the specified behaviors and/or logical functions of the block. Those having ordinary skill in the art will appreciate that behaviors/functions specified or performed by a block may occur in a different order than depicted and/or described, or may occur simultaneous to, or partially/wholly concurrent with, one or more other blocks. Two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order. Additionally, each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented wholly by special-purpose hardware-based systems, or in combination with computer instructions, that perform the behaviors/functions specified by a block or entire block diagram or flowchart. 
     It is to be understood that the above description is intended to be illustrative, and not restrictive. Numerous changes and modifications may be made herein by one of ordinary skill in the art without departing from the general spirit and scope of the invention as defined by the following claims and the equivalents thereof. For example, the above-described embodiments (and/or aspects thereof) may be used in combination with each other. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the various embodiments without departing from their scope. While the dimensions and types of materials described herein are intended to define the parameters of the various embodiments, they are by no means limiting and are merely exemplary. Many other embodiments will be apparent to those of skill in the art upon reviewing the above description. The scope of the various embodiments should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprise” (and any form of comprise, such as “comprises” and “comprising”), “have” (and any form of have, such as “has” and “having”), “include” (and any form of include, such as “includes” and “including”), “contain” (and any form contain, such as “contains” and “containing”), and any other grammatical variant thereof, are open-ended linking verbs. As a result, a method or article that “comprises”, “has”, “includes” or “contains” one or more steps or elements possesses those one or more steps or elements, but is not limited to possessing only those one or more steps or elements. Likewise, a step of a method or an element of an article that “comprises”, “has”, “includes” or “contains” one or more features possesses those one or more features, but is not limited to possessing only those one or more features. 
     As used herein, the terms “comprising,” “has,” “including,” “containing,” and other grammatical variants thereof encompass the terms “consisting of” and “consisting essentially of.” 
     The phrase “consisting essentially of” or grammatical variants thereof when used herein are to be taken as specifying the stated features, integers, steps or components but do not preclude the addition of one or more additional features, integers, steps, components or groups thereof but only if the additional features, integers, steps, components or groups thereof do not materially alter the basic and novel characteristics of the claimed compositions or methods. 
     All publications cited in this specification are herein incorporated by reference as if each individual publication were specifically and individually indicated to be incorporated by reference herein as though fully set forth. 
     Subject matter incorporated by reference is not considered to be an alternative to any claim limitations, unless otherwise explicitly indicated. 
     Where one or more ranges are referred to throughout this specification, each range is intended to be a shorthand format for presenting information, where the range is understood to encompass each discrete point within the range as if the same were fully set forth herein. 
     While several aspects and embodiments of the present invention have been described and depicted herein, alternative aspects and embodiments may be affected by those skilled in the art to accomplish the same objectives. Accordingly, this disclosure and the appended claims are intended to cover all such further and alternative aspects and embodiments as fall within the true spirit and scope of the invention.