Registration method and system for radiographic images and three-dimensional models of an external fixation device

Abstract

A method is disclosed that includes digitally determining an actual position and pose of a set of known objects in a projected three-dimensional space located above a digital two-dimensional radiographic space. The method includes digitally inputting a first digital radiographic image that depicts the set of known objects in the projected three-dimensional space located above the two-dimensional radiographic space. The method further includes using the depiction of the set of known objects in the two-dimensional radiographic space in the first digital radiographic image to determine the actual position and pose of the set of known objects in the projected three-dimensional space located above the two-dimensional radiographic space.

Description

[0001] Cross-reference

[0002] This application claims the benefit of and incorporates by reference in its entirety U.S. Provisional Application No. 62 / 702,378, filed Jul. 24, 2018, entitled “Deformity Analysis Using Multiple Non-Orthogonal Radiographs”. Technical Field

[0003] The present invention generally relates to a registration system and method for two-dimensional images (e.g., radiographic images) and three-dimensional models of fixation devices (e.g., external fixation devices) for deformity and / or orthopedic analysis and / or correction. The system and method determine the relative position and orientation / pose of an image of an 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) fixed to the anatomical structure of interest relative to the fixation device. In some embodiments, the system and method determine the focus of the image and account for perspective distortion in the image and create a coordinate transformation matrix.

[0004] The methods and systems of the present invention are capable of generating three-dimensional computer models of bone segments and fixation devices (e.g., external fixation devices) for planning the movement of bone segments to desired positions via the fixation devices. For example, by operating on the model, the desired position and orientation / pose of the bone segments and the 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. Then, the operations required to create the desired position and orientation / pose of the bone segments can be implemented on the corresponding fixation device and bone segments to achieve the desired position and orientation / pose. However, other devices in addition to external fixation devices can also be used with the system and method. Background Art

[0005] The correction of orthopedic deformities typically requires at least a pair of X-ray radiographs. Typically, these radiographs of a patient are taken along conventional lines in the anterior-to-posterior (AP) direction and the medial-to-lateral (ML) direction, or along other orthogonal or known advantageous positions (or known differences between advantageous positions). By convention, the AP and ML radiographs are taken or assumed to be orthogonal to each other in patient space (patient space is defined as having an X-axis aligned from right to left, a Y-axis aligned from anterior to posterior, and a Z-axis aligned from bottom to top). Measurements are made within the pair of radiographs, and the axes and points of the deformity are labeled. Then, these measurements and labels in the pair of radiographs are compared or otherwise used to reconstruct a three-dimensional representation of the deformity so that the deformity can be manipulated in some way to correct the condition.

[0006] However, the inaccuracies in the favorable positions of the pair of radiographic images and their spatial relationships with each other result in an inaccurate representation of the patient and the objects connected thereto in the images (i.e., artifacts shown in the images). Radiographic images and other patient imaging techniques cannot produce perfect images of the artifacts contained within these images. The relationship between the artifacts shown in the images and the actual objects being imaged is a perspective relationship such that those objects closer to the image have a smaller magnification than those objects farther from the image. In addition, since the arrangement of the patient relative to the imager focal point is manually operated, the favorable position of the image is not perfectly aligned with the conventional line / favorable position (and thus a pair of images is not truly orthogonal). Due to not considering these aspects / inaccuracies of the images, the 3D reconstruction of the patient and / or the objects connected thereto contained in the images is not a true representation of them.

[0007] Accordingly, there is a need for systems and methods that take into account the uncertainties / inaccuracies in the images of a portion of a patient and the objects coupled thereto and construct a true 3D model thereof. In addition, there is a need for systems and methods for determining the position and pose / orientation of the images of a portion of a patient and the objects connected thereto relative to the object based on each image.

[0008] Although certain aspects of conventional techniques have been discussed to facilitate the disclosure of the present invention, the applicant does not in any way disclaim such technical aspects, and it is contemplated that the claimed invention may include one or more aspects of conventional techniques.

[0009] In this specification, when referring to or discussing known literature, acts, or items, such reference or discussion does not admit that the said known literature, act, or item or any combination thereof was available to the public, known to the public, part of common general knowledge, or constituted prior art as of the priority date; or was known in connection with any attempt to solve any problem addressed in this specification. Summary of the Invention

[0010] The present invention can solve one or more of the above-mentioned technical problems and deficiencies. However, it is contemplated that the present invention may prove useful in solving other problems and deficiencies in many technical fields. Accordingly, the claimed invention is not necessarily to be construed as limited to solving any particular problem or deficiency discussed herein.

[0011] In some embodiments, radiographic or other images of a portion of a patient and the objects connected thereto contain the shadows of three-dimensional objects that were positioned and placed / positioned above / below the image (e.g., the film in a radiographic image) at the time of capture. The apparent light source position and orientation of the image source (e.g., the X-ray source) relative to the image that projects the shadow are unknown.

[0012] Ideally, the focus of the imager would be a point source located infinitely far above the image and centered on the image itself. An ideal representation would result in shadows in the image being true two-dimensional projections of the actual three-dimensional object. If two such ideal images / representations were obtained and it was known that the images / representations were orthogonal to each other about a common axis, then the two sets of two-dimensional data could be directly utilized to accurately reconstruct the three-dimensional model of the object and its position and pose in space.

[0013] However, as described above, given the current state of the art in patient imaging (e.g., radiographic techniques involving plain radiographs), perspective distortion results, making this generally impossible. Additionally, for example, considering all the variables involved in acquiring those images on an actual imaging machine (e.g., an x-ray machine), where the actual patient is instructed to lie / pose in a prescribed manner, the likelihood that the images (e.g., radiographs) are truly orthogonal to the trajectory of the image source and orthogonal to each other about a common axis is also almost nil.

[0014] The systems and methods of the present invention utilize two main sources of error, the focus position and pose, and the patient orientation, to draw numerous conclusions in order to ultimately correct for / account for the actual viewing perspective / position of the image and construct a true three-dimensional model of the object within the image (and possibly the image itself).

[0015] Computer-based systems and methods can account for perspective distortion by determining a portion (e.g., a radiopaque portion) of an object attached to the patient having a specific shape and potential size (e.g., a spherical element) and the shadow it projects in a single image (e.g., a single radiographic image) (or based on each image). For example, the systems and methods can utilize multiple known portions of the object in the image (the shadows of which exist as artifacts in the image), as well as the known relative shapes and sizes of these portions, and the relationships between these portions, to determine the apparent focus position and pose of the image source (e.g., the x-ray source of a radiographic image).

[0016] The systems and methods can use multiple closed vector loops passing through the center of the shadow, the center of the actual portion casting the shadow, and the focus position of the imager to determine the position and pose of the known portions of the object in a three-dimensional set in image space. Given the determination of multiple closed vector loops, the systems and methods can construct a coordinate transformation matrix for the set of known three-dimensional portions of the object in shadow image space (i.e., determining the row dimension, column dimension, and height dimension).

[0017] In a first aspect, the present invention provides methods and systems that utilize a known set of three-dimensional objects whose shadows are projected in a two-dimensional x-ray radiographic space to determine the actual position and pose of the known set of objects in a computer-modeled three-dimensional space that is above the two-dimensional radiographic space.

[0018] In some embodiments, the method and system can utilize perspective distortion to determine relative magnification to assist in the reconstruction of a three-dimensional projection space. In some embodiments, the method and system can reconstruct a model of the actual three-dimensional conditions in a corrected relative spatial arrangement.

[0019] Certain embodiments of the systems and methods of the present invention can include several features, none of which alone is uniquely responsible for its desired attributes. Without limiting the scope of the systems and methods, some of their more prominent features will now be briefly discussed. After considering this discussion, and particularly after reading the section entitled "Detailed Description" in this specification, one will appreciate how the features of the various embodiments disclosed herein provide many advantages over the prior art.

[0020] These and other features and advantages of the present invention will become apparent from the following detailed description of various aspects of the invention in conjunction with the appended claims and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The present invention will be described below in conjunction with the following drawings, which are not necessarily drawn to scale for ease of understanding, wherein like reference numerals in the various drawings refer to and represent the same or similar elements, and wherein:

[0022] Figure 1 is a perspective view of an exemplary external fixation device attached to an exemplary bone segment;

[0023] Figure 2 is a front view of a two-dimensional radiographic image depicting an exemplary external fixation device attached to an exemplary bone segment;

[0024] Figure 3 is a perspective view of a constructed digital three-dimensional model that includes a digital two-dimensional radiographic image and a digital three-dimensional model of the external fixation device presented in the model, the digital three-dimensional model of the external fixation device being in the correct relative position and orientation with respect to the determined focus of the radiographic image;

[0025] Figure 4 is a flowchart of an exemplary method for digitally registering a radiographic image and a three-dimensional model of an external fixation device depicted in the radiographic image;

[0026] Figure 5 depicts an exemplary method for digitally constructing a coordinate transformation matrix that identifies the position and orientation of a radiographic image with respect to a three-dimensional model of an external fixation device depicted in the radiographic image;

[0027] Figure 6depicts an exemplary computer system that can be used to implement aspects of the present invention; and

[0028] Figure 7 depicts an embodiment of a computer program product that can be combined with the present invention. DETAILED DESCRIPTION

[0029] Aspects of the present invention and certain of its features, advantages, and details are explained more fully below with reference to the non-limiting embodiments shown in the accompanying drawings. Descriptions of well-known materials, manufacturing tools, processing techniques, etc. are omitted so as not to unnecessarily obscure the details of the present invention. However, it should be understood that the detailed descriptions and specific examples, while indicating embodiments of the present invention, are for illustrative purposes only and not as a limitation. Various substitutions, modifications, additions, and / or arrangements within the spirit and / or scope of the basic inventive concept will be apparent to those skilled in the art in accordance with the present invention.

[0030] First, referring to Figure 1 , body tissues (such as first and second bone segments 102, 104) can be aligned and / or oriented to facilitate bonding or other healing between the body tissues. Alignment and / or orientation of the body tissues can be achieved by connecting the body tissues to an adjustable fixation device (such as an orthopedic external fixation device or fixator 100). The fixation device can include a plurality of discrete fixator platforms or members held outside the patient, but these fixator platforms or members (such as with minimally invasive attachment members) are attached to the respective discrete body tissues. By adjusting the spatial positioning of the platforms relative to each other, the respective body tissues attached thereto can be reoriented and / or otherwise aligned with each other, for example, to facilitate bonding between the body tissues during the healing process. Using an external fixation device in combination with the imaging analysis and positioning techniques described herein can be advantageous.

[0031] The fixator members can be connected to each other by adjusting struts or members, and the adjusting struts are used to facilitate the spatial repositioning of the platforms relative to each other. For example, in Figure 1In the illustrated embodiment, the external fixation device 100 includes a pair of platforms or fixture members in the form of at least one upper ring platform 106 and a lower ring platform 108. The platform rings 106, 108 may be constructed to be the same or different. For example, the platform rings 106, 108 may have the same or different diameters. Similarly, the platform rings 106, 108 may be constructed to have different cross-sectional diameters, thicknesses, etc. It should be understood that the fixture members of the fixation device 100 are not limited to the upper platform ring 106 and the lower platform ring 108 shown, and the fixation device 100 may optionally be constructed in other ways. For example, additional fixture rings may be provided and interconnected with the upper platform ring 106 and / or the lower platform ring 108. It should also be understood that the geometry of the platforms is not limited to rings, and at least one (e.g., any or all) of the platforms may optionally be constructed using any other suitable geometry.

[0032] The first and second bone segments 102, 104 may be firmly connected to the upper platform ring 106 and the lower platform ring 108, respectively, using attachment members (not shown) that can be mounted and / or connected to the platform rings 106, 108. For example, the external fixation device may include connecting rods and / or connecting lines (not shown) that are (e.g., directly or through a clamp or any other mounting mechanism configuration) fixed or connected to the upper platform 106 and the lower platform 108 and the first and second bone segments 102, 104, respectively.

[0033] The attachment members may be detachably mounted to the platform rings 106, 108 at predetermined points along the periphery of the platform rings 106, 108, for example, by connecting them to holes defined by the platforms 106, 108. For each platform 106, 108, the attachment members and / or the mounting mechanisms or members connected thereto may be mounted to the upper surface of the platform, the lower surface of the platform, or any combination thereof. It should be understood that the configuration of the attachment members is not limited to the above configuration. For example, any number of attachment members (e.g., any number of pins, wires, etc.) may be used as needed to fix the bone segments 102, 106 to the corresponding platform 106, 108. It should also be understood that one or more of the attachment members may be configured to be directly mounted to or directly connected to the platform 106, 108 without using an intermediate or additional mounting mechanism, or may be configured to be indirectly mounted to the platform 106, 108 with the help or assistance of a mounting mechanism.

[0034] As Figure 1As shown, the upper platform 106 and the lower platform 108 of the external fixation device 100 are interconnected by a plurality of adjustment struts or members 110. At least one (e.g., all) of the adjustment struts can be configured to be adjusted to adjust the spatial positioning and orientation of the platforms 106, 108 relative to each other. For example, in the illustrated embodiment, the upper platform ring 106 and the lower platform ring 108 are connected to each other by six circumferentially spaced length-adjustable struts 110 (at least partially) extending therebetween. The external fixation device 100 can thus include a hexapod or Stewart platform. However, it should be understood that the construction of the fixation device 100 is not limited to the six struts 110 of the illustrated embodiment, and more or fewer struts 110 can be used as needed.

[0035] As Figure 1 shown, one or more length-adjustable struts 110 can include: an axially elongated screw portion 112 rotatably connected to one of the first platform 106 and the second platform 108 by a joint 116; and an axially elongated cylindrical portion 114 rotatably connected to the other of the first platform 106 and the second platform 108 by another joint 116. The strut 110 is configured such that the screw portion 112 extends telescopically within at least a portion of the cylindrical portion 114 / through at least a portion of the cylindrical portion 114. As Figure 1 shown, in some embodiments, the struts 110 can be arranged in pairs as oppositely oriented struts 110 that are connected to the same part of the first platform 106 or the second platform 108.

[0036] The screw portion 112 and the cylindrical portion 114 are threadedly connected such that rotation of at least a portion of the screw portion 112 or the cylindrical portion 114 relative to the other portion adjusts their relative axial position to adjust (i.e., shorten or lengthen) the overall or total axial length of the strut 110. Thus, the strut 100 can be adjusted to change or alter the relative position and / or orientation / direction between the first platform 106 and the second platform 108. In some embodiments, as Figure 1As shown, the tubular portion 114 may include an adjustment knob that is rotatable (and possibly translatable along) an axis (aligned) of the screw portion 112 and the tubular portion 114, and is configured to rotate at least a portion of the screw portion 112 or the tubular portion 114, the at least a portion being threadedly coupled to the other portion relative to the other portion to adjust the overall length of the strut assembly 110 (i.e., adjust the telescoping arrangement of the screw portion 112 and the tubular portion 114). However, the screw portion 112 and the tubular portion 114 may include any construction or arrangement such that the telescoping axial arrangement of the screw portion 112 and the tubular portion 114 can be adjusted to adjust the overall length of the strut assembly 110. It should also be understood that adjusting the position of the first platform 106 and the second platform 108 is not limited to adjusting the length of the length-adjustable strut 110, and the positioning of the first platform 106 and the second platform 108 relative to each other can be adjusted alternately, e.g., according to the type and / or number of adjustment members connected to the fixture 100).

[0037] Accordingly, the axial length of each strut assembly 110 can be adjusted independently. The length-adjustable struts 110 and the universal joints 116 (by which they are mounted to the platforms 106, 108) allow the fixture 100 to act in a manner similar to a Stewart platform, and more specifically similar to a distraction osteogenesis ring system, a hexapod, or a Taylor spatial frame. Thus, by adjusting the length of the struts 110, the spatial positioning of the platforms 106, 108 can be changed, thereby changing the spatial positioning of the bone segments 102, 104 connected to the platforms 106, 108. For example, in one non-limiting embodiment, changing the length of one or more of the struts 110 can change the relative position and orientation of the upper platform 106 and the lower platform 108, thereby changing the relative position and orientation of the bone segments 102, 104 connected thereto such that the longitudinal axes of the bone segments 102, 104 are substantially aligned with each other (e.g., such that their respective ends are adjacent to each other, thereby promoting union during the healing process, for example).

[0038] Repositioning of the first platform 106 and the second platform 108 of the orthopedic external fixation device 100 can be used to correct angular, translational, rotational, or any combination of the above displacements of the body tissues 102, 104. The fixture 100 used in conjunction with the techniques described herein can correct multiple such displacement defects either individually or simultaneously.

[0039] As Figure 1As shown, the fixture 100 may include a plurality of fiducial markers 118 connected thereto. The fiducial markers 118 may be connected to the first platform 106 or the second platform 108 in a fixed relationship relative to each other, the platforms 106, 108, and at least a portion of the strut assembly 110. For example, the fiducial markers 118 may be positioned in a fixed three-dimensional spatial relationship relative to at least a portion of one or more adjacent strut assemblies 110 (e.g., the joints 116 of one or a pair of adjacent strut assemblies 110).

[0040] The fiducial markers 118 may have a specific shape and size different from any other components of the fixture 100. Thus, the shape and size of the fiducial markers 118 may be unique to the fiducial markers 118. Additionally, at least one fiducial marker 118' may be different from the other fiducial markers 118. For example, as Figure 1 shown, one fiducial marker 118' may be a smaller spherical shape compared to the other fiducial markers 118. The unique fiducial marker 118' can thereby identify the specific platform 106, 108 to which it is connected or distinguish it from other platforms 106, 108. For example, the unique fiducial marker 118' may be connected to the first upper platform 106 and thus be used to identify or infer the first upper platform 106 rather than the second lower platform 108, for example, in an image of the fixture 100 (as described below).

[0041] As Figure 1 shown, in some embodiments, the fiducial markers 118 may include a spherical portion that extends from one of the platforms 106, 108 and / or is positioned adjacent to or near one of the platforms 106, 108. In some embodiments, the fiducial markers 118 may be circumferentially or angularly spaced around the platforms 106, 108. For example, each fiducial marker 118 may be fixedly connected to the same portion or general area of one of the platforms 106, 108 to which a pair of struts 110 is connected. As Figure 1 shown, the fixture 100 may thus include three fiducial markers 118 connected to the first upper platform 106, each fiducial marker 118 positioned adjacent an end of a pair of strut assemblies 110, the ends of the pair of strut assemblies 110 being connected to the first upper platform 106 by respective joints 116. As Figure 1 shown, the fixture 100 may thus also include three fiducial markers 118 connected to the second lower platform 108, each fiducial marker 118 positioned adjacent an end of a pair of strut assemblies 110, the ends of the pair of strut assemblies 110 being connected to the second lower platform 108 by respective joints 116.

[0042] The fiducial marker 118 is configured to be visible when the fixation device 100 is imaged (e.g., examined by X-ray). For example, at least the (spherical) outer surface portion of the fiducial marker 118 can be radiopaque. As described below, the predetermined or known position of the fiducial marker 118 can thus be used to identify or infer the identity 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.

[0043] The fiducial marker 118 can be mounted to a specific pre-identified or known position of a component of the fixation device 100 prior to its imaging (e.g., its radiological imaging), can be embedded in a component of the fixation device 100, or any combination thereof. The marker element can be configured to enhance the visibility of an image of the fixation device 100 when compared to the visibility of other components of the fixation device 100. For example, the fiducial marker 118 can be made of a different material (e.g., a radiopaque material), or can have a geometry that is easily distinguishable from other components of the fixation device 100 in a radiological image of the fixation device 100.

[0044] Now referring Figures 2 to 4 , an exemplary method of digitally registering a digital radiological image 201 depicting an external fixation device (and the anatomical structure, e.g., bone segment or other tissue, connected thereto) and a three-dimensional model 300 of the depicted external fixation device is shown. More specifically, in Figure 2 a digital radiological image 201 of a patient with an external fixation device connected to his / her anatomical structure is shown. The digital radiological image 201 thus includes a depiction of the external fixation device 200 (corresponding to the external fixation device of the patient) and the anatomical structure (e.g., bone segment or other tissue segment) 202, 204 of the platforms 206, 208 connected to the external fixation device 200. In Figure 4 the flowchart of Figure 2 aspects of a method 400 of digitally registering the radiological image 201 of the external fixation device 200 and a three-dimensional model 300 of the external fixation device of the patient (and thus also the depicted external fixation device 200) are shown. Further, Figure 3 a digitally constructed model 325 of the digital radiological image 201 and a digital three-dimensional model 300 of the external fixation device of the patient (and thus also the depicted external fixation device 200 of the radiological image 201) are shown, as well as being in relative position and pose / orientation with respect to the three-dimensionally modeled external fixation device 300 constructed by the method 400 of Figure 4 .

[0045] An external fixation device of a patient to be imaged, and thus the external fixation device 200 depicted in 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 as or similar to the external fixation device 100 described above with reference to Figure 1 For example, the external fixation device of the patient to be imaged, and thus the external fixation device 200 depicted in Image 201 and the three-dimensionally modeled external fixation device 300 of the three-dimensional model 325, may include one or more similar components, aspects, functions, processes, and / or functions similar to those of the Figure 1 external fixation device 100. Thus, for the external fixation device 200 depicted in Image 201, similar reference numerals starting with "2", and for the three-dimensionally modeled external fixation device 300, similar reference numerals starting with "3", are used to indicate similar components, aspects, functions, processes, and / or functions similar to those of the Figure 1 external fixation device 100, and the above description applies equally and, for the sake of brevity and clarity, will not be repeated. For example, the external fixation device connected to and imaged of the patient's anatomical structure, and thus the external fixation device 200 depicted in Image 201 and the modeled external fixation device 300 (depicted in the three-dimensional model 325, where Image 201 is in a true or corrected relative position and pose and with respect to the digitally modeled or identified focus O of Image 201) may be configured as a hexapod that includes at least a first upper platform and a second lower platform respectively connected to at least two bone or tissue segments, six length-adjustable struts extending between the platforms, and spherical fiducial markers at the ends of adjacent strut pairs on each platform (and a unique fiducial marker that identifies a particular platform and thus each platform).

[0046] As Figure 4 shown, in aspect 402, method 400 may include inputting a first two-dimensional digital radiography image, for example, an image 201 of a patient as Figure 2 shown, which depicts an external fixation device 200 connected to first and second bone or tissue segments 202, 204. As Figure 2As shown, 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 radiograph or any other two-dimensional image including perspective distortion and unknown, inaccurate, or mis-identified viewpoints / foci. It should be noted that when the actual fixation device and bone or tissue segments are located between the image detection plane and the focus, the depictions of the fixation device 200 and the first and second bone or tissue segments 202, 204 may be equivalent to or similar to the shadows of the actual fixation device and bone or tissue segments imaged on a film or other image detection plane. Thus, the image 201 includes inherent projection distortion.

[0047] The image 201 may be digitally input by a user, or the image 201 may be obtained from an imager (not shown). For example, digital imaging 201 may be acquired using x-ray imaging, computed tomography, magnetic resonance imaging, ultrasound, infrared imaging, photography, fluoroscopy, visible spectrum imaging, or any combination thereof. The image 201 may be captured from any position and / or orientation relative to the actual fixation device and bone or tissue segments.

[0048] Method 400 may include inputting multiple images of the actual fixation device and bone or tissue segments, thus including external fixation device depictions 200 (including fiducial marker depictions 218) and first and second bone or tissue segment depictions 202, 204 taken from different viewpoints or foci. Method 400 may process each image separately or individually based on each image, rather than comparing, contrasting, or otherwise analyzing the images with each other.

[0049] As Figure 2 shown, an exemplary digitally input image 201 may depict a first upper platform 206 and a second lower platform 208 respectively connected to at least two bone or tissue segments 202, 204, six length-adjustable struts 110 extending between the platforms 206, 208, and spherical fiducial markers 218 (and a unique fiducial marker 218' identifying a particular platform and thus each platform) at the ends of adjacent strut pairs on each platform.

[0050] As Figure 4 shown, at 404, digital dimensions of the actual external device may be digitally input. For example, a user may input one or more dimensions of the actual external device that are digital dimensions or correspond to digital dimensions. For example, digital dimensions corresponding to the diameter of an actual fiducial marker, the distance between the actual fiducial markers on each platform, and the axial length of an actual strut may be digitally input. Method 400 may calculate the distance between the corresponding fiducial markers at opposite ends of each strut through a known relationship between this distance and the axial length of the actual strut.

[0051] Reference Figure 3 , method 400 can digitally model or create a three-dimensional model 325 having an external fixture 300 that is a three-dimensional model corresponding to the actual external fixture of the relative images 201 and an arbitrary focus O. The three-dimensional modeled external fixture 300 can include spaced platforms 306, 308 to which six spherical radiopaque fiducial markers 318 are attached. These markers (by entering digital dimensions) are used as known shapes A, B, C, D, E, F having (by this entered digital dimension) known distances AB, BC, CA between their connecting lines and DE, EF, and FD. The fiducial marker shapes A, B, and C are also spaced from the fiducial marker shapes D, E, and F by a known length (by entering the digital dimension). Thus, Figure 3 depicts a three-by-three (3×3) fiducial marker configuration, which refers to three synchronized fiducial markers on each of the first platform 306 and the second platform 308. In this example, the unique fiducial marker 318’ represented by A is smaller than the remaining (same-sized) fiducial markers 318. The unique fiducial marker 318’A distinguishes the first platform 306 from the second platform 308 and the rotation of the first platform 306 in the image space.

[0052] When the fiducial markers of the actual external fixture are spherical as Figure 1 shown, due to the position of the focus O of the image 201 and the imaging plane relative to the fiducial markers, the fiducial markers in the image 201 are depicted 218 as spherical, as Figure 2 shown. The elliptical fiducial marker depictions 218 in the image 201 can include relatively clear outer edges, as Figure 2 shown. As Figure 4 shown, at 406, method 400 can digitally locate the elliptical fiducial marker depictions 218 in the image 201. Method 400 can utilize the shape edges of the elliptical fiducial marker depictions 218 and conclude that the corresponding fiducial markers that are the source of the fiducial marker depictions 218 are actually points located and positioned somewhere above the shadow / depiction 218. Method 400 can also conclude that each actual fiducial marker lies on the vector of the line between the center of the description of each elliptical fiducial marker depiction 218 and the focus of the source of the image 201, as Figure 3 shown.

[0053] As Figure 4As shown, at 408, method 400 can further determine or relate (or define) the relative distance between each elliptical fiducial mark depiction 218 and the actual corresponding fiducial mark, as well as the distance between each elliptical fiducial mark depiction 218 and the image source or focus O, by way of the magnification factor depicted by each elliptical fiducial mark 218. In some embodiments, method 400 locates and evaluates the size and position of the elliptical fiducial mark depictions 218 within the image 201. In some embodiments, method 400 can utilize the digitally determined minor axis dimension of the fiducial mark depiction 218, which is related to the digitally input actual diameter of the elliptical fiducial mark depiction 218, and which can be related to the relative distance between the image 201 and the focus O and the height along the vector extending therebetween, where the actual fiducial mark lies on the vector. In some embodiments, method 400 can utilize the image resolution to determine the initial image scale and relative size of the fiducial mark depiction 218 relative to its digitally input actual size.

[0054] For example, method 400 can digitally identify or measure the diameter of each elliptical fiducial mark depiction 218 (e.g., identify or measure the minor diameter or average diameter of each elliptical fiducial mark depiction 218), and compare the diameter of each elliptical fiducial mark depiction 218 to the actual diameter of the corresponding actual fiducial mark, thereby digitally determining the magnification factor of each elliptical fiducial mark depiction 218 and utilizing the magnification factor to relate or describe the relative distance between the fiducial mark depiction 218 in the image 201 and the actual fiducial mark, as well as the distance between the fiducial mark depiction 218 and the image source or focus O. Method 400 can thus utilize the digitally determined diameter of each elliptical fiducial mark depiction 218 and the digitally input actual diameter of the corresponding fiducial mark of the actual fixture to determine or describe the relative distance between the elliptical fiducial mark depiction 218 and the actual fiducial mark as a function of the distance between the fiducial mark depiction 218 and the image source or focus O. Accordingly, the method can determine an equation, expression, or relationship for the distance of each actual fiducial mark from the image 201 (e.g., the distance along the Z-axis extending perpendicularly from the image 201).

[0055] The distance between each elliptical fiducial mark depiction 218 and the actual corresponding fiducial mark by itself does not indicate the position and pose of the image source or focus O. Method 400 can utilize the input dimensions related to the distance between the actual fiducial marks to determine the apparent focus position and pose of the image source or focus O.

[0056] The system and method can determine the position and pose of the actual external fixation device corresponding to the external fixation device 200 depicted in the radiographic image 201 via a three-dimensional model 325 that is digitally modeled or created, where the three-dimensional model 325 has an externally fixed device 300 that is three-dimensionally modeled corresponding to the actual external fixation device relative to the opposing image 201 and an arbitrary focal point O, as Figure 3 shown. As Figure 3 shown, the focal point O is defined as an arbitrary point floating in the space above the image 210.

[0057] At 410, the method 400 can define multiple constraints by constructing multiple closed vector loops, each closed vector loop extending through or across at least two of the following: the center of the fiducial marker depiction 218 of the image 201, the center of the modeled fiducial marker 318 of the three-dimensionally modeled external fixation device 300, and an arbitrarily selected focal point location O, as Figure 3 and 4 shown. As a non-limiting example, the method 400 can construct a first closed vector loop 330 of P1A-O-P2A-P1A, a second closed vector loop 332 of B2A-C-E-P1A-B2A, and / or a third closed vector loop 334 of B0A-A-B-B1A-BOA, as Figure 3 shown.

[0058] At 412, the method 400 can solve the multiple closed vector loops (e.g., such that they collapse on their own and / or equal zero) to determine (e.g., in the X and Y and Z coordinates from the image 201) the node positions A, B, C, D, E, F of each actual fiducial marker of the external fixator, and (e.g., in the X and Y and Z coordinates from the image 201) the position of the actual, true, or corrected focal point O of the image 201, as Figure 4 shown. It should be noted that using a finite number of such closed vector loops, the node positions A, B, C, D, E, F of each actual fiducial marker of the external fixator and the position of the actual focal point O of the image 201 can be determined (i.e., a well-constrained problem). However, relatively more such closed vector loops can be used to statistically improve the results.

[0059] After determining all the node positions A, B, C, D, E, F, and O in the image space, at 414, the method 400 can construct a suitable first coordinate transformation matrix (or coordinate transformation) for the actual external fixation device (depicted at least in part by a set of spherical fiducial markers) relative to the image 201 (by the input dimension), as Figure 4as shown. Then, at 414, the method 400 can take the inverse matrix of the coordinate transformation matrix to determine a second coordinate transformation matrix that defines or describes the position (e.g., X, Y, and Z positioning) and orientation (i.e., direction in X, Y, and Z) of the image 201 relative to the actual external fixture, as Figure 4 shown.

[0060] In some embodiments, the method 400 can construct a suitable first coordinate transformation by determining the cross product of a pair of suitable vectors between nodes of a common platform to determine a vector perpendicular to the two suitable vectors, the origin of which is at the common node of the two suitable vectors. For example, the method 400 can take the cross product of AB x AC to determine a vector perpendicular to AB and AC, the origin of which is at A. The method 400 can then cross multiply the resulting vector with one of the previous suitable vectors to determine an orthogonal coordinate system (i.e., a coordinate transformation matrix), which in this case depicts or describes the platform in the image space (defined by the respective nodes chosen, e.g., defined by ABC in the above example). In the case where multiple closed vector loops are determined, the method 400 can thereby define the coordinate transformation (i.e., determine the row dimension, column dimension, and height dimension) of a set of known actual fiducial marks in the shadow image space.

[0061] The method 400 can utilize the second coordinate transformation matrix to create a digital three-dimensional model 325 of the actual external fixture 300 and the image 201 in a relative position and orientation / pose with respect to the three-dimensionally modeled external fixture 300 from the perspective of the image focus O or the camera view. The method can render the three-dimensional model 300 to display the three-dimensional model 300 to the user such that the user can qualitatively inspect or view the three-dimensional model 300 to ensure that the three-dimensional model 300 constructed by the method 400 is in the correct position and pose relative to the image 201.

[0062] In Figure 5 is depicted an example of constructing the second coordinate transformation matrix and the resulting coordinate transformation matrix for the digitally modeled external fixator 300 and the image 201 for Figure 3 .

[0063] In the case where the coordinate system is determined, the method 400 can utilize the set of known three-dimensional objects in each of a plurality of radiographic images that use a consistent method in each image to determine the coordinate transformation between any pair of images within the plurality of images. When constructing the true three-dimensional position and pose of the three-dimensional object, the system and method can correct any non-orthogonal or otherwise rotated pair of images, thereby accurately describing any other annotation or measurement performed within the radiographic images.

[0064] The method and system can use method 400 on a per-image basis for each of a plurality of images 201 to determine a plurality of coordinate systems, all of which describe the same known fiducial markers (external fixtures) in a larger patient space.

[0065] As will be apparent to those of ordinary skill in the art, the present invention provides significant improvements in the fields of external fixture and anatomical structure computer modeling (including hexapod and bone segment modeling), in the field of radiographic imaging (including distortion correction of radiographic images), and in the field of determination of external fixture adjustment prescriptions (including hexapod adjustment prescriptions).

[0066] Those of ordinary skill in the art will recognize that aspects of the present invention may be embodied in a system, method, and / or computer program product. In some embodiments, aspects of the present invention may be embodied entirely in hardware, entirely in software (e.g., firmware, resident software, microcode, etc.), or in a combination of software and hardware, which embodiments are generally referred to herein as a "system" and include circuits and / or modules.

[0067] Figure 6 An example of a computer system incorporating and using one or more aspects of the present invention is described. Computer system 500 may be a computer system of an article manufacturing and / or repair facility, such as a computer system for additively manufacturing an article, and / or a computer system for generating data used by an AM instrument or device to manufacture an article. Figure 6 Computer system 500 is adapted to store and / or execute program code, such as program code for performing the processes described above, and includes at least one processor 502 directly or indirectly connected to a memory 504 via a bus 520. In operation, processor 502 may obtain instructions for execution by the processor from memory 504. Memory 504 may include local memory, mass storage, and cache memory used during actual execution of the program code to reduce the number of times code must be retrieved from mass storage during execution of the program code. A non-limiting list of examples of memory 504 includes hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing. Memory 504 may include an operating system 505 and one or more computer programs 506, such as one or more execution programs for performing the aspects described herein (e.g., adjusting the digital layout of a circuit design).

[0068] Input / output (I / O) devices 512, 514 (e.g., peripheral devices) may be connected directly to the system or through an I / O controller 510. A network adapter 508 may also be connected to the system to enable the computer system to connect to other computer systems via an intervening private or public network. Modems, cable modems, and Ethernet cards are just a few of the currently available types of network adapter 508. In one example, network adapter 508 facilitates obtaining data from remote sources to facilitate various aspects of the present invention.

[0069] The computer system 500 may be connected to a memory 516 (e.g., a non-volatile storage area such as a disk drive, optical drive, tape drive, etc.) having one or more databases. The memory 516 may include internal storage devices or additional or network-accessible memory. Computer programs in the memory 516 may be loaded into the memory 504 and executed by the processor 502.

[0070] The computer system 500 may include fewer components than shown, additional components not shown herein, or some combination of the shown and additional components. The computer system 500 may include any computing device, such as a mainframe, server, personal computer, workstation, laptop computer, handheld computer, smartphone, desktop or other mobile device, telephone device, network device, virtualization device, storage controller, etc.

[0071] Additionally, the above processes may be performed by multiple computer systems 500 working in concert as part of a computing environment.

[0072] In some embodiments, aspects of the present invention may take the form of a computer program product embodied in a computer-readable medium. The computer-readable medium may have computer-readable program code embodied therein. A variety of computer-readable media or combinations thereof may be utilized. For example, the computer-readable medium may include computer-readable storage media, examples of which include (but are not limited to) one or more electronic, magnetic, optical, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. For example, examples of computer-readable storage media include: an electrical connection having one or more wires, a portable computer diskette, a hard disk, or a mass storage device, a random access memory (RAM), a read-only memory (ROM), and / or an erasable programmable read-only memory (e.g., 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 magnetic tape), or any suitable combination of the foregoing. The computer-readable storage medium is defined to include tangible media that can contain or store program code for use by or in connection with an instruction execution system, apparatus, or device (e.g., a processor). Thus, program code stored in or on a computer-readable medium results in an article of manufacture that includes the program code (e.g., a "computer program product").

[0073] Now referring Figure 7 , in one example, computer program product 600 includes, for example, one or more computer-readable media 602 having stored thereon computer-readable program code method or logic 604 to provide and facilitate one or more aspects of the present invention.

[0074] The program code contained in or stored on a computer-readable medium can be obtained and executed by a computer system (including a computer, computer system, etc. of its components) and / or other devices to cause the computer system, its components, and / or other devices to behave / operate in a particular manner. The program code can be transmitted using any suitable medium, including (but not limited to) wireless, wired, optical fiber, and / or radio frequency. The program code for performing operations to execute, implement, or facilitate aspects of the present invention can be written using one or more programming languages. In some embodiments, the programming languages include object-oriented and / or procedural programming languages such as C, C++, C#, Java, etc. The program code can be executed entirely on the user's computer, entirely remote from the user's computer, or in a combination where part is executed on the user's computer and part is executed on a remote computer. In some embodiments, the user's computer and the remote computer communicate via a network such as a local area network (LAN) or a wide area network (WAN) and / or via an external computer (e.g., by using the network of an Internet service provider).

[0075] In one example, the program code includes one or more obtained program instructions that are executed by one or more processors. The computer program instructions can be provided to one or more processors of, for example, one or more computer systems to produce a machine such that the program instructions, when executed by the one or more processors, perform, implement, or facilitate various aspects of the present invention, such as the activities or functions described herein in the flowcharts and / or block diagrams. Thus, in some embodiments, each box or combination of boxes of the flowcharts and / or block diagrams depicted and described herein can be implemented by computer program instructions.

[0076] The flowcharts and block diagrams depicted and described with reference to the accompanying drawings illustrate the architecture, functionality, and operation of possible embodiments of systems, methods, and / or computer program products according to various aspects of the present invention. Thus, according to various aspects of the present invention, these flowcharts and / or block diagrams can be a method, apparatus (system), and / or computer program product.

[0077] In some embodiments, as described above, each box in a flowchart or block diagram can represent a module, segment, or portion of code that includes one or more executable instructions for implementing the specified behavior and / or logical function of that box. Those of ordinary skill in the art will understand that the order in which the acts / functions specified or performed by the boxes occur can differ from the order depicted and / or described, or can occur concurrently with one or more other boxes, or partially / fully concurrently. In fact, two consecutive boxes shown can be executed substantially concurrently, or sometimes can be executed in the reverse order. Additionally, each box of the block diagrams and / or flowcharts, and combinations of boxes in the block diagrams and / or flowcharts, can be implemented entirely by a dedicated hardware-based system that performs the specified act / function of a box or the entire block diagram or flowchart, or in combination with computer instructions.

[0078] It should be understood that the above description is intended to be illustrative and not restrictive. Many changes and modifications can be made by those of ordinary skill in the art without departing from the general spirit and scope of the present invention as defined by the appended claims and their equivalents. For example, the above embodiments (and / or aspects thereof) can be used in combination with each other. Additionally, many modifications can be made to adapt a particular situation or material to the teachings of various embodiments without departing from their scope. Although the dimensions and types of the materials described herein are intended to illustrate the parameters of various embodiments, they are in no way restrictive and are merely exemplary. After reviewing the above description, many other embodiments will be apparent to those of skill in the art. Accordingly, the scope of the various embodiments should be determined with reference to the appended claims and the full scope of the equivalents to which those claims are entitled.

[0079] The terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the present invention. As used herein, unless the context clearly dictates otherwise, the singular forms "a", "an", and "the" are intended to include the plural forms as well. It should also be 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 of "contain", such as "contains" and "containing") and any other grammatical variants thereof are open-ended linking verbs. Thus, a method or article that "comprises", "has", "includes" or "contains" one or more steps or elements has one or more steps or elements, but is not limited to having only those one or more steps or elements. Similarly, a step of a method or an element that "comprises", "has", "includes" or "contains" one or more features has those one or more features, but is not limited to having only those one or more features.

[0080] As used herein, the terms "comprising", "has", "including", "containing" and their other grammatical variants encompass the terms "consisting of" and "consisting essentially of".

[0081] When used herein, the phrase "consisting essentially of" or its grammatical variants shall be regarded as designating the recited feature, integer, step or component, but not excluding the addition of one or more additional features, integers, steps, components or groups thereof, provided that the additional features, integers, steps, components or groups thereof do not materially alter the basic and novel features of the claimed composition or method.

[0082] All publications cited in this specification are hereby incorporated by reference as if each individual publication was specifically and individually indicated to be incorporated by reference as fully set forth herein.

[0083] Subject matter incorporated by reference is not to be considered an alternative to any claim limitation unless expressly stated otherwise.

[0084] Where a range of one or more values is recited in the specification, each such range is to be taken as a shorthand for presenting information, and is understood to include every discrete point within the range as if fully set forth herein.

[0085] Although aspects and embodiments of the invention have been described and depicted herein, alternative aspects and embodiments may occur to those skilled in the art that achieve the same objectives. Accordingly, the invention and the appended claims are intended to cover all such further and alternative aspects and embodiments that fall within the true spirit and scope of the invention.

Claims

1. A method for digitally determining the actual position and pose of a set of known objects from an orthopedic fixation device in a projected three-dimensional space located above a digital two-dimensional radiographic space, the orthopedic fixation device including actual fiducial markers that are spherical in the projected three-dimensional space, the method comprising: Digitally input a first digital radiographic image that depicts the known object set and multiple fiducial marker depictions in the projected three-dimensional space above the two-dimensional radiographic space; Digitally input the digital dimensions of the actual external device, the digital dimensions including digital dimensions corresponding to the diameters of the actual fiducial markers and the distances between the actual fiducial markers; Digitally locate and measure the diameters of the multiple fiducial marker depictions and compare the diameters of the multiple fiducial marker depictions with the digitally input dimensions of the diameters of the actual fiducial markers to determine a magnification factor; Use the magnification factor to determine the relative distances between the multiple fiducial marker depictions and the actual fiducial markers and the distances between the multiple fiducial marker depictions and an arbitrarily selected focus; Construct multiple closed vector loops, each closed vector loop extending through the center of an actual fiducial marker in the projected three-dimensional space determined according to the digital dimensions, the center of one fiducial marker depiction among the multiple fiducial marker depictions, and the arbitrarily selected focus; and Solve the multiple closed vector loops to determine the nodal positions of the actual fiducial markers and the position of the actual focus, thereby determining the actual position and pose of the known object set in the projected three-dimensional space above the two-dimensional radiographic space.

2. The method according to claim 1, further comprising constructing a three-dimensional model of the actual position and pose of the set of known objects in the projected three-dimensional space.

3. The method according to claim 1, wherein, The multiple fiducial marker depictions are elliptical, and measuring the diameters of the multiple fiducial marker depictions includes measuring the average diameter of the ellipses.

4. The method according to claim 3, wherein, The actual fiducial markers of the orthopedic fixation device are radiopaque.

5. The method according to claim 1, wherein, The first digital radiographic image further includes a depiction of at least one anatomical structure connected to the known object set, and further includes constructing a three-dimensional model of the actual position and pose of the at least one anatomical structure in the projected three-dimensional space.

6. The method according to claim 1, wherein, The actual fiducial markers of the orthopedic fixation device include fiducial markers with diameters smaller than other fiducial markers, and the other fiducial markers have the same diameter.

7. The method according to claim 1, wherein, Determining the actual position and pose of the known object set in the projected three-dimensional space above the two-dimensional radiographic space includes constructing a coordinate transformation matrix that defines the position and pose of the known object set relative to the first digital radiographic image.

8. A computer-readable storage medium that can be read by one or more processing circuits and stores instructions executable by one or more processors for performing a method for digitally determining the actual position and pose of a set of known objects from an orthopedic fixation device in a projected three-dimensional space located above a digital two-dimensional radiographic space, the orthopedic fixation device including actual fiducial markers that are spherical in the projected three-dimensional space, the method comprising: Digitally input a first digital radiographic image that depicts the known object set and multiple fiducial marker depictions in the projected three-dimensional space above the two-dimensional radiographic space; Digitally input the digital dimensions of the actual external device, the digital dimensions including digital dimensions corresponding to the diameters of the actual fiducial markers and the distances between the actual fiducial markers; Digitally locate and measure the diameters of the multiple fiducial marker depictions and compare the diameters of the multiple fiducial marker depictions with the digitally input dimensions of the diameters of the actual fiducial markers to determine a magnification factor; and Determine the relative distance between the plurality of fiducial marker depictions and the actual fiducial marker, and the distance between the plurality of fiducial marker depictions and an arbitrarily selected focus using the magnification factor; Construct a plurality of closed vector loops, each closed vector loop extending through the center of one of the plurality of fiducial marker depictions and the arbitrarily selected focus; and Solve the plurality of closed vector loops to determine the node positions of the actual fiducial marker and the position of the actual focus, thereby determining the actual position and pose of the known object set in the projected three-dimensional space above the two-dimensional radiographic space.

9. The computer-readable storage medium according to claim 8, further comprising constructing a three-dimensional model of the actual position and pose of the set of known objects in the projected three-dimensional space.

10. The computer-readable storage medium according to claim 8, wherein, The plurality of fiducial marker depictions are elliptical, and measuring the diameters of the plurality of fiducial marker depictions includes measuring the minor axis of the ellipse.

11. The computer-readable storage medium according to claim 10, wherein, The actual fiducial markers of the orthopedic fixation device are radiopaque.

12. The computer-readable storage medium according to claim 11, wherein, The first digital radiographic image further includes a depiction of at least one anatomical structure connected to the known object set, and further includes constructing a three-dimensional model of the actual position and pose of the at least one anatomical structure in the projected three-dimensional space.

13. The computer-readable storage medium according to claim 8, wherein, The actual fiducial markers of the orthopedic fixation device include fiducial markers having a diameter smaller than other fiducial markers, and the other fiducial markers have the same diameter.

14. The computer-readable storage medium according to claim 8, wherein, Determining the actual position and pose of the known object set in the projected three-dimensional space above the two-dimensional radiographic space includes constructing a coordinate transformation matrix that defines the position and pose of the known object set relative to the first digital radiographic image.

15. A system for digitally determining the actual position and orientation of a known set of objects from an orthopedic fixation device in a projected three-dimensional space located above a digital two-dimensional radiographic space, the orthopedic fixation device including actual fiducial markers that are spherical in the projected three-dimensional space, the system comprising: A memory; At least one processor in communication with the memory; and Program instructions executable by one or more processors via the memory to perform a method for digitally determining the actual position and pose of a known object set from an orthopedic fixation device in a projected three-dimensional space above a digital two-dimensional radiographic space, the method comprising: Digitally input a first digital radiographic image depicting the known object set and a plurality of fiducial marker depictions in the projected three-dimensional space above the two-dimensional radiographic space; Digitally input the digital dimensions of an actual external device, the digital dimensions including digital dimensions corresponding to the diameters of the actual fiducial markers and the distance between the actual fiducial markers; Digitally position and measure the diameters of the plurality of fiducial marker depictions, and compare the diameters of the plurality of fiducial marker depictions with the digitally input dimensions of the diameters of the actual fiducial markers to determine a magnification factor; Determine the relative distance between the plurality of fiducial marker depictions and the actual fiducial marker, and the distance between the plurality of fiducial marker depictions and an arbitrarily selected focus using the magnification factor; Construct a plurality of closed vector loops, each closed vector loop extending through the center of the actual fiducial marker in the projected three-dimensional space determined according to the digital dimensions, the center of one of the plurality of fiducial marker depictions, and the arbitrarily selected focus; and Solve the plurality of closed vector loops to determine the node positions of the actual fiducial markers, thereby determining the actual foci in order to determine the actual positions and poses of the known object set in the projected three-dimensional space located above the two-dimensional radiographic space.

16. The system according to claim 15, further comprising constructing a three-dimensional model of the actual position and orientation of the known set of objects in the projected three-dimensional space.

17. The system according to claim 15, wherein, The plurality of fiducial markers are depicted as ellipses, and measuring the diameters depicted by the plurality of fiducial markers includes measuring the average diameter of the ellipses.

18. The system according to claim 15, further comprising determining the relationship between the first digital radiographic images by comparing common objects of the known set of objects depicted in the first digital radiographic images.

19. The system according to claim 18, wherein, The first digital radiographic image further includes a depiction of at least one anatomical structure connected to the known object set, and further includes constructing a three-dimensional model of the actual position and pose of the at least one anatomical structure in the projected three-dimensional space.

20. The system according to claim 19, wherein, The actual fiducial markers of the orthopedic fixation device are radiopaque.

21. The system according to claim 15, wherein, Determining the actual positions and poses of the known object set in the projected three-dimensional space located above the two-dimensional radiographic space includes constructing a coordinate transformation matrix that defines the position and pose of the known object set relative to the first digital radiographic image.

Images