Patent Publication Number: US-2022237797-A1

Title: Hinge Detection For Orthopedic Fixation

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 16/839,381 filed Apr. 3, 2020, the contents of which are hereby incorporated by reference in their entirety. 
    
    
     BACKGROUND 
     Techniques used to treat fractures and/or deformities of anatomical structures, such as bones, can include the use of external fixators, such as hexapods and other fixation frames, which are surgically mounted to anatomical structure segments on opposed sides of a fracture site. A pair of radiographic images is taken of the fixator and anatomical structure segments at the fracture site. Data from the images is then manipulated to construct a three-dimensional representation of the fixator and the anatomical structures segments that can be used in developing a treatment plan, which may for example comprise realigning the anatomical structure segments through adjustments to the fixator. 
     Existing techniques for controlling fixator manipulation may, however, involve a number of limitations that may introduce inefficiency, complication, and unreliability. For example, some conventional techniques may rely on a surgeon or other user to indicate locations of certain fixator elements, such as hinges, within images that are displayed in a graphical user interface of a computer. However, it may often be difficult for the user to identify and mark positions of the hinges and other fixator elements within the images. In particular, depending upon the location and orientation from which an image is captured, hinges and other fixator elements may not be identified easily, such as because they may wholly or partially overlap one another or may otherwise be obscured within the images. This may make it cumbersome for the user to identify the fixator elements, thereby increasing time required to identify the elements, increasing the probability of errors, and reducing the reliability of the calculations. This may reduce the reliability of the treatment plan, possibly resulting in improper alignment of anatomical structures segments during the healing process, compromised union between the anatomical structure segments, necessitating additional rounds of radiographic imaging to facilitate alignment corrections, or even necessitating additional surgical procedures. 
     SUMMARY 
     Techniques for hinge detection for orthopedic fixation, for example for correction of a deformity of an anatomical structure, such as a bone, are described herein. In particular, in some examples, a fixation apparatus may be attached to first and second anatomical structure segments. Images, such as x-rays, of the fixation apparatus and the attached anatomical structure segments may then be captured from different orientations with respect to the fixation apparatus. 
     In some examples, various manipulations to the fixation apparatus for correction of the anatomical structure deformity may be determined based on positions and orientations of the anatomical structure segments in three-dimensional space. Also, in some examples, the positions and orientations of the anatomical structure segments in three-dimensional space may be determined based on the images. In particular, in some cases, the positions and orientations of the anatomical structure segments in three-dimensional space may be determined by having a surgeon or other user indicate locations of various fixator elements and anatomical structures within the images. However, as described above, it may often be difficult for the user to identify and mark positions of certain fixator elements, such as hinges, within the images. In particular, depending upon the location and orientation from which an image is captured, hinges and other fixator elements may be not be identified easily, such as because they may wholly or partially overlap one another or may otherwise be obscured within the images. This may make it cumbersome for the user to identify the fixator elements, thereby increasing time required to identify the elements, increasing the probability of errors, and reducing the reliability of the calculations. 
     To alleviate the above and other problems, an automated or semi-automated hinge detection process may be employed. Specifically, in some examples, first and second images may be displayed of the first and the second anatomical structure segments with the fixation device attached thereto. Indications may be received of first image hinge locations associated with the plurality of hinges in the first image. Projected second image hinge locations associated with the plurality of hinges in the second image may then be determined based at least in part on the indications of the first image hinge locations. Hinge candidates may be detected in the second image having shapes associated with the plurality of hinges. The hinge candidates may be detected by computer software using automated software-based image analysis techniques. For example, the hinges may have circular shapes, and the computer software may employ circle detection algorithms, such as a Hough transformation, to identify circular shapes in the second image as hinge candidates. Candidate second image hinge locations of the hinge candidates within the second image may then be identified. 
     Adjusted second image hinge locations associated with the plurality of hinges within the second image may then be calculated based at least in part on the projected second image hinge locations and the candidate second image hinge locations. In some examples, in order to calculate the adjusted second image hinge locations, the hinge candidates may be grouped into a set of hinge candidate groups, for example based on similarities of their locations and size characteristics (e.g., radius lengths). The set of hinge candidate groups may then be weighted based at least in part on a number of hinge candidates within each of the set of hinge candidate groups. A highest weighted subset of hinge candidate groups from the set of hinge candidate groups may then be selected. A plurality of average group locations may then be calculated, with each of the average group locations being associated with a respective hinge candidate group of the highest weighted subset of hinge candidate groups. A transformation matrix may then be constructed that describes a spatial relationship between the projected second image hinge locations and the plurality of average group locations. The transformation matrix may then be used to adjust the projected second image hinge locations to the adjusted second image hinge locations. The adjusted second image hinge locations may then be used to determine physical locations of the fixation device and the first and second anatomical structure segments in physical three-dimensional space. The physical locations of the fixation device and the first and second anatomical structure segments may then be used to determine manipulations to the fixation device for the correction of the deformity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
       The foregoing summary, as well as the following detailed description of the preferred embodiments of the application, will be better understood when read in conjunction with the appended drawings. For the purposes of illustrating the methods and/or techniques of orthopedic fixation with imagery analysis, there are shown in the drawings preferred embodiments. It should be understood, however, that the instant application is not limited to the precise arrangements and/or instrumentalities illustrated in the drawings, in which: 
         FIG. 1  is a perspective view of a fixation assembly positioned for imaging in accordance with an embodiment; 
         FIG. 2  is a perspective view of an example imaging process of the fixation assembly illustrated in  FIG. 1 ; 
         FIGS. 3A and 3B  are flow diagrams illustrating an example process for controlling manipulation of a fixation apparatus to correct an anatomical structure deformity; 
         FIG. 4  is a screen shot of an example interface for selecting a Perspective Frame Matching (PFM) technique; 
         FIG. 5  is a screen shot of an example configuration information entry interface for the PFM technique; 
         FIG. 6  is a screen shot of an example first image information entry interface for the PFM technique; 
         FIG. 7  is a screen shot of an example close-up assist interface for the PFM technique; 
         FIGS. 8A-8H  are screen shots of an example second image information entry interface for the PFM technique; 
         FIG. 9  is a screen shot of example deformity parameter interface for the PFM technique; 
         FIG. 10  is a screen shot of an example mounting parameter interface for the PFM technique; 
         FIG. 11  is a screen shot of a first example treatment plan interface for the PFM technique; 
         FIG. 12  is a screen shot of a second example treatment plan interface for the PFM technique; 
         FIG. 13  is a screen shot of a third example treatment plan interface for the PFM technique; 
         FIG. 14A  is a flow diagram illustrating an example process for hinge detection for orthopedic fixation; 
         FIG. 14B  is a flow diagram illustrating an example process for calculating adjusted second image hinge locations; 
         FIG. 15A  is a diagram illustrating example images of first and second anatomical structure segments and a fixator attached thereto; 
         FIG. 15B  is a diagram illustrating example first and second images of a fixator in which hinge locations are indicated in the first image but not the second image; 
         FIG. 16  is a diagram illustrating example graphical projection of a fixator overlaid upon an image; 
         FIG. 17  is a diagram illustrating an example graphical projection of a fixator that is manipulated by a user; 
         FIG. 18  is a diagram illustrating example projected second image hinge locations; 
         FIG. 19  is a diagram illustrating an example hinge candidate list; 
         FIG. 20  is a diagram illustrating an example hinge candidate group list; 
         FIG. 21  is a diagram illustrating an example hinge candidate group; 
         FIG. 22  is a diagram illustrating an example representation of a transformation matrix for calculating adjusted second image hinge locations; 
         FIG. 23  is a diagram illustrating an example adjustment of projected second image hinge locations; 
         FIG. 24  is a diagram illustrating example adjusted second image hinge locations; 
         FIG. 25  is a diagram illustrating example first and second images of a fixator in which hinge locations are indicated in the first image and adjusted second image hinge locations are calculated in the second image; and 
         FIG. 26  is a block diagram of an example computing device for use in accordance with the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     For convenience, the same or equivalent elements in the various embodiments illustrated in the drawings have been identified with the same reference numerals. Certain terminology is used in the following description for convenience only and is not limiting. The words “right”, “left”, “top” and “bottom” designate directions in the drawings to which reference is made. The words “inward”, “inwardly”, “outward”, and “outwardly” refer to directions toward and away from, respectively, the geometric center of the device and designated parts thereof. The terminology intended to be non-limiting includes the above-listed words, derivatives thereof and words of similar import. 
     Referring initially to  FIG. 1 , bodily tissues, for instance first and second anatomical structure segments  102 ,  104 , can be aligned and/or oriented to promote union or other healing between the bodily tissues. Anatomical structures may include, for example, anatomical tissue and artificial anatomical implants. Anatomical tissue may include, for example, bone or other tissue in the body. The alignment and/or orientation of the bodily tissues can be achieved by connecting the bodily tissues to an adjustable fixation apparatus, such as orthopedic fixator  100 . The orthopedic fixator can comprise an external fixation apparatus that includes a plurality of discrete fixator 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. A fixation apparatus may include, for example, a distraction osteogenesis ring system, a hexapod, or a Taylor spatial frame. By adjusting the spatial positioning of the fixator members 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 the healing process. The use of external orthopedic fixators in combination with the imagery analysis and positioning techniques described herein can be advantageous in applications where direct measurement and manipulation of the bodily tissues is not possible, where limited or minimally invasive access to the bodily tissues is desired, or the like. Some examples of orthopedic fixators and their use for correcting deformities of anatomical structure segments, as well as techniques for performing imagery analysis on the fixators and anatomical structure segments are described in U.S. Pat. No. 9,642,649, entitled “ORTHOPEDIC FIXATION WITH IMAGERY ANALYSIS,” issued on May 9, 2017, the entirety of which is hereby incorporated by reference. 
     The fixator members can be connected to each other via adjustment members, the adjustment members configured to facilitate the spatial repositioning of the fixator members with respect to each other. For example, in the illustrated embodiment, the orthopedic fixator  100  comprises a pair of fixator members in the form of an upper fixator ring  106  and a lower fixator ring  108 . The fixator rings  106 ,  108  can be constructed the same or differently. For instance, the fixator rings  106 ,  108  can have diameters that are the same or different. Similarly, the fixator rings  106 ,  108  can be constructed with varying cross sectional diameters, thicknesses, etc. It should be appreciated that the fixator members of the orthopedic fixator  100  are not limited to the illustrated upper and lower fixator rings  106 ,  108 , and that the orthopedic fixator  100  can be alternatively constructed. For example, additional fixator rings can be provided and interconnected with the fixator ring  106  and/or  108 . It should further be appreciated that the geometries of the fixator members are not limited to rings, and that at least one, such as all of the fixator members can be alternatively constructed using any other suitable geometry. 
     The first and second anatomical structure segments  102 ,  104  can be rigidly attached to the upper and lower fixator rings  106 ,  108 , respectively, with attachment members that can be mounted to the fixator rings  106 ,  108 . For example, in the illustrated embodiment, attachment members are provided in the form of attachment rods  110  and attachment wires  112 . 
     The rods  110  and the wires  112  extend between proximal ends attached to mounting members  114  that are mounted to the fixator rings  106 ,  108 , and opposed distal ends that are inserted into or otherwise secured to the anatomical structure segments  102 ,  104 . The mounting members  114  can be removably mounted to the fixator rings  106 ,  108  at predefined points along the peripheries of the fixator rings  106 ,  108 , for example by disposing them into threaded apertures defined by the fixator rings. With respect to each fixator ring  106 ,  108 , the mounting members  114  can be mounted to the upper surface of the ring, the lower surface of the ring, or any combination thereof. It should be appreciated that the attachment members are not limited to the configuration of the illustrated embodiment. For example, any number of attachment members, such as the illustrated rods  110  and wires  112  and any others, can be used to secure the anatomical structure segments to respective fixator members as desired. It should further be appreciated that one or more of the attachment members, for instance the rods  110  and/or wires  112 , can be alternatively configured to mount directly to the fixator rings  106 ,  108 , without utilizing mounting members  114 . 
     The upper and lower fixator rings  106 ,  108  can be connected to each other by at least one, such as a plurality of adjustment members. At least one, such as all, of the adjustment members can be configured to allow the spatial positioning of the fixator rings with respect to each other to be adjusted. For example, in the illustrated embodiment, the upper and lower fixator rings  106 ,  108  are connected to each other with a plurality of adjustment members provided in the form of adjustable length struts  116 . It should be appreciated that the construction of the orthopedic fixator  100  is not limited to the six struts  116  of the illustrated embodiment, and that more or fewer struts can be used as desired. 
     Each of the adjustable length struts  116  can comprise opposed upper and lower strut arms  118 ,  120 . Each of the upper and lower strut arms  118 ,  120  have proximal ends disposed in a coupling member, or sleeve  122 , and opposed distal ends that are coupled to universal joints  124  mounted to the upper and lower fixator rings  106 ,  108 , respectively. The universal joints of the illustrated embodiment are disposed in pairs spaced evenly around the peripheries of the upper and lower fixator rings  106 ,  108 , but can be alternatively placed in any other locations on the fixator rings as desired. 
     The proximal ends of the upper and lower strut arms  118 ,  120  of each strut  116  can have threads defined thereon that are configured to be received by complementary threads defined in the sleeve  122 , such that when the proximal ends of the upper and lower strut arms  118 ,  120  of a strut  116  are received in a respective sleeve  122 , rotation of the sleeve  122  causes the upper and lower strut arms  118 ,  120  to translate within the sleeve  122 , thus causing the strut  116  to be elongated or shortened, depending on the direction of rotation. Thus, the length of each strut  116  can be independently adjusted with respect to the remaining struts. It should be appreciated that the adjustment members are not limited to the length adjustable struts  116  of the illustrated embodiment, and that the adjustment members can be alternatively constructed as desired, for example using one or more alternative geometries, alternative length adjustment mechanisms, and the like. 
     The adjustable length struts  116  and the universal joints  124  by which they are mounted to the upper and lower fixator rings  106 ,  108 , allow the orthopedic fixator  100  to function much like a Stewart platform, and more specifically like a distraction osteogenesis ring system, a hexapod, or a Taylor spatial frame. That is, by making length adjustments to the struts  116 , the spatial positioning of the upper and lower fixator rings  106 ,  108 , and thus the anatomical structure segments  102 ,  104  can be altered. For example, in the illustrated embodiment the first anatomical structure segment  102  is attached to the upper fixator ring  106  and the second anatomical structure segment  104  is attached to the lower fixator ring  108 . It should be appreciated that attachment of the first and second anatomical structure segments  102 ,  104  to the upper and lower fixator rings  106 ,  108  is not limited to the illustrated embodiment (e.g., where the central longitudinal axes L 1 , L 2  of the first and second anatomical structure segments  102 ,  104  are substantially perpendicular to the respective planes of the upper and lower fixator rings  106 ,  108 ), and that a surgeon has complete flexibility in aligning the first and second anatomical structure segments  102 ,  104  within the upper and lower fixator rings  106 ,  108  when configuring the orthopedic fixator  100 . 
     By varying the length of one or more of the struts  116 , the upper and lower fixator rings  106 ,  108 , and thus the anatomical structure segments  102  and  104  can be repositioned with respect to each other such that their respective longitudinal axes L 1 , L 2  are substantially aligned with each other, and such that their respective fractured ends  103 ,  105  abut each other, so as to promote union during the healing process. It should be appreciated that adjustment of the struts  116  is not limited to the length adjustments as described herein, and that the struts  116  can be differently adjusted as desired. It should further be appreciated that adjusting the positions of the fixator members is not limited to adjusting the lengths of the length adjustable struts  116 , and that the positioning of the fixator members 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 apparatus. 
     Repositioning of the fixator members of an orthopedic fixation apparatus, such as orthopedic fixator  100 , can be used to correct displacements of angulation, translation, rotation, or any combination thereof, within bodily tissues. A fixation apparatus, such as orthopedic fixator  100 , utilized with the techniques described herein, can correct a plurality of such displacement defects individually or simultaneously. However, it should be appreciated that the fixation apparatus is not limited to the illustrated orthopedic fixator  100 , and that the fixation apparatus can be alternatively constructed as desired. For example, the fixation apparatus can include additional fixation members, can include fixation members having alternative geometries, can include more or fewer adjustment members, can include alternatively constructed adjustment members, or any combination thereof. 
     Referring now to  FIG. 2 , an example imaging of a fixation apparatus will now be described in detail. The images can be captured using the same or different imaging techniques. For example, the images 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 images can be captured from any position and/or orientation with respect to each other and with respect to the fixator  100  and the anatomical structure segments  102 ,  104 . In other words, there is no requirement that the captured images be orthogonal with respect to each other or aligned with anatomical axes of the patient, thereby providing a surgeon with near complete flexibility in positioning the imagers  130 . Preferably, the images  126 ,  128  are captured from different directions, or orientations, such that the images do not overlap. For example, in the illustrated embodiment, the image planes of the pair of images  126 ,  128  are not perpendicular with respect to each other. In other words, the angle a between the image planes of the images  126 ,  128  is not equal to 90 degrees, such that the images  126 ,  128  are non-orthogonal with respect to each other. Preferably, at least two images are taken, although capturing additional images may increase the accuracy of the method. 
     The images  126 ,  128  can be captured using one or more imaging sources, or imagers, for instance the x-ray imagers  130  and/or corresponding image capturing devices  127 ,  129 . The images  126 ,  128  can be x-ray images captured by a single repositionable x-ray imager  130 , or can be captured by separately positioned imagers  130 . Preferably, the position of the image capturing devices  127 ,  129  and/or the imagers  130  with respect to the space origin  135  of the three-dimensional space, described in more detail below, are known. The imagers  130  can be manually positioned and/or oriented under the control of a surgeon, automatically positioned, for instance by a software assisted imager, or any combination thereof. The fixator  100  may also have a respective fixator origin  145 . 
     Referring now to  FIGS. 3A and 3B , an example process for controlling manipulation of a fixation apparatus including rings and struts to correct an anatomical structure deformity of first and second anatomical structure segments will now be described in detail. In particular, at operation  310 , first and second anatomical structure segments are attached to a fixation apparatus, for example as shown in  FIG. 1  and described in detail above. At operation,  312 , first and second images of the fixation apparatus and the attached first and second anatomical structure segments are captured, for example as shown in  FIG. 2  and described in detail above. 
     The remaining operations of the process of  FIGS. 3A and 3B  (e.g., operations  314 - 342 ) will now be described in association with a treatment technique referred to hereinafter as Perspective Frame Matching, in which images, such as post-operative x-rays, may be used along with a frame to generate deformity and mounting parameters for a strut adjustment plan. For example, referring now to  FIG. 4 , an example treatment planning technique selection interface  400 -A is shown. In the example of  FIG. 4 , the user has selected option  401  in order to use the Perspective Frame Matching (PFM) technique, which will now be described in detail with reference to  FIGS. 5-13 . 
     Referring back to  FIG. 3A , at operation  314 , configuration information associated with a fixation apparatus is received, for example using one or more graphical user interfaces of a computing system. In some examples, the configuration information may include one or more geometric characteristics (e.g., size, length, diameter, etc.) of one or more elements of the fixation apparatus, such as struts, hinges, rings, and others. In some examples, the configuration information may include information such as ring types (e.g., full ring, foot plate, etc.), indications of mounting points (e.g., ring holes) used for strut mounting, and other information. In some examples, the configuration information may also include information about marker elements, for example that are mounted to components of the fixation apparatus, such as struts, hinges, and rings. Referring now to  FIG. 5 , an example configuration information entry interface  500  is shown. As shown, interface  500  includes ring type indicators  501  and  502 , which, in this example, are drop down menus that may be used to select ring types for the proximal and distal rings, respectively. Indicators  501  and  502  are set to the “Full” option to indicate that the proximal and distal rings are full rings. Interface  500  also includes diameter indicators  503  and  504 , which, in this example, are drop down menus that may be used to select diameters or lengths for the proximal and distal rings, respectively. 
     The interface  500  also includes controls for entry of strut information. In particular, interface  500  includes six drop down menus  512  may each be used to indicate a size of a respective strut. Global strut size indicator  511  may also be used to globally select a size for all six struts. Length selectors  513  may be each be used to select a length of a respective strut. Length indicators  514  may be each be used to provide a visual representation of the lengths of the respective struts. It is noted that the length indicators  514  do not necessarily depict the actual exact length of each strut, but rather represent the comparative lengths of the struts with respect to one another. 
     Save and Update button  516  may be selected to save and update the configuration information values shown in interface  500 . In some examples, selection of button  516  may cause interface  500  to display and/or update a graphical representation  520  of the fixation apparatus generated based, at least in part, on the entered configuration information. The graphical representation  520  may be displayed using one or more graphical user interfaces of a computing system. As shown, graphical representation  520  includes six struts that may be color-coded in multiple colors for easy identification. For example, in some cases, each of the struts (or at least two of the struts) may be shown in different colors with respect to one another. The struts in graphical representation  520  may have sizes, lengths, mounting points, and other features corresponding to entered configuration information. Graphical representation  520  also depicts the fixator rings, which may have diameters/lengths, ring types, and other features corresponding to entered configuration information. Graphical representation  520  may, for example, improve efficiency and reliability by providing the user with a visual confirmation of information entered into interface  500 , for example to allow fast and easy identification of errors or other problems. 
     At operation  316 , images of the fixation apparatus and the first and second anatomical structure segments attached thereto are displayed, for example using one or more graphical user interfaces of a computing system. The displayed images may include images that were captured at operation  312 , such as using x-ray imaging, computer tomography, magnetic resonance imaging, ultrasound, infrared imaging, photography, fluoroscopy, visual spectrum imaging, or any combination thereof. Techniques for acquiring images of the fixation apparatus and the first and second anatomical structure segments are described in detail above and are not repeated here. As set forth above, the acquired and displayed images need not necessarily be orthogonal to one another. Referring now to  FIG. 6 , an example first image information entry interface  600  is shown. As shown, interface  600  includes images  601 -A and  601 -B, which show the fixation apparatus and first and second anatomical structure segments from different angles. In the example of  FIG. 6 , image  601 -A corresponds to an anteroposterior (AP) View, while image  601 -B corresponds to a lateral (LAT) view. In some examples, the displayed images  601 -A-B may be loaded and saved in computer memory, for example in a library, database or other local collection of stored images. The displayed images  601 -A-B may then be selected and retrieved, acquired, and/or received from memory for display. 
     At operation  318 , first image information is received, for example using one or more graphical user interfaces of a computing system. The first image information may include indications of one or more locations, within the images, of at least part of one or more elements of the fixation apparatus. For example, the first image information may include one or more indications of locations of struts, hinges, rings, and other fixator elements. In some examples, the first image information may also include information about locations, within the images, of marker elements, for example that are mounted to components of the fixation apparatus, such as struts, hinges, and rings. In some cases, the first image information may include points representing locations of hinges and/or lines or vectors representing locations of struts. In some examples, the first image information may be entered into a computing system by selecting or indicating one or more locations within the displayed images, for example using a mouse, keyboard, touchscreen or other user input devices. In particular, using one or more input devices, a user may select points or other locations in the images, draw lines, circles, and generate other graphical indications within the images. For example, in some cases, a user may generate a point or small circle at a particular location in an image to indicate a location (e.g., center point) of a hinge within the image. As another example, in some cases, a user may generate a line and/or vector within an image to indicate a location and/or length of a strut within the image. 
     For example, as shown in  FIG. 6 , interface  600  includes six AP View strut indicator buttons  611 -A corresponding to each of the six struts of the fixation apparatus shown in AP View image  601 -A. Each button  611 -A includes text indicating a respective strut number (i.e., Strut 1, Strut 2, Strut 3, Strut 4, Strut 5, Strut 6). Buttons  611 -A may be selected by a user to indicate a strut for which first image information (e.g., hinge locations, strut locations, etc.) will be provided by the user in AP View image  601 -A. For example, in some cases, to provide first image information for Strut 1 in AP View image  601 -A, a user may first select the top strut indicator button  611 -A (labeled with the text “Strut 1”) in order to indicate to the software that the user is about to provide first image information for Strut 1 within AP View image  601 -A. In some cases, the strut indicator button  611 -A for Strut 1 may be pre-selected automatically for the user. Upon selection (or automatic pre-selection) of the strut indicator button  611 -A for Strut 1, the user may proceed to draw (or otherwise indicate) a representation of Strut 1 within AP View image  601 -A. For example, in some cases, the user may use a mouse or other input device to select a location  621  (e.g., a center point) of a proximal hinge for Strut 1 within image  601 -A. In some examples, the user may then use a mouse or other input device to select a location  622  (e.g., a center point) of the distal hinge of Strut 1 within image  601 -A. In some examples, the user may indicate the location and/or length of Strut 1 by selecting the locations of the proximal and distal hinges and/or as the endpoints of a line or vector that represents the location and/or length of Strut 1. For example, as shown in  FIG. 6 , the software may generate points or circles at the locations  621  and  622  of the proximal and distal hinges selected by the user within image  601 -A. Additionally, the software may generate a line  623  representing the location and/or length of Strut 1 that connects the points or circles at the locations  621  and  622  and of the proximal and distal hinges selected by the user within image  601 -A. Any other appropriate input techniques may also be employed by the user to indicate a location and/or length of Strut 1 within image  610 -A, such as generating line  623  by dragging and dropping a mouse, using a finger and/or pen on a touch screen, keyboard, and others. In some examples, the above described process may be repeated to draw points representing proximal and distal hinges and lines representing the locations and/or lengths of each of the six struts in the AP View image  601 -A. Furthermore, the above described process may also be repeated using LAT View strut indicator buttons  611 -B to draw points representing proximal and distal hinges and lines representing the locations and/or lengths of each of the six struts in the LAT View image  601 -B. 
     In some examples, the first image information generated within images  601 -A and  601 -B may include color-coded graphical representations of the struts, for example to enable the graphical representations to be more clearly associated with their respective struts. For example, in  FIG. 6 , the graphical representations (e.g., points, circles, and/or lines) of Strut 1 in images  601 A- and  601 -B may be colored in red. This may match a strut icon (which may also be colored red) displayed in the strut indicator buttons  611 -A and  611 -B for Strut 1 (displayed to the right of the text “Strut 1” in buttons  611 -A and  611 -B). As another example, in  FIG. 6 , the graphical representations (e.g., points, circles, and/or lines) of Strut 3 in images  601 -A and  601 -B may be colored in yellow. This may match a strut icon (which may also be colored yellow) displayed in the strut indicator buttons  611 -A and  611 -B for Strut 3 (displayed to the right of the text “Strut 3” in buttons  611 -A and  611 -B). 
       FIG. 6  includes an AP View close-up assist checkbox  616 -A and a LAT View close-up assist checkbox  616 -B, for example provided using one or more graphical interfaces of a computing system. Selection of checkboxes  616 -A and  616 -B may allow close-up views of areas of images  601 -A and  601 -B surrounding the proximal and distal hinges of the struts that are currently being drawn by the user. This may enable more accurate indications of the locations (e.g., center points) of the hinges. Referring now to  FIG. 7 , close-up assist interface  700  depicts another AP View image  701  with the close-up assist being selected to provide a proximal hinge close-up assist view  702  and a distal hinge close-up assist view  703 . As shown, proximal hinge close-up assist view  702  provides an enlarged view of an area of AP View image  701  associated with the proximal hinge, while distal hinge close-up assist view  703  provides an enlarged view of an area of AP View image  701  associated with the distal hinge. The user may manipulate (e.g., drag and drop) the location of the point/circle  721  in proximal hinge close-up assist view  702  in order to more accurately depict the center point of the proximal hinge. The user may also manipulate (e.g., drag and drop) the location of the point/circle  722  in distal hinge close-up assist view  703  in order to more accurately depict the center point of the distal hinge. As should be appreciated, corresponding close-up assist views similar to views  702  and  703  may also be provided for a respective LAT View image, for example using one or more graphical interfaces of a computing system. 
     Referring back to  FIG. 6 , to the right of buttons  611 -A, are six proximal hinge selector buttons  612 -A. Additionally, to the right of buttons  612 -A, are six distal hinge selector buttons  613 -A. Furthermore, to the right of buttons  613 -A, are six strut line selector buttons  614 -A. In some examples, buttons  612 -A and/or  613 -A may be selected to use the locations (e.g., center points) of the proximal and/or distal hinges indicated in AP View image  601 -A in calculating positions and orientations of the first and the second anatomical structure segments and rings of the fixation apparatus in three-dimensional space (see operation  322 ). Additionally, in some examples, buttons  612 -A and/or  613 -A may be selected to use the lines or vectors representing the location and/or length of struts indicated in AP View image  601 -A in calculating positions and orientations of the first and the second anatomical structure segments in three-dimensional space. Similarly, buttons  612 -B,  613 -B, and  614 -B may be used to select the use of locations (e.g., center points) of the proximal and/or distal hinges or strut lines or vectors indicated in LAT View image  601 -B in calculating positions and orientations of the first and the second anatomical structure segments in three-dimensional space. 
     Referring again to  FIG. 3A , at operation  320 , second image information is received, for example using one or more graphical user interfaces of a computing system. The second image information may include indications of one or more locations, within the images, of at least part of the first and the second anatomical structure segments. In some examples, the second image information may include indications of center lines of the first and the second anatomical structure segments and/or one or more reference points (e.g., end points) of the first and the second anatomical structure segments. In some examples, the second image information may also include indications of locations of marker elements, for example implanted or otherwise associated with the first and the second anatomical structure segments. In some examples, the second image information may be entered into a computing system by selecting or indicating one or more locations within the displayed images, for example using a mouse, keyboard, touchscreen or other user input devices. In particular, using one or more input devices, a user may select points or other locations in the images, draw lines, circles, and generate other graphical indications within the images. For example, in some cases, a user may generate points or small circles at particular locations in an image to indicate one or more reference points (e.g., end points) of the first and the second anatomical structure segments within the images. As another example, in some cases, a user may generate a line within an image to indicate a center line of the first and the second anatomical structure segments within the images. 
     Referring now to  FIG. 8A , an example second image information entry interface  800  is shown. As shown, interface  800  includes AP View image  601 -A and LAT View image  601 -B. Additionally, interface  800  includes buttons  801 - 808 , which may be used to assist in indication of anatomical structure center lines and reference points as will be described below. In particular, buttons  801  and  805  may be selected to indicate a proximal anatomical structure reference point in the AP View and LAT View, respectively. Buttons  802  and  806  may be selected to indicate a distal anatomical structure reference point in the AP View and LAT View, respectively. Buttons  803  and  807  may be selected to indicate a proximal anatomical structure center line in the AP View and LAT View, respectively. Buttons  804  and  808  may be selected to indicate a distal anatomical structure center line in the AP View and LAT View, respectively. For example, as shown in  FIG. 8A , a user may select button  807  and then use one or more input devices to draw the center line  831  for the proximal anatomical structure within LAT View image  601 -B. In some examples, the center line  831  may be colored red. Additionally, two guidelines  832  are generated and displayed by the software on both sides of the red center line. In some examples, the guidelines  832  may be colored green. These guidelines  832  may be displayed while the user is drawing the center line  831  in order to assist the user in locating the center of the anatomical structure segment. The guidelines  832  may be generated at equal distances from each side of the center line  831  and may assist the user by, for example, potentially allowing the user to match (or nearly match) the guidelines  832  to sides of the anatomical structure segment. As shown in  FIG. 8B , the user may select button  808  and then use one or more input devices to draw the center line  841  for the distal anatomical structure within LAT View image  601 -B. As shown in  FIG. 8C , the user may select button  803  and then use one or more input devices to draw the center line  851  for the proximal anatomical structure within AP View image  601 -A. As shown in  FIG. 8D , the user may select button  804  and then use one or more input devices to draw the center line  861  for the distal anatomical structure within AP View image  601 -A. As shown in  FIGS. 8B-8D , guidelines  832  may also be displayed for assistance in drawing center lines  841 ,  851  and  861 . 
     As shown in  FIG. 8E , the user may select button  805  and then use one or more input devices to indicate a reference point (e.g., end point) for the proximal anatomical structure within LAT View image  601 -B. As shown, a user has indicated a reference point  811  in LAT View image  601 -B at an end point of the proximal anatomical structure segment. Additionally, upon indication of reference point  811 , the software may generate and display a corresponding dashed reference line  812  in AP View image  601 -A. The reference line  812  is a line drawn across AP View image  601 -A that passes through the location of the LAT View proximal reference point  811  within AP View image  601 -A. The reference line  812  may, therefore, assist the user in determining the location of the corresponding AP View proximal reference point, which may often be at the intersection of the reference line  812  and the AP View proximal center line  851  within the AP View image  601 -A. As shown in  FIG. 8F , the user may select button  801  and then use one or more input devices to indicate a reference point (e.g., end point) for the proximal anatomical structure within AP View image  601 -A. In this example, the AP View proximal anatomical structure reference point  814  is indicated at the intersection of reference line  812  and the AP View proximal center line  851  within the AP View image  601 -A. The software may then generate and display a corresponding dashed reference line  813  in the LAT View image  601 -B. The reference line  813  is a line drawn across LAT View image  601 -B that passes through the location of the AP View proximal reference point  814  within LAT View image  601 -B. The reference line  813  may assist the user by helping the user to confirm that the AP View reference point  814  was placed correctly by showing how well it lines up relative to the LAT View reference point  811 . 
     As shown in  FIG. 8G , the user may select button  806  and then use one or more input devices to indicate a reference point (e.g., end point) for the distal anatomical structure within LAT View image  601 -B. As shown, a user has indicated a reference point  815  in LAT View image  601 -B at an end point of the distal anatomical structure segment. Additionally, upon indication of reference point  815 , the software may generate and display a corresponding dashed reference line  816  in AP View image  601 -A. The reference line  816  is a line drawn across AP View image  601 -A that passes through the location of the LAT View distal reference point  815  within AP View image  601 -A. The reference line  816  may, therefore, assist the user in determining the location of the corresponding AP View distal reference point, which may often be at the intersection of the reference line  816  and the AP View distal center line within the AP View image  601 -A. As shown in  FIG. 8H , the user may select button  802  and then use one or more input devices to indicate a reference point (e.g., end point) for the distal anatomical structure within AP View image  601 -A. In this example, the AP View distal anatomical structure reference point  817  is indicated at the intersection of reference line  816  and the AP View distal center line within the AP View image  601 -A. The software may then generate and display a corresponding dashed reference line  818  in the LAT View image  601 -B. The reference line  818  is a line drawn across LAT View image  601 -B that passes through the location of the AP View distal reference point  817  within LAT View image  601 -B. The reference line  818  may assist the user by helping the user to confirm that the AP View reference point  817  was placed correctly by showing how well it lines up relative to the LAT View reference point  815 . 
     Referring again to  FIG. 3A , at operation  322 , positions and orientations of the first and second anatomical structure segments and rings of the fixation apparatus are determined in three-dimensional space. For example, in some cases, imaging scene parameters pertaining to fixator  100 , the anatomical structure segments  102 ,  104 , imager(s)  130 , and image capturing devices  127 ,  129  are obtained. The imaging scene parameters can be used in constructing a three-dimensional representation of the positioning of the anatomical structure segments  102 ,  104  in the fixator  100 , as described in more detail below. One or more of the imaging scene parameters may be known. Imaging scene parameters that are not known can be obtained, for example by mathematically comparing the locations of fixator element representations in the two-dimensional space of the x-ray images  126 ,  128  to the three-dimensional locations of those elements on the geometry of the fixator  100 . In a preferred embodiment, imaging scene parameters can be calculated using a pin hole or perspective camera models. For example, the imaging scene parameters can be determined numerically using matrix algebra, as described in more detail below. 
     The imaging scene parameters can include, but are not limited to image pixel scale factors, image pixel aspect ratio, the image sensor skew factor, the image size, the focal length, the position and orientation of the imaging source, the position of the principle point (defined as the point in the plane of a respective image  126 ,  128  that is closest to the respective imager  130 ), positions and orientations of elements of the fixator  100 , the position and orientation of a respective image receiver, and the position and orientation of the imaging source&#39;s lens. 
     In a preferred embodiment, at least some, such as all of the imaging scene parameters can be obtained by comparing the locations of representations of particular components, or fixator elements of the fixator  100  within the two-dimensional spaces of the images  126 ,  128 , with the corresponding locations of those same fixator elements in actual, three-dimensional space. The fixator elements comprise components of the orthopedic fixator  100 , and preferably are components that are easy to identify in the images  126 ,  128 . Points, lines, conics, or the like, or any combination thereof can be used to describe the respective geometries of the fixator elements. For example, the representations of fixator elements used in the comparison could include center lines of one or more of the adjustable length struts  116 , center points of the universal joints  124 , center points of the mounting members  114 , and the like. 
     The fixator elements can further include marker elements that are distinct from the above-described components of the fixator  100 . The marker elements can be used in the comparison, as a supplement to or in lieu of using components of the fixator  100 . The marker elements can be mounted to specific locations of components of the fixator  100  prior to imaging, can be imbedded within components of the fixator  100 , or any combination thereof. The marker elements can be configured for enhanced viewability in the images  126 ,  128  when compared to the viewability of the other components of the fixator  100 . For example, the marker elements 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 fixator  100  in the images  126 ,  128 . In an example embodiment, the marker elements can have designated geometries that correspond to their respective locations on the fixator  100 . 
     Fixator elements can be identified for use in the comparison. For example, locations, within the images  126 ,  128  of fixator elements may be indicated using the first image information received at operation  318  and described in detail above. In some examples, the locations of the fixator elements in the two-dimensional space of the images  126 ,  128  may be determined with respect to local origins  125  defined in the imaging planes of the images  126 ,  128 . The local origins  125  serve as a “zero points” for determining the locations of the fixator elements in the images  126 ,  128 . The locations of the fixator elements can be defined by their respective x and y coordinates with respect to a respective local origin  125 . The location of the local origin  125  within the respective image can be arbitrary so long it is in the plane of the image. Typically, the origin is located at the center of the image or at a corner of the image, such as the lower left hand corner. It should be appreciated that the locations of the local origins are not limited to illustrated local origins  125 , and that the local origins  125  can be alternatively defined at any other locations. 
     In some examples, a respective transformation matrix P may then be computed for each of the images  126 ,  128 . The transformation matrices can be utilized to map location coordinates of one or more respective fixator elements in actual three-dimensional space to corresponding location coordinates of the fixator element(s) in the two-dimensional space of the respective image  126 ,  128 . It should be appreciated that the same fixator element(s) need not be used in the comparisons of both images  126 ,  128 . For example, a fixator element used in constructing the transformation matrix associated with image  126  can be the same or different from the fixator element used in constructing the transformation matrix associated with image  128 . It should further be appreciated that increasing the number of fixator elements used in computing the transformation matrices can increase the accuracy method. The following equation represents this operation: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           x 
                         
                       
                       
                         
                           y 
                         
                       
                       
                         
                           1 
                         
                       
                     
                     ] 
                   
                   = 
                   
                     P 
                     · 
                     
                       [ 
                       
                         
                           
                             X 
                           
                         
                         
                           
                             Y 
                           
                         
                         
                           
                             Z 
                           
                         
                         
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     The symbols x and y represent location coordinates, with respect to the local origin  125 , of a fixator element point in the two-dimensional space of images  126 ,  128 . The symbols X, Y and Z represent corresponding location coordinates, with respect to a space origin  135 , of the fixator element point in actual three-dimensional space. In the illustrated embodiment, the point corresponding to the center of the plane defined by the upper surface of the upper fixator ring  106  has been designated as the space origin  135 . The illustrated matrix P can be at least four elements wide and three elements tall. In a preferred embodiment, the elements of the matrix P can be computed by solving the following matrix equation: 
     
       
         
           
             
               
                 
                   
                     A 
                     · 
                     p 
                   
                   = 
                   B 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The vector p can contain eleven elements representing values of the matrix P. The following equations present arrangements of the elements in the vector p and the matrix P: 
     
       
         
           
             
               
                 
                   p 
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               p 
                               1 
                             
                           
                           
                             
                               p 
                               2 
                             
                           
                           
                             
                               p 
                               3 
                             
                           
                           
                             
                               p 
                               4 
                             
                           
                           
                             
                               p 
                               5 
                             
                           
                           
                             
                               p 
                               6 
                             
                           
                           
                             
                               p 
                               7 
                             
                           
                           
                             
                               p 
                               8 
                             
                           
                           
                             
                               p 
                               9 
                             
                           
                           
                             
                               p 
                               10 
                             
                           
                           
                             
                               p 
                               11 
                             
                           
                         
                       
                       ] 
                     
                     T 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   P 
                   = 
                   
                     [ 
                     
                       
                         
                           
                             p 
                             1 
                           
                         
                         
                           
                             p 
                             2 
                           
                         
                         
                           
                             p 
                             3 
                           
                         
                         
                           
                             p 
                             4 
                           
                         
                       
                       
                         
                           
                             p 
                             5 
                           
                         
                         
                           
                             p 
                             6 
                           
                         
                         
                           
                             p 
                             7 
                           
                         
                         
                           
                             p 
                             8 
                           
                         
                       
                       
                         
                           
                             p 
                             9 
                           
                         
                         
                           
                             p 
                             10 
                           
                         
                         
                           
                             p 
                             
                               1 
                               ⁢ 
                               1 
                             
                           
                         
                         
                           
                             p 
                             
                               1 
                               ⁢ 
                               2 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In the preferred embodiment, the twelfth element p 12  of the matrix P can be set to a numerical value of one. The matrices A and B can be assembled using the two-dimensional and three-dimensional information of the fixator elements. For every point representing a respective fixator element, two rows of matrices A and B can be constructed. The following equation presents the values of the two rows added to the matrices A and B for every point of a fixator element (e.g., a center point of a respective universal joint  124 ): 
     
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                         
                         
                           
                             X 
                           
                           
                             Y 
                           
                           
                             Z 
                           
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               
                                 - 
                                 x 
                               
                               · 
                               X 
                             
                           
                           
                             
                               
                                 - 
                                 x 
                               
                               · 
                               Y 
                             
                           
                           
                             
                               
                                 - 
                                 x 
                               
                               · 
                               Z 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             X 
                           
                           
                             Y 
                           
                           
                             Z 
                           
                           
                             1 
                           
                           
                             
                               
                                 - 
                                 y 
                               
                               · 
                               X 
                             
                           
                           
                             
                               
                                 - 
                                 y 
                               
                               · 
                               Y 
                             
                           
                           
                             
                               
                                 - 
                                 y 
                               
                               · 
                               Z 
                             
                           
                         
                         
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                           
                             … 
                           
                         
                       
                       ] 
                     
                     · 
                     p 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           … 
                         
                       
                       
                         
                           x 
                         
                       
                       
                         
                           y 
                         
                       
                       
                         
                           … 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     The symbols X, Y and Z represent location coordinate values of a fixator element point in actual three-dimensional space relative to the space origin  135 , and the symbols x and y represent location coordinate values of the corresponding fixator element point in the two-dimensional space of the respective image  126 ,  128  relative to local origin  125 . 
     For every line representing a respective fixator element, two rows of matrices A and B can be constructed. The following equation presents the values of the two rows added to the matrices A and B for every line of a fixator element (e.g., a center line of a respective adjustable length strut  116 ): 
     
       
         
           
                                                                                                                                                                            
             
               
                 ( 
                 6 
                 ) 
               
               ⁢ 
               
 
               
                 
                   [ 
                   
                     
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                     
                     
                       
                         
                           X 
                           · 
                           a 
                         
                       
                       
                         
                           Y 
                           · 
                           a 
                         
                       
                       
                         
                           Z 
                           · 
                           a 
                         
                       
                       
                         a 
                       
                       
                         
                           X 
                           · 
                           b 
                         
                       
                       
                         
                           Y 
                           · 
                           b 
                         
                       
                       
                         
                           Z 
                           · 
                           b 
                         
                       
                       
                         b 
                       
                       
                         
                           X 
                           · 
                           c 
                         
                       
                       
                         
                           Y 
                           · 
                           c 
                         
                       
                       
                         
                           Z 
                           · 
                           c 
                         
                       
                     
                     
                       
                         
                           dX 
                           · 
                           a 
                         
                       
                       
                         
                           dY 
                           · 
                           a 
                         
                       
                       
                         
                           dZ 
                           · 
                           a 
                         
                       
                       
                         0 
                       
                       
                         
                           dX 
                           · 
                           b 
                         
                       
                       
                         
                           dY 
                           · 
                           b 
                         
                       
                       
                         
                           dZ 
                           · 
                           b 
                         
                       
                       
                         0 
                       
                       
                         
                           dY 
                           · 
                           c 
                         
                       
                       
                         
                           dY 
                           · 
                           c 
                         
                       
                       
                         
                           dZ 
                           · 
                           c 
                         
                       
                     
                     
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                       
                         … 
                       
                     
                   
                   ] 
                 
                 · 
                 
                    
                   
                     p 
                     = 
                     
                       [ 
                       
                         
                           
                             … 
                           
                         
                         
                           
                             
                               - 
                               c 
                             
                           
                         
                         
                           
                             0 
                           
                         
                         
                           
                             … 
                           
                         
                       
                       ] 
                     
                   
                 
               
             
           
         
       
     
     The symbols X, Y and Z represent location coordinate values of a point belonging to a line of a fixator element in actual three-dimensional space relative to the space origin  135 . The symbols dX, dY and dZ represent gradient values of the line in actual three-dimensional space. The symbols a, b and c represent constants defining a line in the two-dimensional space of a respective image  126 ,  128 . For example, a, b, and c can be computed using two points belonging to a line on a respective image  126 ,  128 . In a preferred embodiment, the value of b is assumed to be 1, unless the line is a vertical line, in which case the value of b is zero. A correlation of constants a, b and c with the respective image coordinates x and y is presented in the following equation: 
     
       
         
           
             
               
                 
                   
                     
                       a 
                       · 
                       x 
                     
                     + 
                     
                       b 
                       · 
                       y 
                     
                     + 
                     c 
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The equation (2) can be over constrained by using six or more fixator elements, for example the adjustable length struts  116 . It should be appreciated that it is not necessary for all of the fixator elements to be visible in a single one of the images  126 ,  128  in order to obtain the matrix P. It should further be appreciated that if one or more of the above-described imaging scene parameters are known, the known parameters can be used to reduce the minimum number of the fixator elements required to constrain equation (2). For instance, such information could be obtained from modern imaging systems in DICOM image headers. Preferably, a singular value decomposition or least squares method can be used to solve equation (2) for values of the vector p. 
     In some examples, the transformation matrices may then be decomposed into imaging scene parameters. The following equation can be used to relate the matrix P to matrices E and I: 
     
       
         
           
             
               
                 
                   P 
                   = 
                   
                     I 
                     · 
                     E 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     It should be appreciated that additional terms can be introduced when decomposing the matrix P. For example, the method presented by Tsai, described in “A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using of-the-shelf TV Cameras and Lenses”, IEEE Journal of Robotics &amp; Automation, RA-3, No. 4, 323-344, August 1987, which is incorporated herein by reference in its entirety, can be used to correct images  126 ,  128 , for radial distortion. 
     Matrices E and I contain imaging scene parameters. The following equation represents a composition of the matrix I: 
     
       
         
           
             
               
                 
                   I 
                   = 
                   
                     [ 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             x 
                           
                         
                         
                           0 
                         
                         
                           
                             
                               - 
                               t 
                             
                             ⁢ 
                             x 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             s 
                             ⁢ 
                             y 
                           
                         
                         
                           
                             
                               - 
                               t 
                             
                             ⁢ 
                             y 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             1 
                             / 
                             f 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     The symbols sx and sy represent values of image coordinate scale factors (e.g., pixel scale factors). The symbol f, representing the focal length, corresponds to the value of the shortest distance between a respective imaging source  130  and the plane of a corresponding image  126 ,  128 . The symbols tx and ty represent the coordinates of the principle point relative to the local origin  125  of the respective image  126 ,  128 . The following equation represents the composition of the matrix E: 
     
       
         
           
             
               
                 
                   E 
                   = 
                   
                     [ 
                     
                       
                         
                           
                             r 
                             1 
                           
                         
                         
                           
                             r 
                             2 
                           
                         
                         
                           
                             r 
                             3 
                           
                         
                         
                           
                             - 
                             
                               ( 
                               
                                 
                                   
                                     r 
                                     1 
                                   
                                   · 
                                   
                                     o 
                                     x 
                                   
                                 
                                 + 
                                 
                                   
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     The symbols o x , o y  and o z  represent values of the position of the fixator  100  in actual three-dimensional space. The symbols r 1  to r 9  describe the orientation of the fixator  100 . These values can be assembled into a three-dimensional rotational matrix R represented by the following equation: 
     
       
         
           
             
               
                 
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     The methods of Trucco and Verri, as described in “Introductory Techniques of 3-D Computer Vision”, Prentice Hall, 1998, or the method of Hartley, as described in “Euclidian Reconstruction from Uncalibrated Views”, Applications of Invariance in Computer Vision, pages 237-256, Springer Verlag, Berlin Heidelberg, 1994, which are incorporated herein by reference in their entireties, can be used to obtain values of the matrices E and/or I. Utilizing the resulting values of matrices E and I, a complete three-dimensional imaging scene of the fixator  100  and the anatomical structure segments  102 ,  104  can be reconstructed. 
     For example,  FIG. 2  illustrates an example three-dimensional imaging scene reconstructed from the x-ray images  126 ,  128 . In the illustrated embodiment, x-rays are emitted from x-ray imagers  130 . It should be appreciated that the x-ray imagers  130  can be the same or different imagers, as described above. The x-rays emitted from the imagers  130  are received on by corresponding imaging devices, thus capturing the images  126 ,  128 . Preferably, the positioning of the imagers  130  with respect to the local origins  125  is known. 
     In some examples, the images  126 ,  128  and the imaging scene parameters may then be used to obtain the positions and/or orientations of the anatomical structure segments  102 ,  104  in three-dimensional space. The position and/or orientation data obtained can be used to develop a treatment plan for a patient, for example to change the orientation and/or position of the fractured first and second anatomical structure segments  102 ,  104  in order to promote union between the anatomical structure segments  102 ,  104 , as described in more detail below. It should be appreciated that the methods and techniques described herein are not limited to applications of repositioning broken anatomical structures, and that orthopedic fixation with imagery analysis can be used in any other type of fixation procedure as desired, for example lengthening of anatomical structures, correction of anatomical defects, and the like. 
     In some examples, anatomical structure elements comprising representations of particular portions (e.g., anatomical features) of the anatomical structure segments  102 ,  104 , may then be identified and their locations within the images  126 ,  128  determined. For example, locations, within the images  126 ,  128  of the first and the second anatomical structure segments may be indicated using the second image information received at operation  320  and described in detail above. In some examples, the locations of the anatomical structure elements may be determined with respect to the respective local origins  125  of images  126 ,  128 . 
     The anatomical structure elements can be used in the construction of the three-dimensional representation of the position and/or orientation of the anatomical structure segments  102 ,  104 . Preferably, the anatomical structure elements are easy to identify in the images  126 ,  128 . Points, lines, conics, or the like, or any combination thereof can be used to describe the respective geometries of the anatomical structure elements. For example, in the illustrated embodiment, points  134  and  136  representing the fractured ends  103 ,  105  of the anatomical structure segments  102 ,  104 , respectively, are identified as anatomical structure elements in the images  126 ,  128 . 
     The anatomical structure elements can further include marker elements that are implanted into the anatomical structure segments  102 ,  104  prior to imaging. The marker elements can be used as a supplement to or in lieu of the above-described anatomical structure elements identified in the images  126 ,  128 . The marker elements can be configured for enhanced viewability in the images  126 ,  128  when compared to the viewability of anatomical features of the anatomical structure segments  102 ,  104 . For example, the marker elements may be constructed of a radio-opaque material, or may be constructed with readily distinguishable geometries. 
     A three-dimensional representation  200  of the anatomical structure segments  102 ,  104  can be reconstructed. The three-dimensional representation can be constructed with or without a corresponding representation of the fixator  100 . In the illustrated embodiment, pairs of ray-lines, such as ray lines  138 ,  140  and  142 ,  144  can be constructed for the anatomical structure element points  134 ,  136 , respectively. Each ray line connects an anatomical structure element in one of the images  126 ,  128  with a respective imager  130 . Each pair of ray lines can be analyzed for a common intersection point, such as points  146 ,  148 . The common intersection points  146 ,  148  represent the respective positions of the anatomical structure element points  134 ,  136 , in the three-dimensional representation of the anatomical structure segments  102 ,  104 . Of course more than a pair of ray lines, such as a plurality, can be constructed, for example if more than two images were captured. If the ray lines of a particular set do not intersect, a point closest to all the ray lines in the set can be used as the common intersection point. 
     The positions and/or orientations of the anatomical structure segments  102 ,  104  can be quantified or measured using common intersection points, for instance points  146 ,  148 . For example, lines representing center lines of the anatomical structure segments  102 ,  104  can be constructed and can be compared to the anatomical axes of the patient. Additionally, the distance between the fractured ends  103 ,  105  of the anatomical structure segments  102 ,  104  can be quantified. Using these or similar techniques, the positions and/or orientations of the anatomical structure segments  102 ,  104  can be determined. It is further noted that, in some examples, in addition to the positions and orientations of the first and second anatomical structure segments, the positions and orientation of rings (and/or other elements of the fixation apparatus) in three-dimensional space may also be determined, for example using any of the techniques described. For example, in some cases, locations of the rings within the images  126 ,  128  may be determined based on the first image information and/or other provided information. In some examples, these locations may then be used to determine the positions and orientations of the rings in three-dimensional space. Additionally, in some examples, configuration information for the fixation apparatus, such as ring diameters and strut length and mounting information, may also be used to determine positions and orientations of the rings in three-dimensional space. 
     Referring now to  FIG. 3B , at operation  324 , one or more deformity parameters are calculated. The deformity parameters may include parameters relating to the deformity associated with the first and second anatomical structure segments. For example, in some cases, the deformity parameters may include an amount of translation (e.g., lateral, medial, anterior, and/or posterior), a degree of coronal angulation (e.g., valgus and/or varus), a degree of sagittal angulation, an amount by which anatomical structure length is too short and/or too long, a degree of clinical rotational deformity (e.g., internal and/or external), and others. In some examples, the deformity parameters may be calculated as part of the process determining the positions and orientations of the first and segment anatomical structure segments described above at operation  422 , for example using the techniques described above with reference to operation  422 . 
     At operation  326 , the deformity parameters calculated at operation  424  are displayed, for example using one or more graphical user interfaces of a computing system. Referring now to  FIG. 9 , a deformity parameter interface  900  is shown. As shown, interface  900  includes various fields  901 - 906  for displaying calculated values of various example deformity parameters, including AP View translation and coronal angulation, LAT View translation and sagittal angulation, an amount by which anatomical structure length is too short or too long, and a degree of clinical rotational deformity. In the example of  FIG. 9 , fields  901 - 905  each have a respective PFM badge  915  (including the text “PFM”) that is displayed to the left of each field  901 - 905 . Each PFM badge  915  indicates that the value shown in the respective field  901 - 905  has been calculated by the software. Interface  900  allows the deformity parameter values that are displayed in each field  901 - 906  to be edited by a user, for example by typing a number in the fields  901 - 906  and/or by using number increment controls  916  displayed to the right of each field  901 - 906 . When a user edits a value that was calculated by the software, the PFM badge  915  adjacent to the respective field may be removed to indicate that the value for the field has been edited by the user. In some examples, after editing the values in one or more fields, the user may select Refresh Perspective Frame Matching Data button  920  to return each of the fields to the value that was calculated by the software. Also, in some examples, after editing the values in one or more fields, the user may select Save and Update button  921  to cause the deformity parameters to be recalculated based on the edited values provided by the user, for example by repeating all or any portion of the calculations performed at operation  322 . 
     At operation  328 , a graphical representation of the position and orientation of the first and the second anatomical structure segments is generated and displayed. The graphical representation of the position and orientation of the first and the second anatomical structure segments may be displayed using one or more graphical user interfaces of a computing system. For example, as shown in  FIG. 9 , interface  900  includes a graphical representation  950  of the position and orientation of the first and the second anatomical structure segments. Graphical representation  950  includes a representation  931  of the proximal anatomical structure segment and a representation  932  of the distal anatomical structure segment. In some examples, the graphical representation  950  may be generated based, at least in part, on the positions and orientations of the first and segment anatomical structure segments determined at operation  322 . In some examples, when the user edits one or more deformity parameters and selects Save and Update button  921 , the graphical representation  950  may also be adjusted to reflect the saved edits to the deformity parameters. Graphical representation  950  may, for example, improve efficiency and reliability by providing the user with a visual confirmation of information entered into interface  900 , for example to allow fast and easy identification of errors or other problems. 
     At operation  330 , one or more mounting parameters are calculated. The mounting parameters may include parameters relating to mounting of a reference ring of the fixator onto a respective anatomical structure segment. For example, in some cases, the mounting parameters may include an amount of offset (e.g., lateral, medial, anterior, and/or posterior) such as for a center of the reference ring with respect to a reference point, a degree of tilt (e.g., proximal and/or distal), an amount of axial offset, a master tab rotation, and others. In some examples, the mounting parameters may be calculated as part of the process determining the positions and orientations of the first and segment anatomical structure segments described above at operation  322 , for example using the techniques described above with reference to operation  322 . It is noted that, for the process of  FIG. 3 , the reference ring is not necessarily required to be orthogonal with respect to the respective anatomical structure segment on which it is mounted. Thus, in some examples, the reference ring may be non-orthogonal with respect to the respective anatomical structure segment on which it is mounted. 
     At operation  432 , the mounting parameters calculated at operation  430  are displayed, for example using one or more graphical user interfaces of a computing system. Referring now to  FIG. 10 , a mounting parameter interface  1000  is shown. As shown, interface  1000  includes various fields  1001 - 1006  for displaying calculated values of various example mounting parameters, including AP View offset and tilt, LAT View offset and tilt, axial offset, and master tab rotation. In the example of  FIG. 10 , fields  1001 - 1006  each have a respective PFM badge  1015  that is displayed to the left of each field  1001 - 1006 . Each PFM badge  1015  indicates that the value shown in the respective field  1001 - 1006  has been calculated by the software. Interface  1000  allows the mounting parameter values that are displayed in each field  1001 - 1006  to be edited by a user, for example by typing a number in the fields  1001 - 1006  and/or by using number increment controls  1016  displayed to the right of each field  1001 - 1006 . When a user edits a value that was calculated by the software, the PFM badge  1015  adjacent to the respective field may be removed to indicate that the value for the field has been edited by the user. In some examples, after editing the values in one or more fields, the user may select Refresh Perspective Frame Matching Data button  1020  to return each of the fields to the value that was calculated by the software. Also, in some examples, after editing the values in one or more fields, the user may select Save and Update button  1021  to cause the deformity parameters to be recalculated based on the edited values provided by the user, for example by repeating all or any portion of the calculations performed at operation  322 . 
     At operation  334 , a graphical representation of the position and orientation of the reference ring and the respective anatomical structure segment to which it is mounted is generated and displayed. The graphical representation of the position and orientation of the reference ring and the respective anatomical structure segment may be displayed using one or more graphical user interfaces of a computing system. For example, as shown in  FIG. 10 , interface  1000  includes a graphical representation  1050  of the position and orientation of the reference ring and the respective anatomical structure segment. Graphical representation  1050  includes a representation  1031  of the proximal anatomical structure segment, a representation  1033  of the proximal (reference) ring, and a representation  1032  of the distal anatomical structure segment. In some examples, the graphical representation  1050  may be generated based, at least in part, on the positions and orientations of the reference ring and the respective anatomical structure segment determined at operation  322 . The graphical representation of the reference ring and the respective anatomical structure segment may, therefore, reflect and/or indicate the positions and orientations of reference ring and the respective anatomical structure segment determined at operation  322 . In some examples, when the user edits one or more mounting parameters and selects Save and Update button  1021 , the graphical representation  1050  may also be adjusted to reflect the saved edits to the mounting parameters. Graphical representation  1050  may, for example, improve efficiency and reliability by providing the user with a visual confirmation of information entered into interface  1000 , for example to allow fast and easy identification of errors or other problems. 
     At operation  336 , one or more treatment plan options are received, for example using one or more graphical user interfaces of a computing system. A treatment plan is a plan for manipulating the fixation apparatus, for example in order to correct the deformity of the first and the second anatomical structure segments. The treatment plan may include, for example, a plan for making gradual adjustments to the positions and orientations of the fixator rings with respect to each other, for example by changing the lengths of the struts of the fixation apparatus. Referring now to  FIG. 11 , an example treatment plan interface  1100 A is shown. The interface  1100 A includes controls for selecting, by a user, various treatment plan options. In particular, controls  1101  and/or  1102  allow selecting of a treatment plan start date, control  1103  allows selection of an option to perform axial movement first (e.g., in an initial part of the treatment, such as prior to rotational movement), control  1104  allows selection of an option to indicate a final distance between reference points, control  1105  allows selection of an option to calculate the treatment plan based on a specified duration (e.g., a number of days) for axial movement, control  1106  allows selection of an option to calculate the treatment plan based on a rate of distraction at the reference point (e.g., for example millimeters (mm)/day) for axial movement, control  1108  allows selection of an option to calculate the treatment plan based on a specified duration (e.g., a number of days) for deformity correction, control  1109  allows selection of an option to calculate the treatment plan based on a rate of distraction at the reference point (e.g., for example millimeters (mm)/day) for deformity correction, and control  1107  allows selection of an option to perform two adjustments per day. In some examples, when control  1007  is not selected, a default option of one adjustment per day may be used. In some examples, after selecting desired treatment plan options, the user may select Update Adjustment Plan button  1110  to trigger generation of the treatment plan. Additionally, after initial generation of the treatment plan, the user may also be permitted to adjust the treatment plan options and have the treatment plan re-generated with the adjusted options by re-selecting Update Adjustment Plan button  1110 . 
     In some examples, the software may allow the treatment plan to be split into multiple treatment phases. This may allow for greater control of the deformity correction, such as by allowing the surgeon to define starting and target poses for each treatment phase, to control the options for each treatment phase, and to control the type of movement in each treatment phase. For example, in some cases, a user may be allowed to create multiple treatment phases. Each of the multiple treatment phases may be defined by an assigned starting pose and an assigned target (i.e., ending) pose. The starting pose for the first (initial) treatment phase may be the initial anatomical structure deformity position from which the treatment begins on the first day of treatment. The target pose for the final treatment phase may be the desired positions of the anatomical structure segments at the conclusion of treatment. The starting pose for each subsequent treatment phase (after the initial treatment phase) may be same as the target pose of each preceding treatment phase. For example, the starting pose of a second treatment phase may be the same as the target pose of the first treatment phase, and so forth. The multiple phases (1 to N) may be combined in a list, and the plans of the individual N phases may be combined into the treatment plan. 
     The software may provide an interface that allows the user to select the quantity of desired treatment phases, the starting pose and the target pose for each treatment phase, and separate options for each treatment phase. For example, for each treatment phase, the software may allow the user to select a respective duration (e.g., a number of days), a rate of distraction, a quantity of degrees of adjustment per day, of a number of adjustments (e.g., strut movements) per day. The options for each treatment phase may be different from one another. For example, the duration, rate of distraction, quantity of degrees of adjustment per day and/or number of adjustments per day for the first treatment phase may be different from the duration, rate of distraction, quantity of degrees of adjustment per day and/or number of adjustments per day for the second treatment phase. In some examples, the input parameters for each treatment phase may include a starting pose of the distal fragment, a target pose of the distal fragment, and plan options for the phase (duration/distraction rate at given point/degrees per day, etc.). In some examples, the multiple treatment phases may allow for overcorrection of the deformity. For example, the multiple treatment phases may allow for compression, which may be calculated by using an overcorrection with a negative value for the axial distraction. The multiple treatment phases may also provide a simple and intuitive mechanism to allow axial movement to be performed in an initial phase of the treatment, and to allow additional axial lengthening/distraction. In some examples, the user may describe the treatment plan in clinical terms (e.g. residual deformity as overcorrection, number of phases, distraction first, etc.). A software layer may then interpret the clinical language and create corresponding treatment phases according to the phase definitions described above. 
     At operation  338 , manipulations to the fixation apparatus for correction of the anatomical structure deformity (i.e., a treatment plan) are determined. The manipulations to the fixation apparatus may include adjustments to the struts of the fixation apparatus, such as adjustments to the sizes and/or lengths of the struts. In some examples, operation  338  may be performed based, at least in part, on the treatment plan options received at operation  336 . For example, operation  338  may be performed based, at least in part, on specified start date, on instructions to perform axial movement first (e.g., in an initial part of the treatment, such as prior to rotational movement), a specified final distance between reference points, instructions to perform additional lengthening by a specified amount, instructions to generate an axial gap to ensure anatomical structure clearance, a specified duration (e.g., a number of days) of treatment, a specified rate of distraction, and/or instructions to perform two perform a specified quantity (e.g., one, two, etc.) of adjustments per day. 
     In some examples, the treatment plan may also be determined based, at least in part, on a determination of desired changes to the positions and/or orientations of the anatomical structure segments  102 ,  104 , for instance how the anatomical structure segments  102 ,  104  can be repositioned with respect to each other in order to promote union between the anatomical structure segments  102 ,  104 . For example, in some cases, it may be desirable to change the angulation of the second anatomical structure segment  104  such that the axes L 1  and L 2  are brought into alignment, and to change the position of the second anatomical structure segment such that the fractured ends  103 ,  105  of the anatomical structure segments  102 ,  104  abut each other. Once the desired changes to the positions and/or orientations of the anatomical structure segments  102 ,  104  have been determined, a treatment plan for effecting the position and/or orientation changes can be determined. In a preferred embodiment, the desired changes to the positions and/or orientations of the anatomical structure segments  102 ,  104  can be effected gradually, in a series of smaller changes. The positions and/or orientations of the anatomical structure segments  102 ,  104  can be changed by changing the positions and/or orientations of the upper and lower fixator rings  106 ,  108  with respect to each other, for instance by lengthening or shortening one or more of the length adjustable struts  116 . 
     The required changes to the geometry of the fixator  100  (i.e., the position and/or orientation of the fixator  100 ) that can enable the desired changes to the positions and/or orientations of the anatomical structure segments  102 ,  104  can be computed using the matrix algebra described above. For example, the required repositioning and/or reorientation of the second anatomical structure segment  104  with respect to the first anatomical structure segment  102  can be translated to changes in the position and/or orientation of the lower fixator ring  108  with respect to the upper fixator ring  106 . 
     At operation  340 , indications of the determined manipulations to the fixation apparatus are provided to one or more users. For example, in some cases, indications of the determined manipulations to the fixation apparatus may be provided using one or more graphical user interfaces of a computing system, using a printed hard copy, using audio feedback, and/or using other techniques. In particular, referring now to  FIG. 12 , it is seen that indications of the determined manipulations to the fixation apparatus may be provided within interface  1100 B. Specifically, selection of Strut Adjustment Plan tab  1122  may cause treatment plan interface  1100 B to provide a chart  1130 , including day-by-day manipulation information for each strut within the fixation apparatus. In this example, chart  1130  shows a length for each strut on each day of treatment. In some examples, one or more alerts may be generated for one or more manipulations to the fixation apparatus that result in at least one of strut movement of more than a threshold amount. For example, in some cases, strut movements exceeding particular threshold amount (e.g., 3 mm per day), which may be referred to as rapid strut movements, may be indicated by displaying a red triangle icon next to the indication of the strut movement in chart  1130 . As also shown in  FIG. 12 , a PDF version of the chart  1130  may be generated by selecting View Draft PDF button  1131 . The generated PDF may, in some examples, be printed to create a hard copy version of chart  1130 . 
     In the example of  FIG. 12 , chart  1130  includes blocks  1132 -A and  1132 -B indicating ranges of dates on which changes of strut sizes, referred to as strut swaps, may be performed. In particular, block  1132 -A indicates that a strut swap may be performed for Strut 4 on Day 0 through Day 2, while block  1132 -B indicates that a strut swap may be performed for Strut 4 on Day 3 through Day 14 (and subsequent days). In some examples, blocks  1132 -A and  1132 -B may be color-coded to match a color assigned to a respective strut. For example, blocks  1132 -A and  1132 -B may be colored green to match a green color that may be assigned to Strut 4. Referring now to  FIG. 13 , Strut Swaps Calendar tab  1123  of treatment plan interface  1100 -C may be selected to generate a calendar  1140  indicating ranges of dates on which strut swaps may be performed. 
     In some examples, the struts of the fixation apparatus attached to the patient may be color-coded, for example using color-coded caps, marker, or other color-coded materials included within and/or attached to the struts. In some examples, the physical color-coding of the struts in the fixation apparatus attached to the patient may match the color-coding of struts used in the software. For example, the physical color-coding of the struts in the fixation apparatus may match the color-coding of struts that may be used to color-code the blocks  1132 -A and  1132 -B of chart  1130 , graphical representation  520 , and other color-coded representations of the struts displayed by the software. In some examples, this may make it easier for physicians and/or patients to confirm that, when they physically adjust a strut on the fixation apparatus, they are adjusting the correct strut by the correct amount. 
     At operation  342 , one or more graphical representations of the position and orientation of the first and second anatomical structure segments and the rings of the fixation apparatus is generated and displayed. The graphical representation of the position and orientation of the first and the second anatomical structure segments and the rings of the fixation apparatus may be displayed using one or more graphical user interfaces of a computing system. For example, referring back to  FIG. 11 , selection of Treatment Simulation tab  1121  may cause interface  1100  to display a graphical representation  1150  of the position and orientation of the first and the second anatomical structure segments and the rings of the fixation apparatus. Graphical representation  1150  includes a representation  1031  of the proximal anatomical structure segment, a representation  1033  of the proximal (reference) ring, a representation  1032  of the distal anatomical structure segment, and a representation  1034  of the distal ring. In some examples, the one or more graphical representations of the position and orientation of the first and second anatomical structure segments and the rings of the fixation apparatus may include day-by-day graphical representations of the position and orientation of the first and second anatomical structure segments and the rings of the fixation apparatus throughout treatment for the anatomical structure deformity. For example, as shown in  FIG. 11 , a user may select a particular day of treatment for which to generate and display a graphical representation  1150  using controls  1151 ,  1152 ,  1153 , and/or  1154 . For example, control  1151  may be selected to allow incrementing of the selected day, control  1154  may be selected to allow decrementing of the selected day, and slider  1152  may be slid along bar  1153  to increment and/or decrement the selected day. It is also noted that slider  1152  displays an indication of the currently selected day, which, in the example of  FIG. 11 , is treatment day zero. Thus, in  FIG. 11 , graphical representation  1150  shows the position and orientation of the first and second anatomical structure segments and the rings of the fixation apparatus at treatment day zero. Using controls  1151 - 1154  to select a different day of treatment may cause graphical representation  1150  to be adjusted to show the position and orientation of the first and second anatomical structure segments and the rings of the fixation apparatus on the selected different day. As should be appreciated, allowing the surgeon and/or patient to see graphical representations of the position and orientation of the first and second anatomical structure segments and the rings of the fixation apparatus throughout treatment may be beneficial by, for example, providing an additional visual tool to improve accuracy and assist in planning of treatment. Additionally, graphical representation  1150  (as well as graphical representations described herein) may, for example, improve efficiency and reliability by providing the user with a visual confirmation of information entered into interface  1100 , for example to allow fast and easy identification of errors or other problems. It is further noted that the view of graphical representation  1150  (as well as other graphical representations described herein) may be rotated (for example by a complete 360 degrees), zoomed in and out, moved in direction, and otherwise manipulated, for example using controls  1181 - 1184  adjacent to the upper right side of the graphical representation  1150 . This may allow views of the first and second anatomical structure segments and/or the rings of the fixation apparatus from various orientations that may not be available, or may be difficult to obtain, using x-rays and other imaging techniques, thereby also improving reliability and accuracy and providing additional visual confirmation of calculated values. In particular, view of the graphical representation  1150  may be rotated using control  1181 , zoomed in using control  1182 , zoomed out using control  1183 , and panned using control  1184 . Also, in some examples, other controls, such as a mouse and touchscreen, may also be employed to rotate, zoom, pan, and otherwise manipulate graphical representation  1150 . Additionally, in some examples, control  1185  may be used to select an anteroposterior (AP) view, control  1186  may be used to select a lateral view, and control  1187  may be used to select a proximal view. 
     At operation  344 , the treatment plan may be implemented, that is the geometry of the fixation apparatus may be changed, for example based on the manipulations determined at operation  338 , in order to change positions and orientations of the anatomical structure segments. 
     Hinge Detection for Orthopedic Fixation 
     As described above, a frame matching process may be employed to determine positions and orientations of anatomical structure segments in three-dimensional space, such as for generating a treatment plan for correction of an anatomical deformity. As also described above, in some examples, as part of the frame matching process, a surgeon or other user may identify locations of fixator elements (e.g., hinges, struts, etc.) within displayed images (e.g., x-rays) that show the fixator attached to the anatomical structure segments. Some examples of this process are described above with reference to operation  318  of  FIG. 3A  and  FIG. 6 . For example, as shown in  FIG. 6  and described above, a user may identify locations of hinges within AP View image  601 -A and LAT View image  601 -B as part of the frame matching process. However, it may often be difficult for the user to identify and mark positions of certain fixator elements, such as hinges, within the images. In particular, depending upon the location and orientation from which an image is captured, hinges and other fixator elements may not be identified easily, such as because they may wholly or partially overlap one another or may otherwise be obscured within the images. 
     In some examples, to alleviate the above and other problems, an automated or semi-automated hinge detection technique may be employed. Some examples of these hinge detection technique will now be described with reference to  FIGS. 14A-25 . Specifically, referring now to  FIG. 14A , an example process for hinge detection for orthopedic fixation will now be described in detail. Any or all of the operations and sub-operations depicted in  FIGS. 14A-B  may be performed by one or more computing devices, such as by computer software executing on the one or more computing devices. As described above, a fixator may include fixator elements such as rings, struts and a plurality of hinges and may be used for correcting a deformity of first and second anatomical structure segments to which the fixator is attached. The process of  FIG. 14  is initiated at operation  1410 , at which first and second images of the first and the second anatomical structure segments and the fixator attached thereto are displayed. The first and the second images may have respective image planes. As shown in  FIG. 2  and described above, there is an angle α between the image planes of the images  126 ,  128 . 
     A first example of the display of the first and the second images at operation  1410  is shown in  FIG. 6 , which includes AP View image  601 -A and LAT View image  601 -B as described above. An additional example of the display of the first and the second images at operation  1410  is shown in  FIG. 15A , which will now be described in detail. In particular,  FIG. 15A  displays an AP View image  1501 -A and a LAT View image  1501 -B, which are images of a fixator  1510  including proximal fixator ring  1511 , distal fixator ring  1512 , fixator struts  1513 , and twelve hinges  1541  (shown as black circles at the endpoints of the struts  1513 ). The hinges  1541  include six proximal hinges (adjacent to proximal fixator ring  1511 ) and six distal hinges (adjacent to distal fixator ring  1512 ). The images  1501 -A and  1501 -B show the fixator  1510  attached to a first anatomical structure segment  1521  and a second anatomical structure segment  1522 . The first and second images of the first and the second anatomical structure segments and the fixator attached thereto may be displayed at operation  1410  using one or more graphical user interfaces of a computing system. For example, images  1501 -A and  1501 -B of  FIGS. 15A-25  may be displayed using one or more graphical user interfaces of a computing system. It is noted that, in some examples, any, or all, of the contents shown in each of  FIGS. 15A-25  may be displayed using one or more graphical user interfaces of a computing system. 
     It is noted that, in the examples of  FIGS. 15A-25 , the images  1501 -A and  1501 -B are simulated images—as opposed to actual x-rays (as in  FIG. 6 ) or other images captured from an imager or imaging source. It is noted that the simulated images of  FIGS. 15A-25  are provided merely for ease of illustration of the concepts described herein. In practice, the images  1501 -A and  1501 -B may be non-simulated images, such as x-rays, which are captured using an imager, imaging source, x-ray imager, camera or other image capture device, and that show an actual fixator that is physically attached to an actual anatomical structure segment (such as shown in  FIG. 6 ). Thus, even though images  1501 -A and  1501 -B are displayed as simulations, the concepts described herein should be understood to also be applicable to non-simulated images (i.e., images that were captured using an imager, imaging source, x-ray imager, camera or other image capture device) similar to the images  601 -A and  601 -B of  FIG. 6 . 
     At operation  1412 , indications are received of first image hinge locations associated with the plurality of hinges in the first image, for example using the one or more graphical user interfaces of the computing system. For example, as described above with respect to  FIG. 6 , the user may indicate locations of hinges within the AP View image  601 -A, such as by clicking on the hinges using an attached mouse or other input device. As described above, the strut indicator button  611 -A for Strut 1 may be pre-selected automatically for the user. Upon selection (or automatic pre-selection) of the strut indicator button  611 -A for Strut 1, the user may proceed to draw (or otherwise indicate) a representation of the hinges at endpoints of Strut 1 within AP View image  601 -A. For example, in some cases, the user may use a mouse or other input device to select a location  621  (e.g., a center point) of a proximal hinge for Strut 1 within image  601 -A. In some examples, the user may then use a mouse or other input device to select a location  622  (e.g., a center point) of the distal hinge of Strut 1 within image  601 -A. As shown in  FIG. 6 , the software may generate points or circles at the locations  621  and  622  of the proximal and distal hinges selected by the user within image  601 -A. Additionally, the software may generate a line  623  representing the location and/or length of Strut 1 that connects the points or circles at the locations  621  and  622  and of the proximal and distal hinges selected by the user within image  601 -A. In some examples, the above described process may be repeated to draw points representing proximal and distal hinges at endpoints of each of the six struts in the AP View image  601 -A. A similar technique may also be employed to indicate the locations of each of the twelve hinges  1541  in AP View image  1501 -A of  FIG. 15A . 
     In some examples, after the user indicates locations of the hinges  1541  within the AP View image  1501 -A, the software may use the indicated hinge locations to determine locations of the fixator rings  1511  and  1512  within the AP View image  1501 -A. The software may then generate ring graphical representations  1531  and  1532 , corresponding to the fixator rings  1511  and  1512 , respectively, and display the ring graphical representations  1531  and  1532  at the determined locations of the fixator rings  1511  and  1512  within the AP View image  1501 -A. Referring now to  FIG. 15B , it is seen that ring graphical representations  1531  and  1532  are generated by the software and displayed within AP View image  1501 -A at the corresponding locations of the respective fixator rings  1511  and  1512 . It is noted that the fixator ring graphical representations  1531  and  1532  are shown in  FIG. 15B  with a different shade/color than the actual fixator rings  1511  and  1512  to indicate that the fixator ring graphical representations  1531  and  1532  are generated by the software and are not included in the actual underlying AP View image  1501 -A. Specifically, the fixator ring graphical representations  1531  and  1532  are shown in blue color/shades, while the fixator rings  1511  and  1512  are shown in black color/shades. 
     At operation  1414 , a graphical projection of the fixator is overlaid, for example using the one or more graphical user interfaces of the computing system, on the second image. For example, referring now to  FIG. 16 , it is seen that a graphical projection  1600  of the fixator is displayed that includes a graphical representation  1611  of the proximal ring and a graphical representation  1612  of the distal ring. As shown, the graphical projection  1600 , including graphical representations  1611  and  1612  is overlaid on the second image, which in this example is the LAT View image  1501 -B. 
     The graphical projection  1600  of the fixator may be rotated relative to fixator elements in the first image, such as based at least in part on an angle (such as at the exact angle or at an approximation of the angle) of image planes of the first and the second images with respect to one another. As shown in  FIG. 2  and described above, there is an angle α between the image planes of the images  126 ,  128 . Thus, in the example of  FIG. 16 , the AP View image  1501 -A may have a respective AP View image plane, and the LAT View image  1501 -B may have a respective LAT View image plane at an angle of ninety degrees with respect to the AP View image plane. Accordingly, in the example of  FIG. 16 , the graphical projection  1600  of the fixator is rotated ninety degrees relative to the first locations of the plurality of fixator elements identified in the first image. For example, both the proximal ring graphical representation  1611  and the distal ring graphical representation  1612  of  FIG. 16  are rotated ninety degrees relative to the proximal fixator ring  1511  (and/or the respective ring representation  1531 ) and distal fixator ring  1512  (and/or the respective ring representation  1532 ) in the AP View image  1501 -A. 
     The graphical projection  1600  of the fixator may be rotated based at least in part on the angle between image planes of the images because that rotation may correspond to the expected position of the fixator in the second image. For example, if an image plane of the LAT View image  1501 -B is at an angle of ninety degrees to an image plane of the AP View image  1501 -A, then it may be expected that the locations of the fixator rings in the LAT View image  1501 -B will be rotated ninety degrees relative to the locations of the fixator rings in the AP View image  1501 -A. In this way, the overlaying of the graphical projection  1600  on the second image may assist the user in identifying locations of the plurality of fixator elements in the second image. In some examples, a user may provide a numerical value, such as a quantity of degrees (e.g., ninety degrees), that expressly indicates to the software the value of the angle between image planes of the images. In other examples, the value of the angle may be inferred by the software based on descriptions of the images (e.g., anteroposterior, anterior, posterior, lateral, medial, etc.) or using other techniques. In the examples of  FIGS. 15A-17 , image  1501 -A is an AP View image and image  1501 -B is a lateral image. It is noted, however, that the techniques described herein may be used between any different combinations of images taken from any directions and orientations and having image planes at any angle with respect to one another. 
     Additionally, it is noted that the software may also manipulate other features of the graphical projection  1600  (e.g. size, location, orientations, etc.) such as to correct for other differences (e.g., location, orientation, zoom level, etc.) between the first and the second images. For example, in some cases, if the second image was captured from a closer location to the fixator and/or is more zoomed-in than the first image, then the software may correct for this by enlarging the size of the graphical projection  1600  relative to the size of the fixator elements in the first image. By contrast, in some cases, if the second image was captured from a further location from the fixator and/or is more zoomed-out than the first image, then the software may correct for this by reducing the size of the graphical projection  1600  relative to the size of the fixator elements in the first image. 
     Thus, in some examples, the graphical projection  1600  of the fixator may be generated based, at least in part, on locations of fixator elements in the first image. Additionally or alternatively, in some examples, the graphical projection  1600  of the fixator may be generated based, at least in part, on configuration information for the fixator that is provided to the software by the user, such as ring types (e.g., full ring, foot plate, etc.), ring sizes, strut lengths, indications of mounting points (e.g., ring holes), and other information. Various types of configuration information and techniques for providing such information to the software are described in detail above, such as with respect to  FIG. 5  and operation  314  of  FIG. 3A , and are not repeated here. 
     At operation  1416 , the software may allow a user to manipulate (e.g., resize, rotate, move, etc.) the graphical projection and/or the second image. For example, the user may manipulate the graphical projection to make it more precisely align with the positions of the fixator elements in the second image. For example, the software may provide controls that allow resizing (making the graphical projection larger or smaller) or rotating of the graphical projection relative to its initial placement by the software when being overlaid upon the second image at operation  1414 . For example, in some cases, it may be necessary to resize and/or rotate the graphical projection to correct for slight differences in the actual angle between the first and the second images relative to the expected angle (e.g., if the images are actually at an angle of ninety-two degrees rather than ninety degrees, etc.), to correct for differences in distance, position or orientation of the first and the second images relative to the objects included in the images, or for other reasons. In some examples, the software may provide various controls, such as buttons, that allow selections of operations such as move, resize and rotate, and the software may be configured to receive input from input devices, such as a mouse or keyboard, to accomplish those manipulations, for example via drag-and-drop, button clicks, keystrokes, etc. 
     In some examples, in addition or as an alternative to allowing a user to manipulate the graphical projection, the software may allow the user to manipulate the second image (e.g., LAT View image  1501 -B) upon which the graphical projection is overlaid. For example, in some cases, the software may allow the user to resize, rotate and/or move the second image and/or elements shown within the second image, such as to assist in aligning the fixator elements shown in the second image with corresponding elements of the graphical projection. Referring now to  FIG. 17 , it is seen that the user has manipulated the second image, which is LAT View image  1501 -B, by moving the LAT View image  1501 -B down and to the right from its prior screen/interface location shown in  FIG. 16 . By moving the LAT View image  1501 -B in this manner (without moving the graphical projection  1600 ), this allows the fixator elements in the LAT View image  1501 -B to be moved down and to the right such that they align with corresponding elements of graphical projection  1600 . For example, as shown in  FIG. 17 , the graphical representations  1611  and  1612  of the fixator rings substantially align with the respective fixator rings  1511  and  1512 . Thus, only small portions of the fixator rings  1511  and  1512  are visible in  FIG. 17  because they have been almost entirely overlaid by the respective graphical representations  1611  and  1612  of the fixator rings. In particular, in  FIG. 17 , proximal ring graphical representation  1611  substantially aligns with (and almost entirely overlays) proximal fixator ring  1511 , and distal ring graphical representation  1612  substantially aligns with (and almost entirely overlays) distal fixator ring  1512 . It is noted that, while the use of the graphical overlay shown in  FIGS. 16 and 17  may sometimes be advantageous to assist in correlating the first and second image with one another, there is no requirement that the hinge detection techniques described herein must include the use of a graphical overlay. 
     At operation  1418 , projected second image hinge locations associated with the plurality of hinges in the second image are determined. In some examples, the software may determine the projected second image hinge locations based at least in part on the indications of the first image hinge locations received at operation  1412 . The projected second hinge locations are the software&#39;s estimated locations of where the software expects the hinges to be located within the second image based on the user&#39;s indications of the hinge locations in the first image. For example, because the software knows the spatial relationship (e.g., angle) between the first and second images, the software can use the locations of the hinges in the first image to project/estimate where the locations of the hinges are expected to be in the second image. In some examples, the projected second image hinge locations may be expressed by the software via X and Y coordinate values within the second image.  FIG. 18  shows a diagram of the second image (e.g., LAT View image  1501 -B) that shows the fixator struts  1513  and twelve hinges  1541 , which are all included in the second image (e.g., LAT View image  1501 -B). It is appreciated that, although the second image (e.g., LAT View image  1501 -B) would also include the fixator rings and anatomical structure segments to which the fixator is attached (as shown in  FIGS. 15A-17 ), the fixator rings and anatomical structure segments are not shown in  FIGS. 18 and 22-24  in order to reduce clutter in the diagrams. As shown in  FIG. 18 , the software may determine projected second image hinge locations  1841  corresponding to the hinges  1541  in the LAT View image  1501 -B. It is appreciated that the actual locations of hinges  1541  that are part of the LAT View image  1501 -B are shown in  FIG. 18  as twelve circles with a normal (thinner) outline. By contrast, the projected second image hinge locations  1841  are shown in  FIG. 18  as twelve circles with a heavier (thicker) outline. It is noted that the projected second image hinge locations  1841  are in close-proximity (i.e. adjacent—but not identical) to the actual locations of the hinges  1541  in the LAT View image  1501 -B. In particular, in this example, the projected second image hinge locations  1841  are positioned up and to the right of respective actual locations of the hinges within the LAT View image  1501 -B 
     In some examples, the software may determine the projected second image hinge locations  1841  by rotating the first image hinge locations in the first image, such as based at least in part on an angle (such as at the exact angle or at an approximation of the angle) of image planes of the first and the second images with respect to one another. As shown in  FIG. 2  and described above, there is an angle a between the image planes of the images  126 ,  128 . Thus, as described above, the AP View image  1501 -A may have a respective AP View image plane, and the LAT View image  1501 -B may have a respective LAT View image plane at an angle of ninety degrees with respect to the AP View image plane. Accordingly, in the example of  FIG. 18 , projected second image hinge locations  1841  are rotated ninety degrees relative to the first image hinge locations of the hinges  1541  identified in the first image. 
     The projected second image hinge locations  1841  may be rotated based at least in part on the angle between image planes of the images because that rotation may correspond to the expected position of the fixator in the second image. For example, if an image plane of the LAT View image  1501 -B is at an angle of ninety degrees to an image plane of the AP View image  1501 -A, then it may be expected that the locations of the hinges  1541  in the LAT View image  1501 -B will be rotated ninety degrees relative to the locations of the hinges  1541  in the AP View image  1501 -A. In some examples, a user may provide a numerical value, such as a quantity of degrees (e.g., ninety degrees), that expressly indicates to the software the value of the angle between image planes of the images. In other examples, the value of the angle may be inferred by the software based on descriptions of the images (e.g., anteroposterior, anterior, posterior, lateral, medial, etc.) or using other techniques. 
     At operation  1420 , hinge candidates are detected in the second image. The hinge candidates have shapes associated with the plurality of hinges. A hinge candidate is an area of the second image that has a shape that is associated with (e.g., that resembles) a hinge. For example, a hinge candidate may be an area of the second image that is defined by a same or similar visual feature (e.g., a same or similar shade of white, black or gray or another color) and that has a shape (e.g., a substantially circular shape) that matches or corresponds to a shape of one of the hinges. The hinge candidates may be detected by computer software using automated software-based image analysis techniques that are performed on the second image. For example, the hinges may have circular shapes, and the performing of hinge detection by the computer software may include employing circle detection algorithms, such as a Hough transformation, on the second image to identify circular shapes in the second image as hinge candidates. It is noted that the identification of a circular shape for purposes of hinge detection, as that term is used herein, is meant to encompass identifying of both exactly circular shapes and shapes that are substantially circular, such as a circle that may be partly obfuscated or that has an oval shape. In many cases, the number of hinge candidates that are detected in the second image may be greater than the number of actual fixator hinges. This may be because the, in addition to detecting the actual hinges, the software may detect a number of false positive hinge candidates, such as other circular shapes (e.g., wires, other objects, etc.) in the second image. In addition, in some examples, even a single hinge may sometimes be detected as multiple hinge candidates, such different circles that have similar or adjacent locations but that have different size characteristics (e.g., radius lengths). 
     In some examples, in order to improve the hinge candidate detection results, the software may use a priori knowledge to detect the hinge candidates. In some cases, the software may determine a range of expected size characteristics (e.g., radius lengths) for the plurality of hinges, and the software may limit the hinge candidates to circular shapes having determined size characteristics that are within the range of expected size characteristics. For example, the software may determine a range of expected radius lengths for a hinge, and the software may limit the hinge candidates to circular shapes having radii whose lengths are within the range of expected radius lengths. For example, a range of expected radius lengths may include a minimum expected radius length and a maximum expected radius length as well as all lengths between the minimum and maximum expected radius lengths. In some examples, the minimum expected radius length may be based on the smallest detected hinge radius in the first image (e.g., AP View image  1501 -A). For example, the minimum expected radius length may be equal to the smallest detected hinge radius in the first image (e.g., AP View image  1501 -A) minus a selected offset value. Also, in some examples, the maximum expected radius length may be based on the largest detected hinge radius in the first image (e.g., AP View image  1501 -A). For example, the maximum expected radius length may be equal to the largest detected hinge radius in the first image (e.g., AP View image  1501 -A) plus a selected offset value. In some cases, the radius lengths or other size characteristics of the hinges in the first image may be determined by the software by also performing an automated image analysis (e.g., using a Hough transformation) on the first image to detect the size characteristics of circles at the locations of the first image that were indicated by the user for the hinges in the first image. In some examples, because the second image and the first image may be captured from a same or similar distance to the fixator, the software may reasonably assume that the size characteristics (e.g., radius length) of the hinges should be the same or similar in the first and the second images. Thus, the size characteristics of the hinges in the first image may be used as a priori knowledge to more accurately identify hinge candidates, such as by excluding certain false positives, for example shapes or objects that have a size characteristic (e.g., radius length) that is too big or too small to be an actual hinge. It is noted that, in addition or as an alternative to radius lengths, other size characteristics (e.g., circumference, diameter, etc.) may be used to limit the detected hinge range of hinge candidates in a corresponding fashion as the radius length features described above. 
     Additionally, in some examples, a priori knowledge used to improve hinge detection results may include hinge orientation. For example, in some cases, the software may expect one or more rings of the fixator to be displayed at a certain angle within the image, such as substantially perpendicular to a bone segment, which may result in the ring being substantially horizontal in the second image. Moreover, the software may also expect hinges corresponding to a particular ring to be aligned with one another in a straight line. For example, the software may expect proximal hinges adjacent to a proximal ring to be aligned with one another in a straight line. The software may also expect distal hinges adjacent to the distal ring to be aligned with one another in a straight line. The software may also expect the line to have the same or similar angle as the respective ring. The software may use this a priori knowledge to more accurately identify hinge candidates, such as by excluding certain false positives. For example, in some cases, if the software identifies an outlying circular shape that is not aligned with any other detected circular shapes, then the software may consider this outlying circular shape to be a false positive and may not include it within the group of detected hinge candidates. Thus, in some examples, the detecting of the hinge candidates may be performed based at least in part on orientations of detected shapes within the second image. 
     At operation  1422 , candidate second image hinge locations are identified. The candidate second image hinge locations are the locations of the hinge candidates in the second image. In some examples, the software may identify the candidate second image hinge locations by determining coordinate values (e.g., X and Y coordinate values) for each of the detected hinge candidates within the second image. Referring now to  FIG. 19 , an example is shown of a hinge candidate list  1900  that includes information corresponding to example hinge candidates that may be detected by the software at operation  1420 . Specifically, each row of the hinge candidate list  1900  includes information for a respective hinge candidate. The first (i.e., left-most) value listed in each row is the respective X coordinate value of the location (e.g., center point) for the hinge candidate within the second image. The second (i.e., center) value listed in each row is the respective Y coordinate value of the location (e.g., center point) for the hinge candidate within the second image. The third (i.e., right-most) value listed in each row is the respective determined radius length of the hinge candidate. 
     At operation  1424 , adjusted second image hinge locations associated with the plurality of hinges in the second image are calculated. The adjusted second image hinge locations may be calculated based, at least in part, on the projected second image hinge locations (determined at operation  1418 ) and the candidate second image hinge locations (determined at operation  1422 ). For example,  FIG. 14B  shows an example of a group of sub-operations  1424 A-F that may be included in operation  1424  in order to calculate the adjusted second image hinge locations. In particular, at sub-operation  1424 A, the hinge candidates are grouped into a set of hinge candidate groups. In some examples, the hinge candidates may be grouped based at least in part on a similarity of size characteristics (e.g., radius lengths) and/or locations. For example, in some cases, two or more hinge candidates may be grouped together if their respective size characteristics (e.g., radius lengths) are within a selected allowed threshold size/length of one another. Also, in some cases, two or more hinge candidates may be grouped together if their respective locations are within a selected allowed threshold distance of one another. For example, two or more hinge candidates may be grouped together if their respective X coordinate location (e.g., center point) values are within a selected allowed threshold distance of one another and their respective Y coordinate location (e.g., center point) values are within a selected allowed threshold distance of one another. For example, as shown in  FIG. 19 , four of the rows of the hinge candidate list  1900  are underlined in order to indicate an example of four hinge candidates that may be grouped into a hinge candidate group. Specifically, it can be seen that the four underlined rows include X coordinate values (X:134, X:134, X:136 and X:138) in close proximity to one another, for example such that they are within a selected allowed X coordinate threshold distance. It can also be seen that the four underlined rows include Y coordinate values (Y:376, Y:378, Y:378 and Y:378) in close proximity to one another, for example such that they are within a selected allowed Y coordinate threshold distance. In some examples, the radius lengths of the four underlined rows (11, 12, 12, and 14) are close to one another, for example such that they are within a selected allowed radius length threshold. Thus, four hinge candidates corresponding to the four underlined rows in  FIG. 19  may be grouped into a respective hinge candidate group. As should be appreciated, although not shown in  FIG. 19 , other hinge candidates corresponding to other rows in  FIG. 19  may also be grouped into other hinge candidate groups. 
     Referring now to  FIG. 20 , an example is shown of a hinge candidate group list  2000  that includes information corresponding to example hinge candidate groups that may be formed from the hinge candidates identified in hinge candidate list  1900  of  FIG. 19 . Specifically, each row of the hinge candidate group list  2000  includes information for a respective hinge candidate group. The first (i.e., left-most) value listed in each row is a number of hinge candidates that are included in the respective group. The second (i.e., center) value listed in each row is the average of the X coordinate location values for the hinge candidates within the respective group. The third (i.e., right-most) value listed in each row is the average of the Y coordinate location values for the hinge candidates within the respective group. The underlined row in hinge candidate group list  2000  includes information for the hinge candidate group formed from the four hinge candidates corresponding to the four underlined rows in hinge candidate list  1900 . 
     At sub-operation  1424 B, the set of hinge candidate groups are weighted. In some examples, the set of hinge candidate groups may be weighted based at least in part on a number of hinge candidates within each of the set of hinge candidate groups. In some examples, hinge candidate groups with more included hinge candidates may be assigned a higher priority weight, while hinge candidate groups with fewer included hinge candidates may be assigned a lower priority weight. In some examples, the number of hinge candidates in each group may correspond to the exact weight assigned to the group. As shown in hinge candidate group list  2000 , the weight assigned to each hinge candidate group may be the first (i.e. left-most) value shown in each row that indicates the number of hinge candidates included in the respective group. For example, the underlined row of hinge candidate group list  2000  indicates that the respective hinge candidate group includes four hinge candidates, and this group may therefore receive a weight of four. By contrast, the top row of hinge candidate group list  2000  indicates that the respective hinge candidate group includes five hinge candidates, and this group may therefore receive a weight of five. 
     At sub-operation  1424 C, a highest weighted subset of hinge candidate groups may be selected from the set of hinge candidate groups. For example, if a subset of the four highest weighted hinge candidate groups were selected from the hinge candidate group list  2000 , then this subset would include hinge candidate groups represented by the first/top four rows on the hinge candidate group list  2000  (e.g., with respective weights of five or four). As another example, if a subset of the seven highest weighted hinge candidate groups were selected from the hinge candidate group list  2000 , then this subset would include hinge candidate groups represented by the first/top seven rows on the hinge candidate group list  2000  (e.g., with respective weights of five, four or three). 
     At sub-operation  1424 D, the software calculates a plurality of average group locations for the subset of highest weighted hinge candidate groups. Each of the average group locations may be associated with a respective hinge candidate group of the highest weighted subset of hinge candidate groups. For example, the average group location for a group may include an average of the X coordinate values of all of the hinge candidates in the group (i.e., the second/center value shown in each row of hinge candidate group list  2000 ) and an average of the Y coordinate values of all of the hinge candidates in the group (i.e., the third/right-most value shown in each row of hinge candidate group list  2000 ). Referring now to  FIG. 21 , an example is shown of an average group location  2120  that may be calculated for a hinge candidate group  2100  that includes four hinge candidates  2111 ,  2112 ,  2113  and  2114 . The hinge candidates  2111 ,  2112 ,  2113  and  2114  are labeled with the letters HC and include solid outlines, while the average group location  2120  is labeled with the letter A and includes a dashed outline. As shown, the average group location  2120  is positioned in  FIG. 21  at a horizontal (X axis) location that is the average of the horizontal locations of the four hinge candidates  2111 ,  2112 ,  2113  and  2114  in the hinge candidate group  2100 . Additionally, the average group location  2120  is positioned in  FIG. 21  at a vertical (Y axis) location that is the average of the vertical locations of the four hinge candidates  2111 ,  2112 ,  2113  and  2114  in the hinge candidate group  2100 . 
     At sub-operation  1424 E, a transformation matrix is constructed that describes a spatial relationship between the projected second image hinge locations (determined at operation  1418 ) and the plurality of average group locations (determined at sub-operation  1424 D). Referring now to  FIG. 22 , an example is shown in which the subset of highest weighted hinge candidate groups (selected at sub-operation  1424 C) includes six hinge candidate groups. As shown in  FIG. 22 , six average group locations  2200  are calculated, including one for each of the six hinge candidate groups in the highest weighted subset of hinge candidate groups. In  FIG. 22 , the six average group locations  2200  are each labeled with the letter A and include a dashed outline. In the particular example of  FIG. 22 , each of the six average group locations  2200  directly aligns with a respective actual hinge location. This is merely a simplistic example that is selected for purposes of clarity and ease of illustration. In practice, there is no requirement that the average group locations  2200  must directly align with respective actual hinge locations—and may often be close (but not exactly identical) to the respective actual hinge locations. As shown in  FIG. 22 , six arrows (pointing diagonally up and to the right) are drawn between the average group locations  2200  and the six closest respective projected second image hinge locations  1841  (shown as circles with bold/heavy outline) to which they correspond. These six diagonal arrows in  FIG. 22  represent the transformation matrix that describes the spatial relationship between the projected second image hinge locations  1841  and the plurality of average group locations  2200 . As should be appreciated, in the example of  FIG. 22 , because a subset of only six of the highest weighted hinge candidates is selected, the six average group locations  2200  correspond to only six (and not all twelve) of the projected second image hinge locations  1841 . In some examples, one or more relevant algorithms may be used by the software to calculate the transformation matrix, such as an iterative point cloud or iterative closest point (ICP) algorithm and/or a coherent point drift (CPD) algorithm. 
     At sub-operation  1424 F, the transformation matrix is used to adjust the projected second image hinge locations to the adjusted second image hinge locations. This may include, for example, determining spatial relationships that correlate the average group locations to the projected second image hinge locations and then using those spatial relationships (e.g., by reversing the spatial relationships) to adjust (e.g., transform) the projected second image hinge locations. For example, referring now to  FIG. 23 , the six diagonal arrows from  FIG. 22  (point diagonally up and to the right) that were used point from the average group locations  2200  to their respective closest projected second image hinge locations  1841  (and which represent the transformation matrix) are now reversed (to point diagonally down and to the left) to represent the adjustment that may be made to the projected second image hinge locations  1841  using the transformation matrix. Additionally, it is noted that, instead of only six arrows,  FIG. 23  includes twelve diagonal arrows to indicate that all twelve of the projected second image hinge locations  1841  may be transformed in this manner. Referring now to  FIG. 24 , the output of the adjustment (e.g., transformation) performed at sub-operation  1424 F is shown. In particular, each of the twelve projected second image hinge locations  1841  are shifted diagonally down and to the left (as shown by the twelve arrows in  FIG. 23 ) to form twelve adjusted second image hinge locations  2400  (represented by circles with bold outlines). In the particular example of  FIG. 24 , each of the twelve adjusted second image hinge locations  2400  directly aligns with a respective actual hinge location. This is merely a simplistic example that is selected for purposes of clarity and ease of illustration. In practice, there is no requirement that any or all of the adjusted second image hinge locations  2400  must directly align with respective actual hinge locations—and may often be close (but not exactly identical) to the respective actual hinge locations. 
     In some examples, the software may use the adjusted second image hinge locations  2400  to determine locations of the fixator rings  1511  and  1512  within the LAT View image  1501 -B. The software may then generate ring graphical representations corresponding to the fixator rings  1511  and  1512  and display the ring graphical representations at the determined locations of the fixator rings  1511  and  1512  within the LAT View image  1501 -B. Referring now to  FIG. 25 , it is seen that graphical representations  1731  and  1732  are generated by the software and displayed within LAT View image  1501 -B at the corresponding locations of the respective fixator rings  1511  and  1512 . 
     Referring back to  FIG. 14A , at operation  1426 , the adjusted second image hinge locations  2400  are used to determine positions and orientations of the first and second anatomical structure segments in three-dimensional space. For example, as described in detail above with respect to operation  322  of  FIG. 3A , imaging scene parameters may be used to determine positions and orientations of the first and second anatomical structure segments in three-dimensional space. As also described above, the imaging scene parameters may be obtained by comparing the locations of representations of particular components, or fixator elements of the fixator within the two-dimensional spaces of the first and the second images, with the corresponding locations of those same fixator elements in actual, three-dimensional space. At operation  1428 , the physical locations of the fixation device and the first and second anatomical structures in three-dimensional space may be used to determine manipulations to the fixation device for the correction of the deformity. For example, as also described above, such as with respect to operation  338  of  FIG. 3B , manipulations to the fixation apparatus for correction of the anatomical structure deformity (i.e., a treatment plan) may be determined using the positions and orientations of the first and second anatomical structure segments in three-dimensional space. Specifically, the treatment plan may be determined based, at least in part, on a determination of desired changes to the positions and/or orientations of the anatomical structure segments, for instance how the anatomical structure segments can be repositioned with respect to each other in order to promote union between the anatomical structure segments. 
     It is noted that the above description of the hinge detection techniques includes examples in which a priori knowledge from the first image is used for various purposes with respect to the second image, such as to determine projected second image hinge locations in the second image and to assist in identifying hinge candidates in the second image. It is noted, however, that the techniques described herein do not necessarily require a priori knowledge from the first image in order to perform hinge detection in the second image (or vice versa). For example, in some cases, hinge candidates could be detected in an image, such as by performing automated software-based image analysis techniques. The image analysis techniques may include performing a Hough transformation to detect circular shapes within the image. Hinge locations within the image may then be determined based at least in part on the detected hinge candidates, in some examples without the use of any a priori knowledge from another image. In some examples, various techniques described above, such as the grouping, weighting, location averaging and/or other techniques, may also optionally be employed. For example, in some cases, the detected hinge candidates may be grouped, such as using the grouping techniques described above. In some examples, only a selected subset of the highest weighted hinge groups may be used. In some examples, average group locations may be calculated for the hinge groups, such as using the techniques described above. In some examples, these average group locations may be used as the determined hinge locations, or the determined hinge locations may otherwise be calculated based at least in part on these average group locations. The determined hinge locations may then be used to determine physical locations of the fixation device and the first and the second anatomical structure segments in three-dimensional space. The physical locations of the fixation device and the first and the second anatomical structure segments may then be used to determine manipulations to the fixation device for the correction of the deformity. 
     Example Computing Device 
     Referring to  FIG. 26 , a suitable computing device such as example computing device  78  can be configured to perform any or all of the techniques set forth above. It will be understood that the computing device  78  can include any appropriate device, examples of which include a desktop computing device, a server computing device, or a portable computing device, such as a laptop, tablet, or smart phone. 
     In an example configuration, the computing device  78  includes a processing portion  80 , a memory portion  82 , an input/output portion  84 , and a user interface (UI) portion  86 . It is emphasized that the block diagram depiction of the computing device  78  is exemplary and not intended to imply a specific implementation and/or configuration. The processing portion  80 , memory portion  82 , input/output portion  84 , and user interface portion  86  can be coupled together to allow communications therebetween. As should be appreciated, any of the above components may be distributed across one or more separate devices and/or locations. 
     In various embodiments, the input/output portion  84  includes a receiver of the computing device  78 , a transmitter of the computing device  78 , or a combination thereof. The input/output portion  84  is capable of receiving and/or providing information pertaining to communicate a network such as, for example, the Internet. As should be appreciated, transmit and receive functionality may also be provided by one or more devices external to the computing device  78 . 
     The processing portion  80  may include one or more processors. Depending upon the exact configuration and type of processor, the memory portion  82  can be volatile (such as some types of RAM), non-volatile (such as ROM, flash memory, etc.), or a combination thereof. The computing device  78  can include additional storage (e.g., removable storage and/or non-removable storage) including, but not limited to, tape, flash memory, smart cards, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, universal serial bus (USB) compatible memory, or any other medium which can be used to store information and which can be accessed by the computing device  78 . 
     The computing device  78  also can contain the user interface portion  86  allowing a user to communicate with the computing device  78 . The user interface  86  can include inputs that provide the ability to control the computing device  78 , via, for example, buttons, soft keys, a mouse, voice actuated controls, a touch screen, movement of the computing device  78 , visual cues (e.g., moving a hand in front of a camera on the computing device  78 ), or the like. The user interface portion  86  can provide outputs, including visual information (e.g., via a display), audio information (e.g., via speaker), mechanically (e.g., via a vibrating mechanism), or a combination thereof. In various configurations, the user interface portion  86  can include a display, one or more graphical user interfaces, a touch screen, a keyboard, a mouse, an accelerometer, a motion detector, a speaker, a microphone, a camera, a tilt sensor, or any combination thereof Thus, a computing system including, for example, one or more computing devices  78  can include a processor, a display coupled to the processor, and a memory in communication with the processor, one or more graphical user interfaces, and various other components. The memory can have stored therein instructions that, upon execution by the processor, cause the computer system to perform operations, such as the operations described above. As used herein, the term computing system can refer to a system that includes one or more computing devices  78 . For instance, the computing system can include one or more server computing devices that communicate with one or more client computing devices. 
     While example embodiments of devices for executing the disclosed techniques are described herein, the underlying concepts can be applied to any computing device, processor, or system capable of communicating and presenting information as described herein. The various techniques described herein can be implemented in connection with hardware or software or, where appropriate, with a combination of both. Thus, the methods and apparatuses described herein can be implemented, or certain aspects or portions thereof, can take the form of program code (i.e., instructions) embodied in tangible non-transitory storage media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium (computer-readable storage medium), wherein, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for performing the techniques described herein. In the case of program code execution on programmable computers, the computing device will generally include a processor, a storage medium readable by the processor (including volatile and non-volatile memory and/or storage elements), at least one input device, and at least one output device, for instance a display. The display can be configured to display visual information. The program(s) can be implemented in assembly or machine language, if desired. The language can be a compiled or interpreted language, and combined with hardware implementations. 
     It should be appreciated that the orthopedic fixation with imagery analysis techniques described herein provide not only for the use of non-orthogonal images, but also allow the use of overlapping images, images captured using different imaging techniques, images captured in different settings, and the like, thereby presenting a surgeon with greater flexibility when compared with existing fixation and imagery techniques. 
     The techniques described herein also can be practiced via communications embodied in the form of program code that is transmitted over some transmission medium, such as over electrical wiring or cabling, through fiber optics, or via any other form of transmission. When implemented on a general-purpose processor, the program code combines with the processor to provide a unique apparatus that operates to invoke the functionality described herein. Additionally, any storage techniques used in connection with the techniques described herein can invariably be a combination of hardware and software. 
     While the techniques described herein can be implemented and have been described in connection with the various embodiments of the various figures, it is to be understood that other similar embodiments can be used or modifications and additions can be made to the described embodiments without deviating therefrom. For example, it should be appreciated that the steps disclosed above can be performed in the order set forth above, or in any other order as desired. Further, one skilled in the art will recognize that the techniques described in the present application may apply to any environment, whether wired or wireless, and may be applied to any number of such devices connected via a communications network and interacting across the network. Therefore, the techniques described herein should not be limited to any single embodiment, but rather should be construed in breadth and scope in accordance with the appended claims.