Patent Publication Number: US-2023149083-A1

Title: Method and navigation system for registering two-dimensional image data set with three-dimensional image data set of body of interest

Description:
RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application Ser. No. 63/264,250, filed Nov. 18, 2021, the entire contents of which are incorporated herein by reference as if fully set forth below in its entirety and for all applicable purposes. 
    
    
     BACKGROUND 
     Field of Invention 
     The present disclosure relates to a method and a navigation system for establishing a relation between a two-dimensional image data and a three-dimensional image data both corresponding to a body of interest. More particularly, the present disclosure relates to a method and a navigation system for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest. 
     Description of Related Art 
     At present, the rate of occurrence of diseases corresponding to the spine is increasing day by day, and the health of human is seriously affected. Spinal surgery is a main treatment for spinal diseases, and how to minimize wounds during and after a procedure becomes more and more important, such that infection risks can be reduced and patients are able to quickly recover without hospitalization. For this purpose, an image guided surgical procedure with a navigation system is introduced into spinal surgeries. During the image guided medical procedure, the area of interest of a patient that has been imaged is displayed on a display of the navigation system. Meanwhile, the system can track surgical instruments and/or implants and then integrate their simulated images with the area of interest of the patient body. By taking advantage of such a procedure and system, physicians are able to see the location of the instruments and/or implants relative to a target anatomical structure without the need to frequent use of C-Arm fluoroscopy throughout the entire surgical procedure is generally disclosed in U.S. Pat. No. 6,470,207, entitled “Navigational Guidance Via Computer-Assisted Fluoroscopic Imaging,” issued Oct. 22, 2002, which is incorporated herein by reference in its entirety. 
     However, the spine navigation system usually needs to use the X-ray inspection for obtaining the internal body of the patient. The patient is therefore in danger due to the radiation exposure. In view of the foregoing, problems and disadvantages are associated with existing systems that require further improvement. However, those skilled in the art have yet to find a solution. 
     There are many ways to achieve two-directional (2D) to three-directional (3D) registration by adopting obtained 2D images to register 3D images which are known in the art. The registrations from 2D to 3D include contour algorithms, point registration algorithms, surface registration algorithms, density comparison algorithms, and pattern intensity registration algorithms. The foregoing registrations, however, need a great deal of calculation and therefore, usually take several minutes to execute the 2D to 3D registration. Actually, some of these registrations may take upwards of twenty minutes to an hour to execute the registration. Furthermore, these registration processes could also result in an inexact registration after waiting for such long time. 
     In view of the foregoing, problems and disadvantages are associated with existing technologies that require further improvement, and there is a need to provide a method and equipment for executing 2D to 3D registration in a more accurate and efficient way. Moreover, the flows of the method for executing 2D to 3D registration shall also be improved. 
     In addition, 2D images (e.g., X-ray images) generally cover more than one level of vertebrae. Matching 2D images with digitally reconstructed radiographs (DRR) from computed tomography (CT) data is not efficient and easy to cause registration failures, errors, or inaccuracy due to interference in regions of interest such as pedicle screw, cage, ribs, and Ilium. Specialized algorithm focusing on separated local comparison instead of global matching may be used to help the comparison in such anatomical images. 
     SUMMARY 
     The foregoing presents a simplified summary of the disclosure in order to provide a basic understanding to the reader. This summary is not an extensive overview of the disclosure and it does not identify key/critical elements of the present disclosure or delineate the scope of the present disclosure. Its sole purpose is to present some concepts disclosed herein in a simplified form as a prelude to the more detailed description that is presented later. 
     One aspect of the present disclosure is to provide a method for registering a two-dimensional image data set of a body of interest with a three-dimensional image data set of the body of interest. The method comprises following steps: generating a first reconstructed image from the three-dimensional image data set with a first spatial parameter; calculating a reference similarity value according to the first reconstructed image and the two-dimensional image data set; generating a second reconstructed image from the three-dimensional image data set with a second spatial parameter; calculating a comparison similarity value according to the second reconstructed image and the two-dimensional image data set; comparing the comparison similarity value with the reference similarity value; and registering the two-dimensional image data set to the three-dimensional image data set if the comparison similarity value is not greater than the reference similarity value for computer-assisted surgical navigation based on the two-dimensional image data set and the three-dimensional image data set after registering. 
     Another aspect of the present disclosure is to provide a navigation system for registering a two-dimensional image data set of a body of interest with a three-dimensional image data set of the body of interest. The navigation system comprises a memory and a processor. The memory is configured to store a plurality of commands. The processor is configured to obtain the plurality of commands from the memory to perform following steps: generating a first reconstructed image from the three-dimensional image data set with a first spatial parameter; calculating a reference similarity value according to the first reconstructed image and the two-dimensional image data set; generating a second reconstructed image from the three-dimensional image data set with a second spatial parameter; calculating a comparison similarity value according to the second reconstructed image and the two-dimensional image data set; comparing the comparison similarity value with the reference similarity value; and registering the two-dimensional image data set to the three-dimensional image data set if the comparison similarity value is not greater than the reference similarity value for computer-assisted surgical navigation based on the two-dimensional image data set and the three-dimensional image data set after registering. 
     It is to be understood that both the foregoing general description and the following detailed description are by examples, and are intended to provide further explanation of the invention as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. In the drawings. 
         FIG.  1    depicts a schematic diagram of a navigation system according to one embodiment of the present disclosure; 
         FIG.  2    depicts a schematic diagram of a calculating device, a database, and an optical tracker of the navigation system shown in  FIG.  1    according to one embodiment of the present disclosure; 
         FIG.  3    depicts a flow diagram of a method for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest according to one embodiment of the present disclosure; 
         FIG.  4    depicts a schematic diagram of a portion of a body of interest according to one embodiment of the present disclosure; 
         FIG.  5    depicts a schematic diagram of a portion of a body of interest according to one embodiment of the present disclosure; 
         FIG.  6    depicts a schematic diagram of a portion of a body of interest according to one embodiment of the present disclosure; 
         FIG.  7    depicts a schematic diagram of a portion of a body of interest according to one embodiment of the present disclosure; 
         FIG.  8    depicts a schematic diagram of operations of the C-arm device shown in  FIG.  1    according to one embodiment of the present disclosure; 
         FIG.  9    depicts a schematic diagram of operations of the C-arm device shown in  FIG.  1    according to one embodiment of the present disclosure; 
         FIG.  10    depicts a flow diagram of a method for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest according to one embodiment of the present disclosure; 
         FIG.  11    depicts a flow diagram of a method for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest according to one embodiment of the present disclosure; 
         FIG.  12    depicts a flow diagram of a method for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest according to one embodiment of the present disclosure; 
         FIG.  13    depicts a flow diagram of a method for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest according to one embodiment of the present disclosure; 
         FIG.  14    depicts a schematic diagram of a virtual camera simulated by the calculating device of the navigation system shown in  FIG.  1    according to one embodiment of the present disclosure; 
         FIG.  15    depicts a flow diagram of a method for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest according to one embodiment of the present disclosure; and 
         FIG.  16    depicts a flow diagram of a method for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest according to one embodiment of the present disclosure. 
     
    
    
     According to the usual mode of operation, various features and elements in the figures have not been drawn to scale, which are drawn to the best way to present specific features and elements related to the disclosure. In addition, among the different figures, the same or similar element symbols refer to similar elements/components. 
     DESCRIPTION OF THE EMBODIMENTS 
     To make the contents of the present disclosure more thorough and complete, the following illustrative description is given with regard to the implementation aspects and embodiments of the present disclosure, which is not intended to limit the scope of the present disclosure. The features of the embodiments and the steps of the method and their sequences that constitute and implement the embodiments are described. However, other embodiments may be used to achieve the same or equivalent functions and step sequences. 
     Unless otherwise defined herein, scientific and technical terminologies employed in the present disclosure shall have the meanings that are commonly understood and used by one of ordinary skill in the art. Unless otherwise required by context, it will be understood that singular terms shall include plural forms of the same and plural terms shall include the singular. Specifically, as used herein and in the claims, the singular forms “a” and “an” include the plural reference unless the context clearly indicates otherwise. 
       FIG.  1    depicts a schematic diagram of a navigation system  1000  having a calculating device  1100 , a database  1200 , and an optical tracker  1400  according to one embodiment of the present disclosure. The navigation system  1000  can be used to navigate an instrument  9500  during a surgical operation of an object  9000 , but the present disclosure is not limited thereto. In some embodiments, the navigation system  1000  can be used to navigate any kind of tools during any type of operations depending on actual requirements. For instances, the navigation system  1000  can be used to navigate screws, graspers, clamps, surgical scissors, cutters, needle drivers, retractors, distractors, dilators, suction tips and tubes, sealing devices, irrigation and injection needles, powered devices, scopes and probes, carriers and appliers, ultrasound tissue disruptors, cryotomes and cutting laser guides, and measurement devices. The navigation system  1000  can also be used to navigate any type of implant including orthopedic implants, spinal implants, cardiovascular implants, neurovascular implants, soft tissue implants, or any other devices implanted in an objective  9000  such as a patient. 
     The calculating device  1100  can be but not limited to a computer, a desktop, a notebook, a tablet, or any other devices that can perform calculating function. The database  1200  can be but not limited to a data storage, a computer, a server, a cloud storage, or any other devices that can store data. The database  1200  is used to store pre-acquired three-dimensional (3D) image data set of the object  9000 . The 3D image data set can be obtained by using a computerized tomography (CT) to scan the object  9000 . 
     The imaging device  1300  can be established and performed separately from the navigation system  1000 , and the imaging device  1300  can be but not limited to a C-arm mobile fluoroscopy machine or a mobile X-ray image intensifier. The imaging device  1300  includes a X-ray emitter  1310  and a X-ray receiver  1320 . The former emits X-rays that penetrate the body of the object  9000 , and the latter receives and converts the X-rays into digital two-dimensional (2D) images on a display of imaging device  1300 . According to the planes along which the imaging device  1300  obtains images, the 2D images may be an anterior/posterior (AP) image and a lateral view (LA) 2D image of the object  9000 . The object  9000  can be but not limited to a patient. 
     The calibrator  1510  including calibration markers is used to both calibrate the imaging device  1300  and track the location of the imaging device  1300  during an image is obtained. The calibrator  1510  is included in or disposed on the X-ray receiver  1320 , and the dynamic reference frames  1520 A are disposed on or close to the X-ray receiver  1320  and the body of interest of the object  9000 . The calibrator  1510  is in the path from the X-ray emitter  1310  to the X-ray receiver  1320  and opaque- or semi-opaque to the X-ray. Therefore, the X-ray entering the object  9000  and also the calibrator  1510  are partially absorbed by particular tissues and the calibration markers in the calibrator  1510  before received by the X-ray receiver  1320  in operation. This makes the two-dimensional images present the body of interest of the object  9000  and the calibration markers of the calibrator  1510 . The calculating device  1100  may acquire the relation of the X-ray emitter  1310  and the X-ray receiver  1320  by calculating the pattern of the calibration markers presented on the two-dimensional images. The AP two-dimensional image and the LA two-dimensional image of the vertebral bodies of interest of the object  9000  are involved the two-dimensional image data set in the present embodiment. Alternatively, in another embodiment, it can be only AP two-dimensional image or LA two-dimensional image in the two-dimensional image data set. Then, the two-dimensional image data set can be transmitted as an electronic file to the calculating device  1100  for later use. 
     The three-dimensional image data set in the database  1200 , the two-dimensional image data set generated from the imaging device  1300 , the optical tracker  1400 , the calibrators  1510 , the dynamic reference frame  1520 A, and the object  9000  have their own coordinates in different coordinate systems. The navigation system  1000  of the present disclosure can establish relations among those coordinate systems, such that surgeons may use the navigation system  1000  to navigate the instrument  9500  or during the surgical operation. The relation among those coordinates is described below. The calibrator  1510  and the dynamic reference frame  1520 A are disposed on the X-ray receiver  1320 , the location of the three can be substantially treated as the same, and therefore, the relation between the calibrator coordinate system and the imaging device coordinate system is established. The optical tracker  1400  then tracks the dynamic reference frame  1520 A including reflector to introduce the calibrator  1510 , the dynamic reference frame  1520 A, and the X-ray receiver  1320  into the tracker coordinate system, and therefore, the location of the X-ray receiver  1320  in the tracker coordinate system is obtained. In some embodiments, the optical tracker  1400  can also track the calibrator  1530  including reflector to introduce the calibrator  1530  into the tracker coordinate system, and therefore, the location of the calibrator  1530  in the tracker coordinate system is obtained. Since the relation of the X-ray emitter  1310  and the X-ray receiver  1320  is acquired as described above, the location of the X-ray emitter  1310  in the tracker coordinate system can be acquired as well. It is noted that, the present disclosure is not limited to the structures and the operations as shown in  FIG.  1   , and it is merely an example for illustrating one of the implements of the present disclosure. 
     It is noted that the registration procedure of the navigation system  1000  substantially consists of three stages which are initialization alignment, 2D to 3D registration, and realignment. In some embodiments, the program installed in the navigation system  1000  runs through these three stages, further discussed herein. Alternatively, in other embodiments, the program can run only the initial alignment process, the 2D to 3D registration, the re-registration, or a combination thereof depending on the situations and/or the functions needed. 
     More details will be discussed below. 
     Initialization Alignment 
     Before using the navigation system  1000 , an initial alignment process would be performed to the navigation system  1000  so as to improve the efficiency and enhance the precision of the navigation system  1000 , which will be described below. 
       FIG.  2    depicts a schematic diagram of the calculating device  1100 , the database  1200 , and the optical tracker  1400  of the navigation system  1000  shown in  FIG.  1    according to one embodiment of the present disclosure. As shown in the figure, the calculating device  1100  is electrically connected to the database  1200  and the Imaging device  1300 . 
     The calculating device  1100  includes a memory  1110 , a processor  1120 , and an I/O interface  1130 . The processor  1120  is electrically connected to the memory  1110  and the I/O interface  1130 . The memory  1110  is used to store a plurality of commands, and the processor  1120  is used to obtain the plurality of commands from the memory  1110  to perform steps of a method  2000  shown in  FIG.  3    for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest. 
     In some embodiments, the memory  1110  can include, but not limited to, at least one of a flash memory, a hard disk drive (HDD), a solid-state drive (SSD), a dynamic random access memory (DRAM) and a static random access memory or a combination thereof. In some embodiments, as being a non-transitory computer readable medium, the memory  1110  can store the computer readable commands that can be accessed by the processor  1120 . 
     In some embodiments, the processor  1120  can include, but not limited to, a single processor or an integration of multiple microprocessors, such as a central processing unit (CPU), a graphics processing unit (GPU) or an application-specific integrated circuit (ASIC), etc. 
     Reference is now made to both  FIG.  2    and  FIG.  3   . In operation, the step  2100  is performed by the processor  1120  to adjust a first virtual camera according to a distance parameter calculated corresponding to the two-dimensional image data set and the body of interest. 
     For example, the processor  1120  of the calculating device  1100  may obtain the X-ray images directly from the imaging device  1300  or pre-stored in the database  1200 . As discussed above, the two-dimensional data set includes at least the AP and LA two-dimensional images which both include the calibrator  1510  in  FIG.  1   . The calibrator  1510  can be used to identify the location of the imaging device  1300  in operation in accordance with the abovementioned calculation of the relation. Once the location of the imaging device  1300  is acquired, the processor  1120  may estimate the distance between the X-ray emitter  1310  and the targeted vertebral body of interest in the objective  9000 . The estimated distance then is converted to a distance parameter for by the processor  1120  of the calculating device  1100 . 
     The initialization alignment  2000  according to the embodiment disclosed herein is illustrated. Briefly, the initialization alignment  2000  can include three steps  2100 ,  2200 ,  2300 . 
     As a first step, the surgeon is asked to acquire a first Image or an anterior/posterior (AP) image and a second image or a lateral (LA) image from the imaging device  1300 . These images are used for refinement and navigation, but also to initialize the orientation. Since the imaging device  1300  includes the calibrator  1510 , the location of the X-ray emitter  1310  during image acquisition with respect to the patient coordinate system is known (i.e., patient AP direction and patient LA direction). This knowledge is combined with the knowledge of how the patient  9000  is oriented during the three-dimensional volume scan by the setting of the user. Given the estimated orientation, digitally reconstructed radiographs (DRRs) are created from the three-dimensional data set acquired by CT scan. Owing to the DRRs being a kind of digital images, it is helpful to explain how and where they are generated with virtual cameras. That is to say, the AP and LA DRRs are captured by two virtual cameras simulatively for example located at the particular spots toward to the vertebral body of interest of the patient  9000  along the AP and LA planes respectively. The DRRs correspond to the actual interoperative AP and lateral LA radiographs. The surgeon is presented with the DRRs and the actual radiographs and is asked to identify a common point in all images. This step provides a common point or position in the CT image data and the dynamic reference frame  1520 A or patient space coordinates. Once the position and orientation of the patient  9000  in the three-dimensional data set and the dynamic reference frame coordinates are known, the method proceeds to the refinement step. After refinement, all of the systems involved are linked and known. 
     During the initialization step, the surgeon is asked to acquire AP and LA radiographs or radiographs along any two planes using the imaging device  1300 . In a spinal procedure, the surgeon is prompted to identify the center of the vertebral body that the surgeon is interested in. Putting together all of this data, a good estimate of the orientation and the position is known and is used to calculate the DRRs that correspond closely to the actual radiographs for an initial two-dimensional to three-dimensional registration. These DRRs are created by adopting the three-dimensional data from the CT scan combined with the information from the C-arm localization target. 
     The processor  1120  of the calculating device  1100  may access the three-dimensional image data set stored in the database  1200 , and an AP virtual camera or an LA virtual camera corresponding to the three-dimensional image data set can be created by the processor  1120 . Each of the virtual cameras has its own spatial parameters indicating the position and orientation corresponding to the body of interest in the three-dimensional image. Just like an actual camera, that the positions and orientations of the cameras corresponding to the target objective determines what images will be obtained. Therefore, changing the spatial parameter of a virtual camera will generate different reconstructed images from the three-dimensional image data set. In the present embodiment, the spatial parameter includes at least a distance parameter which indicates the distance from the target body of interest of the object  9000  to the virtual camera. 
     Preliminary Registration 
     In the preliminary registration step, software is used to provide matching algorithms that reprocess the preliminary two-dimensional to three-dimensional registration. The software is adopting to adjust the initial position and the orientation in a way as to minimize differences between the DRRs and the actual radiographs, thereby refining the registration. In the preliminary step, similarity or cost measures are implemented to identify how well the images match. An iterative preliminary algorithm adjusts the initial position and the orientation parameters simultaneously to maximize the similarity between the DRRs and the actual radiographs. The similarity or cost measures that are implemented are selected from known similarity and cost measures, such as normalized mutual information, mutual information, gradient difference algorithms, surface contour algorithms, pattern intensity algorithms, sum of squared differences, normalized cross-correlation, local normalized correlation, and correlation ratio. This procedure results in an efficient and accurate manner to provide two-dimensional to three-dimensional registration. 
     Subsequently, the processor  1120  of the calculating device  1100  may adjust the AP virtual camera or the LA virtual camera according to the distance parameter. 
     In some embodiments, the distance parameter is calculated according to the actual distance between two plain marks on an image of the two-dimensional image data set. For example, surgeons may be asked to manually make two marks on the single AP or LA two-dimensional image where they are interested in. 
     In the present embodiment shown in  FIG.  4   , the object  9000  is a patient under a vertebral disorder, the surgeon may manually make two marks V 0  and V 1  on but not limited to the center of two target vertebral bodies of the object  9000  through the I/O interface  1130  in  FIG.  2   . As such, the distance between the marks V 0  and V 1  can be calculated by the processor  1120  of the calculating device  1100  with an imaging recognition technology. In some embodiments, the I/O interface  1130  can be electrically connected to any kind of input devices such as a mouse, a keyboard, and a touch panel for inputting. 
     As can be seen in  FIG.  5   , it is an AP digitally reconstructed radiograph (DRR) image generated by the processor  1120  with inputs combining the information of where the object  9000  was positioned or oriented corresponding to the imaging device  1300  during X-ray image acquisition. 
     Virtual camera in some embodiments is a modularized coding of the two-dimensional to three-dimensional registration program for generation of two-dimensional image from a three-dimensional volume at a parameter-driven position along with a parameter-driven orientation or perspective by the processor  1120  with known DRR algorithm. 
     Using this estimate of the orientation, the DRR image in  FIG.  5    from the CT scan is created to correspond substantially to the actual interoperative radiograph in  FIG.  4   . By using the patient orientation information from the three-dimensional image data with the patient orientation information on the location of the imaging device  1300 , this information is implemented in combination with known DRR algorithms to create the DRR. In other words, since it is known where the fluoroscopic scans were taken, and the right/left and AP directions of the CT data or any other directions are known, if a person takes a view through the three-dimensional volume data, along the direction of the fluoroscopic scan and an accurate DRR is obtained. The DRR is essentially a two-dimensional image taken from a three-dimensional volume where a view through the three-dimensional volume is generated by looking through three-dimensional volume from the proper orientation or perspective, to create a line for every voxel. Each line is considered to create a new voxel value, which generates the DRR. 
     However, the initial DRRs are not precisely matching with the AP and LA X-ray images. That is why there is a need to perform an alignment procedure during two-dimensional to three-dimensional registration. 
     The surgeons may manually make another two marks V 0 ′ and V 1 ′ on the target two vertebral bodies of the AP DRR image through the I/O interface  1130  in  FIG.  2   . As such, a distance between two marks V 0 ′ and V 1 ′ on the AP DRR image in  FIG.  5    can be calculated by the processor  1120 . Subsequently, if the distance between two marks V 0  and V 1  on the AP 2D image in  FIG.  4    is, for example, 100 pixels, the processor  1120  may adjust the distance parameter of the AP virtual camera to regenerate an adjusted AP DRR image which has the distance between two marks V 0 ′ and V 1 ′ to be also 100 pixels. Therefore, the size of the target vertebral bodies shown on the AP DRR image in  FIG.  5    is adjusted to be similar to the size of those shown on the AP 2D image in  FIG.  4   . In view of the above, it merely needs to focus on the distances regarding the marks on the AP 2D image in  FIG.  4    and the AP DRR image in  FIG.  5   , and then adjusts the distances to be the same for alignment, and therefore, the alignment process can be very fast. 
     Besides, in the present embodiment shown in  FIG.  6   , the surgeons may manually make marks V 0  and V 1  on two target vertebral bodies of the object  9000  through the I/O interface  1130  in  FIG.  2   . As such, the distance between the marks V 0  and V 1  can be calculated by the processor  1120  of the calculating device  1100  with an imaging recognition technology. 
     As can be seen in  FIG.  7   , it is a LA DRR image generated by the processor  1120  with inputs combining the information of where the object  9000  was positioned or oriented corresponding to the imaging device  1300  during X-ray image acquisition. The surgeon may manually make two mark V 0 ′ and V 1 ′ on two target vertebral bodies of the object through the I/O interface  1130  in  FIG.  2   . As such, the distance between the marks V 0 ′ and V 1 ′ can be calculated by the processor  1120  of the calculating device  1100  with an imaging recognition technology. Subsequently, if the distance between two marks V 0  and V 1  on the LA 2D image in  FIG.  6    is, for example, 100 pixels, the processor  1120  may adjust the distance parameter of the LA virtual camera to regenerate an adjusted LA DRR image which has the distance between two marks V 0 ′ and V 1 ′ to be also 100 pixels. Therefore, the size of the target vertebral bodies shown on  FIG.  7    is adjusted to be similar to the size of those shown on the LA 2D image in  FIG.  6   . In view of the above, it merely needs to focus on the distances regarding the marks on the LA 2D image in  FIG.  6    and the LA DRR image in  FIG.  7   , and then adjusts the distances to be the same for alignment, and therefore, the alignment process can be very fast. 
     In some embodiments, the distance parameter is calculated according to a distance between an estimated position of an emitter and an estimated position of the body of interest. For example, as discussed above, the calibrator  1510  shown on the X-ray two-dimensional image generated by the imaging device  1300  in  FIG.  1    can be used as a reference for the calculating device  1100  to calculate the estimated position of the X-ray emitter  1310 . In addition, the estimated position of the object  9000  can be calculated by the calculating device  1100  according to the X-ray image showing the calibrators  1510  and the estimated position of the X-ray emitter  1310 . Thereafter, if the estimated position of the X-ray emitter  1310  and the estimated position of the object  9000  are obtained, the distance between the X-ray emitter  1310  and the estimated position of the object  9000  is able to be calculated by the calculating device  1100 . 
     In some embodiments, the estimated position of the emitter is calculated according to the two-dimensional image data set, and the estimated position of the body of interest is at a position at which a first virtual line and a second virtual line are the closest. For example, the calculating device  1100  in  FIG.  2    may obtain the X-ray images from the imaging device  1300 . As discussed above, the X-ray images from the imaging device  1300  may include the calibrator  1510  in  FIG.  1   . Therefore, the calculating device  1100  may calculate the estimated position of the X-ray emitter  1310  according to the X-ray image including the calibrator  1510 . Referring to  FIG.  8   , there is a first virtual line VL 1  which is generated between the estimated position of the X-ray emitter  1310  and the calibrator  1510 . Referring to  FIG.  9   , there is a second virtual line VL 2  which is generated between the estimated position of the X-ray emitter  1310  and the calibrator  1510 . If the first virtual line VL 1  in  FIG.  8    and the second virtual line VL 2  in  FIG.  9    are located in the same coordinate system, the estimated position of the object  9000  is determined at a position at which the first virtual line VL 1  and the second virtual line VL 2  are the closest. 
     In some embodiments, the two-dimensional image data set includes first and second two-dimensional images, the first virtual line is generated between the estimated position of the emitter and a central point of at least two reflectors which are radiated when the first two-dimensional image data set is captured, the second virtual line is generated between the estimated position of the emitter and the central point of the at least two reflectors which are radiated when the second two-dimensional image data set is captured. 
     For example, the X-ray images from the imaging device  1300  in  FIG.  1    include the AP 2D image and the LA 2D image of the object  9000 . Referring to  FIG.  8   , the first virtual line VL 1  is generated between the estimated position of the X-ray emitter  1310  and a central point  1521  of reflectors  1523 ,  1525 ,  1527  which can be related to the dynamic reference frame  1520 A in  FIG.  1    and are obtained by the optical tracker  1400 . Referring to  FIG.  9   , the second virtual line VL 2  is generated between the estimated position of the X-ray emitter  1310  and a central point  1521  of reflectors  1523 ,  1525 ,  1527  which can be related to the dynamic reference frame  1520 A in  FIG.  1    and obtained by the optical tracker  1400 . It is noted that the central point  1521  can be an original point of the calibrator coordinate constructed by the reflectors  1523 ,  1525 ,  1527 , and the location of the central point  1521  in not limited to the physical center of the reflectors  1523 ,  1525 ,  1527 . 
     Referring to both  FIG.  2    and  FIG.  3   , in operation, the step  2200  is performed by the processor  1120  to rotate the first virtual camera according to an angle difference between a first vector and a second vector, wherein the first vector is calculated from two spatial marks in the three-dimensional image data set, and the second vector Is calculated from two first plain marks in the two-dimensional image data set. 
     For example, the first vector is calculated from two spatial marks in the three-dimensional image generated by the AP virtual camera with proper DDR algorithm. Referring to  FIG.  4   , the second vector is calculated from two plain marks V 0  and V 1  on the AP two-dimensional image. When the first vector and the second vector are obtained, the processor  1120  may calculate an angle difference between the first vector and the second vector. Subsequently, the processor  1120  can rotate the AP virtual camera according to the angle difference. Therefore, the orientation or perspective of the AP virtual camera is adjusted to be similar or identical in the best to that of the X-ray emitter  1310  of the imaging device  1300  along the AP plain in  FIG.  4   . This step is executed by the calculating device  1100  to adjust or modify the orientation or perspective parameter of the DRR algorithm so as to generate an adjusted or modified DRR image which is more similar or identical in the best to the AP two-dimensional X-ray image. In view of the above, the vertebral bodies in the AP two-dimensional image and the AP DRR image can be adjusted to be identical, and the elevation angles regarding the LA two-dimensional image and the LA DRR image can be adjusted to be similar. 
     Furthermore, the first vector is calculated from two spatial marks in the three-dimensional image generated by the LA virtual camera with proper DDR algorithm. Referring to  FIG.  6   , the second vector is calculated from two plain marks V 0  and V 1  on the LA two-dimensional image. When the first vector and the second vector are obtained, the processor  1120  may calculate an angle difference between the first vector and the second vector. Subsequently, the processor  1120  can rotate the LA virtual camera according to the angle difference. Therefore, the orientation or perspective of the LA virtual camera is adjusted to be similar or identical in the best to that of the X-ray emitter  1310  of the imaging device  1300  along the LA plain in  FIG.  6   . This step is executed by the calculating device  1100  to adjust or modify the orientation or perspective parameter of the DRR algorithm so as to generate an adjusted or modified DRR image which is more similar or identical in the best to the LA two-dimensional X-ray image. In view of the above, the vertebral bodies in the LA two-dimensional image and the LA DRR image can be adjusted to be identical, and the elevation angles regarding the AP two-dimensional image and the AP DRR image can be adjusted to be similar. 
     In some embodiments, the two-dimensional image data set includes a first two-dimensional image, the first vector is calculated from the two spatial marks in the three-dimensional image data set generated by the first virtual camera, and the second vector is calculated by the two first plain marks in the first two-dimensional image data. For example, the two-dimensional image data set includes the AP two-dimensional image in  FIG.  4   . The first vector is calculated from two spatial marks in the three-dimensional image data set generated by the AP virtual camera. The second vector is calculated by two plain marks V 0  and V 1  in the AP two-dimensional image in  FIG.  4   . 
     In some embodiments, the two-dimensional image data set includes a second two-dimensional image, and the second vector is calculated from the two second plain marks in the second two-dimensional image data. For example, the two-dimensional image data set includes the LA two-dimensional Image in  FIG.  6   . The first vector is calculated from two spatial marks in the three-dimensional image data set generated by the LA virtual camera. The second vector is calculated from the two plain marks V 0  and V 1  in the LA two-dimensional image in  FIG.  6   . 
     Reference is now made to both  FIG.  2    and  FIG.  3   . In operation, the step  2300  is performed by the processor  1120  to rotate the first virtual camera according to an angle which is corresponding to a maximum similarity value of a plurality of similarity values calculated in accordance with reconstructed images of the three-dimensional image data set which includes one generated by the first virtual camera and the others generated by other virtual cameras with different angles or different pixels from the one generated by the first virtual camera and the two-dimensional image data set for implementing in the two-dimensional image data set to the three-dimensional image data set registration of the navigation system  1000  after adjusting and rotating. 
     For example, first, a few LA DRR images are generated by adjusting the pre-determined position and/or orientation of the LA virtual camera in the coordinate system of the three-dimensional image date set. The pre-determined position and/or orientation of the LA virtual camera can be chosen by the surgeon in accordance with the volume of interest in the three-dimensional data set. 
     The LA DRR images can be generated by taking the pre-determined position and/or orientation of the LA virtual camera as the center and then rotating its roll angle in a range from −20 degrees to 20 degrees and/or moving its position in a range from −15 pixels to 15 pixels for DRR generation. Since different LA DRR images have different contents, a plurality of similarity values can be calculated in accordance with the LA DRR images and the pre-determined LA two-dimensional image, which is chosen by the surgeon in accordance with the region of interest corresponding to the volume of interest. Then, the maximum similarity value will be obtained from the plurality of similarity values. For a higher alignment between the two-dimensional and DRR Image, the current position and/or orientation of the LA virtual camera will be adjusted according to the pixel and roll angle corresponding to the maximum similarity value. In other words, the vertebras in the LA DRR image are adjusted to be similar to the vertebras of the LA two-dimensional image. The AP virtual camera regarding each vertebral bodies of the object  9000  can be adjusted according to LA virtual camera in accordance with corresponding vertebral bodies of the object  9000 . 
     In addition, a few AP DRR images are generated by adjusting the pre-determined position and/or orientation of the AP virtual camera in the coordinate system of the three-dimensional image data set. The pre-determined position and/or orientation of the AP virtual camera can be chosen by the surgeon in accordance with the volume of interest in the three-dimensional data set. 
     The AP DRR images can be generated by taking the pre-determined position and/or orientation of the AP virtual camera as the center and then rotating its azimuth angles in a range from −15 degrees to 15 degrees and/or moving its position in a range from −15 pixels to 15 pixels for DRR generation. Since different AP DRR images have different contents, a plurality of similarity values can be calculated in accordance with the AP DRR images and the pre-determined AP two-dimensional image, which is chosen by the surgeon in accordance with the region of interest corresponding to the volume of interest. Then, the maximum similarity value will be obtained from the plurality of similarity values. For a higher alignment between the two-dimensional and DRR image, the current position and/or orientation of the AP virtual camera will be adjusted according to the pixel and azimuth angle corresponding to the maximum similarity value. In other words, the vertebras in the AP DRR image are adjusted to be similar to the vertebras of the AP 2D image. The LA virtual camera regarding each vertebral bodies of the object  9000  can be adjusted according to AP virtual camera in accordance with corresponding vertebral bodies of the object  9000 . 
     In some embodiments, an adjusted first virtual camera is generated after the rotation of the first virtual camera. The processor  1120  is used to perform a step of rotating the adjusted first virtual camera according to the angle which is corresponding to an adjusted maximum similarity value of the plurality of similarity values calculated in accordance with adjusted reconstructed images which includes one generated by the adjusted first virtual camera and the others generated by other virtual cameras with different angles from the one generated by the adjusted first virtual camera and the two-dimensional image data set. 
     For example, adjusted AP virtual camera or adjusted LA virtual camera are generated after the rotation of the AP virtual camera or the LA virtual camera. The adjusted LA DRR images are generated by the adjusted LA virtual camera with roll angles in a range from −20 degrees to 20 degrees and/or moving its position in a range from −15 pixels to 15 pixels for DRR generation. Since different LA DRR images have different contents, a he plurality of similarity values can be calculated in accordance with the adjusted LA DRR images and the pre-determined LA two-dimensional image, which is chosen by the surgeon in accordance with the region of interest corresponding to the volume of interest. Then, the adjusted maximum similarity value will be obtained from the plurality of similarity values. For a higher alignment between the two-dimensional and DRR image, the current position and/or orientation of the LA virtual camera will be adjusted according to the pixel and roll angle corresponding to the maximum similarity value. In other words, the vertebras in the LA DRR image are adjusted to be similar to the vertebras of the LA two-dimensional image. 
     Besides, the adjusted AP DRR images are generated by the adjusted AP virtual camera with azimuth angles in a range from −15 degrees to 15 degrees and/or moving its position in a range from −15 pixels to 15 pixels for DRR generation. Since different APDRR images have different contents, a he plurality of similarity values can be calculated in accordance with the adjusted AP DRR images and the AP two-dimensional image, which is chosen by the surgeon in accordance with the region of interest corresponding to the volume of interest. Then, the adjusted maximum similarity value will be obtained from the plurality of similarity values. For a higher alignment between the two-dimensional and DRR image, the current position and/or orientation of the AP virtual camera will be adjusted according to the pixel and roll angle corresponding to the maximum similarity value. In other words, the vertebras in the AP DRR image are adjusted to be similar to the vertebras of the AP two-dimensional image. 
     It is noted that, the present disclosure is not limited to the structures and the operations as shown in  FIG.  2    to  FIG.  9   , and it is merely an example for Illustrating one of the implements of the present disclosure. 
     In some embodiments, the processor  1120  is used to perform a step of adjusting the first virtual camera of the plurality of virtual cameras corresponding to the three-dimensional image data set according to a matrix corresponding to the two-dimensional image data set. For example, both of the AP two-dimensional image and the LA two-dimensional image from the imaging device  1300  in  FIG.  1    includes the calibrator  1510 . The processor  1120  may calculate the matrix which functions to transform the coordinate system of the AP two-dimensional image to the coordinate system of the LA two-dimensional image by the given parameter of the calibrator  1510 . Therefore, the matrix corresponding to the relation between the AP two-dimensional image and the LA two-dimensional image is obtained. Subsequently, the processor  1120  may adjust the AP virtual camera or the LA virtual camera according to the matrix, such that the relation between the AP virtual camera and the LA virtual camera is similar to the relation between the AP two-dimensional image and the LA two-dimensional image. 
     2D to 3D Registration 
     Once the initialization alignment as the first stage is completed, the navigation system  1000  proceeds to establish the relation between the three-dimensional image data set stored in the database  1200  and the X-ray two-dimensional images of the two-dimensional image data set shown on the monitor of the imaging device  1300  or stored in the database  1200 , which will be described below. 
       FIG.  10    depicts a flow diagram of a method for registering at least one two-dimensional image of the two-dimensional image data set of a body of interest with a three-dimensional image data set of the same body of interest according to one embodiment of the present disclosure. Reference is now made to both  FIG.  2    and  FIG.  10   . In operation, the step  3100  is performed by the processor  1120  to generate a first reconstructed image from the three-dimensional image data set with a first spatial parameter. 
     For example, the processor  1120  of the calculating device  1100  may access the database  1200  and simulate a virtual camera corresponding to the three-dimensional image data set with the first spatial parameter so as to generate a first DRR image. In the present embodiment, the virtual camera has been aligned in advance (through the initialization alignment and/or other one or more adjustment means of facilitating two-dimensional to three-dimensional registration), but, however, the virtual camera in other embodiment of the present invention hasn&#39;t been adjusted through the initialization alignment and/or other one or more adjustment means. 
     Referring to both  FIG.  2    and  FIG.  10   , in operation, the step  3200  is performed by the processor  1120  to calculate a reference similarity value according to the first reconstructed image and the at least one two-dimensional image data set. For example, the processor  1120  of the calculating device  1100  may calculate the reference similarity value according to the first DRR image and the 2D image data. 
     Reference is now made to both  FIG.  2    and  FIG.  10   . In operation, the step  3300  is performed by the processor  1120  to generate a second reconstructed image from the three-dimensional image data set with a second spatial parameter. For example, the processor  1120  of the calculating device  1100  may access the database  1200  and simulate the virtual camera corresponding to the 3D image data set with the second spatial parameter so as to generate a second DRR image. 
     Referring to both  FIG.  2    and  FIG.  10   , in operation, the step  3400  is performed by the processor  1120  to calculate a comparison similarity value according to the second reconstructed image and the at least one two-dimensional image data set. For example, the processor  1120  of the calculating device  1100  may calculate the comparison similarity value according to the second DRR image and the 2D image data. 
     Reference is now made to both  FIG.  2    and  FIG.  10   . In operation, the step  3500  is performed by the processor  1120  to compare the comparison similarity value with the reference similarity value. For example, the processor  1120  of the calculating device  1100  may compare the comparison similarity value with the reference similarity value. 
     Referring to both  FIG.  2    and  FIG.  10   , in operation, the step  3600  is performed by the processor  1120  to register the at least one the two-dimensional image data set to the three-dimensional image data set if the comparison similarity value is not greater than the reference similarity value for computer-assisted surgical navigation based on the two-dimensional image data set and the three-dimensional image data set after registering. For example, if the comparison similarity value is not greater than the reference similarity value, it means that the second DRR image is aligned with the 2D image data. Therefore, the processor  1120  of the calculating device  1100  may register the 2D image data set from the imaging device  1300  to the 3D image data set stored in the database  1200 . Thereafter, since the 2D image data set from the imaging device  1300  is registered to the 3D image data set stored in the database  1200 , the method  3000  in  FIG.  10    of the present disclosure can be used for computer-assisted surgical navigation based on the two-dimensional image data set and the three-dimensional image data set. 
     It is noted that, the present disclosure is not limited to the operations as shown in  FIG.  10   , and it is merely an example for illustrating one of the implements of the present disclosure. In addition, the method  3000  in  FIG.  10    can be performed by the processor  1120  to register the two-dimensional image data set including an AP two-dimensional image and a LA two-dimensional image to the three-dimensional image data set from which an AP DRR image and a LA DRR image derived. 
     In some embodiments, the steps of generating the first reconstructed image or the second reconstructed image from the three-dimensional image data set with the first reconstructed image or the second reconstructed image which are performed by the processor comprise: positioning a virtual camera corresponding to a three-dimensional subject composed in accordance with the first reconstructed image or the second reconstructed image so as to capture the first reconstructed image or the second reconstructed image of the three-dimensional subject by the virtual camera. 
     For example, the three-dimensional image data set may be a volume of voxels obtained after the CT scanning of the object  9000  including the body of interest. The volume of voxels can be presented in a way of volume rendering and then a three-dimensional subject, also known as a three-dimensional model, of the body of interest can be shown on a display and stored in the database  1200  simultaneously. The processor  1120  may access the database  1200  for the three-dimensional model, and also determining the position and orientation of a virtual camera corresponding to the three-dimensional model with the spatial parameter given to the virtual camera. Once the virtual camera is set, the processor  1100  is able to acquire one or a plurality of two-dimensional images as the first DRR image or the second DRR image by the DRR algorithm in the art. 
     In some embodiments, the virtual camera is defined by a modularized function. The modularized function includes an algorithm and an equation. In some embodiments, the virtual camera is simulated by but not limited to a ray projection volume rendering. 
     In the initialization alignment, the virtual camera will be adjusted to preset an initial spatial parameter including a position and/or an orientation of the virtual camera so as to improve the efficiency and enhance the precision of the navigation system  1000 . However, for medical purpose there are still insufficiency, and therefore, the adjusted virtual camera after performing the initialization alignment should be further refined in the two-dimensional to three-dimensional registration for becoming more accurate. In some embodiments, each of the first spatial parameter and the second spatial parameter is used to define a position and/or an orientation of the adjusted virtual camera corresponding to the three-dimensional subject or the three-dimensional subject corresponding to the adjusted virtual camera. As mentioned above, the adjusted virtual camera should be further refined, and the way to refine the adjusted virtual camera is to adjust spatial parameter including a position and/or an orientation of the adjusted virtual camera. For example, each of the first spatial parameter and the second spatial parameter is used to define a position and/or an orientation of the adjusted virtual camera corresponding to the three-dimensional subject or the three-dimensional subject corresponding to the adjusted virtual camera. 
     In some embodiments, each of the first spatial parameter and the second spatial parameter individually comprises one of a position, an orientation, and a parameter comprising the position and the orientation. For example, the first spatial parameter can be a position, an orientation, or a parameter including the position and the orientation, and the second spatial parameter can be a position, an orientation, and a parameter including the position and the orientation. 
     In some embodiments, each of the comparison similarity value and the reference similarity value is calculated by but not limited to local normalized correlation (LNC), sum of squared differences (SSD), normalized cross-correlation (NCC), or correlation ratio (CR). 
     In some embodiments, the three-dimensional image data set (e.g., the 3D image data set stored in the database  1200  in  FIG.  1   ) is generated by one of a magnetic resonance imaging (MRI) device, an iso-centric imaging fluoroscopic imaging device, an O arm device, a bi-plane fluoroscopy device, a computed tomography (CT) device, a multi-slice computed tomography (MSCT) device, a high frequency ultrasound (HIFU) device, an optical coherence tomography (OCT) device, an intra-vascular ultrasound (IVUS) device, a 3D or 4D ultrasound device, and an intraoperative CT device. 
     In some embodiments, the two-dimensional image data set is generated by one of a C-arm fluoroscopic imaging device, a magnetic resonance imaging (MRI) device, an iso-centric C-arm fluoroscopic imaging device, an O-arm device, a bi-plane fluoroscopy device, a computed tomography (CT) device, a multi-slice computed tomography (MSCT) device, a high frequency ultrasound (HIFU) device, an optical coherence tomography (OCT) device, an intra-vascular ultrasound (IVUS) device, a two-dimensional, three-dimensional or four-dimensional ultrasound device, and an intraoperative CT device. 
     In some embodiments, the first spatial parameter is generated in accordance with a spatial relationship between at least one maker on a two-dimensional image capturing device and the body of interest. As mentioned above, the virtual camera will be adjusted to preset the initial spatial parameter in the initialization alignment so as to improve the efficiency and enhance the precision of the navigation system  1000 , and the adjusted spatial parameter after the initialization alignment is subsequently used as the first spatial parameter in this two-dimensional to three-dimensional registration. For example, the first spatial parameter is generated in accordance with a spatial relationship between the calibrator  1510  on the X-ray receiver  1320  and the object  9000  in  FIG.  1   . 
     In some embodiments, the first spatial parameter is a spatial parameter which has a maximum similarity among a plurality of similarities generated in a previous comparison step. For example, the comparison steps may be performed many times, and each comparison steps will generate a similarity. The first spatial parameter is obtained by finding the parameter that has the maximum similarity among the plurality of similarities. 
     In some embodiments, the adjusted virtual camera in the beginning of the two-dimensional to three-dimensional registration has the first spatial parameter including the first distance and/or the first orientation. When the two-dimensional to three-dimensional registration starts, the adjusted virtual camera will be moved from the first spatial parameter to the second spatial parameter including the second distance and/or the second orientation. Therefore, the second spatial parameter is different from the first spatial parameter aspect of defining a distance and/or an orientation of the corresponding virtual camera corresponding to the three-dimensional image date set (e.g., the three-dimensional image data set stored in the database  1200  in  FIG.  1   ). In more detail, since the adjusted virtual camera described in the present embodiment is a modularized function including an algorithm, equation and one or a plurality of parameters involved therein, the processor  1100  can use the parameters and then stimulate the adjusted virtual cameras at particular locations in the coordinate system of the three-dimensional image data set. 
     In some embodiments, the processor  1120  is further used to perform the following steps: generating a third reconstructed image from the three-dimensional image data set with a third spatial parameter if the comparison similarity value is greater than the reference similarity value; calculating a second comparison similarity value according to the third reconstructed image and the at least one two-dimensional image data set; comparing the second comparison similarity value with the reference similarity value; and registering the at least one the two-dimensional image data set to the three-dimensional image data set if the second comparison similarity value is not greater than the reference similarity value. 
     For example, if the comparison similarity value is greater than the reference similarity in the previous comparison, the processor  1120  of the calculating device  1100  may access the database  1200  and simulate the adjusted virtual camera corresponding to the 3D image data set at a third location so as to generate a third DRR image. 
     Besides, the processor  1120  of the calculating device  1100  may calculate the second comparison similarity value according to the third AP and/or LA DRR images and the corresponding AP and/or LA two-dimensional images of the two-dimensional image data set. 
     In addition, the processor  1120  of the calculating device  1100  may compare the second comparison similarity value with the reference similarity value. 
     Furthermore, if the second comparison similarity value is not greater than the reference similarity value, it means that the third AP and/or LA DRR images are aligned with the corresponding AP and/or LA two-dimensional images of the two-dimensional image data set. Then, the two-dimensional image data set acquired by the imaging device  1300  in real-time operation can be considered being registered to the three-dimensional image data set acquired previously and pre-stored in the database  1200 . 
       FIG.  11    depicts a flow diagram of a method  4000  for registering a two-dimensional image data set of a body of interest with a three-dimensional image data set of the body of interest according to one embodiment of the present disclosure. Reference is now made to both  FIG.  2    and  FIG.  11   . In operation, the step  4100  is performed by the processor  1120  to simulatively move the adjusted virtual camera from an original or a former spatial position of the coordinate system of the three-dimensional image data set to a first spatial position, and the step  4150  is performed by the processor  1120  to generate a first DRR image, also known as a first reconstructed image, corresponding to the first spatial position of the first virtual camera. The step  4200  is then performed by the processor  1120  to calculate a first similarity value according to the first DRR image and a two-dimensional image, which can be AP or LA two-dimensional image, generated from the imaging device  1300 , and step  4250  is performed by the processor  1120  to move the adjusted virtual camera back to the original spatial position. 
     Subsequently, the step  4300  is performed by the processor  1120  to determine whether the adjusted virtual camera is moved from the original spatial position to every spatial position. For example, the adjusted virtual camera can be moved from the original spatial position to a first spatial position (e.g., moved from (0,0) to (1,0) in the Cartesian coordinate system), then moved from the original spatial position to a second spatial position (e.g., moved from (0,0) to (−1,0) in the Cartesian coordinate system), and so on. The movement of the adjusted virtual camera is preset according to actual requirements. If it is determined that the adjusted virtual camera is not moved to every spatial position, the method  4000  is back to the step  4100  so as to move the adjusted virtual camera to another spatial position such as a second spatial position. 
     The steps  4150 ,  4200  are then performed by the processor  1120  to generate another DRR image such as a second DRR image, and calculate another similarity value such as a second similarity value. Thereafter, the step  4250  is performed by the processor  1120  to move the adjusted virtual camera back to the original spatial position. 
     If it is determined that the adjusted virtual camera is moved to every spatial position, the method  4000  proceeds to the step  4350 . The step  4350  is then performed by the processor  1120  to determine whether a similarity value corresponding to the moved virtual camera is greater. If it is determined that similarity value corresponding to the moved virtual camera is greater, it means that the DRR image generated by the adjusted virtual camera at the latter position is more similar to the two-dimensional image than the DRR image generated by the adjusted virtual camera at the original or former spatial position. Therefore, the step  4400  is then performed by the processor  1120  to adjust the adjusted virtual camera from the original or former spatial position to the latter spatial position. The original spatial position described in the present embodiment represents a position at which the adjusted virtual camera is located by the processor  1120  in the very beginning, and additionally the former spatial position represents at which the adjusted virtual camera is relocated after an adjustment which may result from any of or any combination of the abovementioned alignment or registration processes such as the initialization alignment. 
     After the step  4400  is performed, the method  4000  is back to step  4100 . The steps  4100 ,  4150 ,  4200 ,  4250 ,  4300 , and  4350  are then performed by the processor  1120 . Referring to the step  4350 , if it is determined that the similarity value corresponding to the adjusted virtual camera at the latter position is not greater than any one of the former similarity values, the method  4000  proceeds to the step  4450 . 
     After the step  4450  is performed, the step  4500  is performed by the processor  1120  to reduce the adjustment. For example, if the previous adjustment is to move the adjusted virtual camera for 1 mm from the former position In the coordinate system of the three-dimensional subject presented by the three-dimensional image data set, the step  4500  is performed by the processor  1120  to reduce the adjustment to 0.5 mm. Thereafter, the step  4550  is performed by the processor  1120  to determine whether the adjustment is less than a preset spatial value, which is for example 0.75 mm. If it is determined that the adjustment is not less than the preset spatial value, the method  4000  is back to the step  4100 . 
     If it is determined that the adjustment is less than the preset spatial value, it means that the DRR image is adequately aligned with the two-dimensional image. Therefore, it can define that the two-dimensional image data set from the imaging device  1300  has been registered to the three-dimensional image data set pre-stored in the database  1200 . 
     In some embodiments, if a difference between the first spatial parameter and the second spatial parameter is not greater than a preset spatial value, registering the two-dimensional image data set to the three-dimensional image data set. For example, as can be seen in the step  4550  in  FIG.  11   , the difference between the first spatial position and the second spatial position is the adjustment in the step  4550 . If the adjustment between the first spatial position and the second spatial position is not greater than the preset spatial value, it means that the DRR image is aligned with the two-dimensional image data. For example, the present spatial value can be 0.01 mm. If the adjustment is not greater than 0.01 mm, it means that the DRR image is already aligned with the two-dimensional image data. Therefore, the processor  1120  of the calculating device  1100  may register the 2D image data set from the imaging device  1300  to the 3D image data set stored in the database  1200 . 
     It is noted that, the present disclosure is not limited to the operations as shown in  FIG.  11   , and it is merely an example for illustrating one of the implements of the present disclosure. 
       FIG.  12    depicts a flow diagram of a method  5000  for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest according to one embodiment of the present disclosure. Reference is now made to both  FIG.  2    and  FIG.  12   . In operation, the step  5100  is performed by the processor  1120  to execute an Initialization alignment process to the navigation platform  1000  so as to enhance the precision of the navigation platform  1000 . 
     The step  5200  is performed by the processor  1120  to execute a XY location alignment process to preset the XY location of the adjusted virtual camera corresponding to the three-dimensional image data set pre-stored in the database  1200  of the navigation platform  1000 . 
     The step  5300  is performed by the processor  1120  to execute a contracted drawing alignment to the adjusted virtual camera corresponding to the three-dimensional image data set pre-stored in the database  1200  of the navigation platform  1000  preliminarily. 
     The step  5400  is performed by the processor  1120  to execute an original drawing alignment to the adjusted virtual camera corresponding to the three-dimensional image data set pre-stored in the database  1200  of the navigation platform  1000 . 
     It is noted that a flow diagram of the XY coordinate alignment in the step  5200 , the thumbnail alignment in the step  5300 , and the original alignment in the step  5400  is shown in  FIG.  11   . The difference is that the XY coordinate alignment is focused on alignment of the images on the X coordinate and the Y, the thumbnail alignment uses preview or zoom-out images to achieve a quick alignment, and the original alignment is performed to further improve the alignment after the preview alignment. 
     The step  5500  is performed by the processor  1120  to determine whether realignment is required. The realignment process is required if an error or alignment failure determined by the processor  1120  or a judgement from a surgeon. For example, while the difference is always greater than a preset value after several calculation cycles, and the method  5000  proceeds to the step  5600  for realignment. On the contrary, the method  5000  proceeds to the step  5700  if the alignment is adequate and no realignment process is needed. In that situation, the whole alignment process in  FIG.  12    is completed. 
     In some embodiments, the navigation system  1000  uses low-resolution images for preliminary alignment with the two-dimensional images before stimulation adjusted virtual cameras for generating the first and the second reconstructed images. The low-resolution format used herein is to reduce interference or noise signal between two similar images and therefore facilitate the preliminary alignment. As in the step  5300  of the method  5000 , the DRR images used in the thumbnail alignment are low-resolution images. 
     Realignment 
     It is noted that, the present disclosure is not limited to the operations as shown in  FIG.  12   , and it is merely an example for illustrating one of the implements of the present disclosure. 
     The step  5600  for realignment in the method  5000  will be described in the following  FIG.  13   .  FIG.  13    depicts a flow diagram of a method  6000  for realignment according to one embodiment of the present disclosure. In clinical practice, the two-dimensional image to three-dimensional registration procedure fails in the alignment stages from time to time. It may result from neither of AP nor LA two-dimensional images don&#39;t successfully align with the DRR images generated according to the three-dimensional image data set. However, the alignment failure is caused more often by only one of the two-dimensional images fails to align with the corresponding DRR Image. Navigation system in prior art is programmed to stop proceed the registration procedure once any kind of failure abovementioned occurs. The consequence is to technicians or surgeons have to go back to the first step and redo it again. This significantly slows down the whole process of registration. In the present embodiment, the navigation system  1000  can address this issue by performing the realignment stage. 
     Referring to  FIG.  2    and  FIG.  13   , if a LA DRR image, which is also known as LA three-dimensional reconstructed image, doesn&#39;t align with the LA C-arm X-ray image, which is also known as the two-dimensional image, and they need realignment, the processor  1120  may obtain a spatial parameter of a AP virtual camera corresponding to the AP DRR image which is successfully registered with the AP C-arm X-ray image in the previous steps. In view of the above, the AP virtual camera is regard as a registered virtual camera in the following description, and the LA virtual camera is regard as an unregistered virtual camera in the following description. However, the present disclosure is not limited to the above-mentioned embodiments, the AP virtual camera can be the unregistered virtual camera, and the LA virtual camera can be the registered virtual camera depending on actual situations. 
     For facilitating the understanding of the method  6000  in  FIG.  13   , reference is made to  FIG.  14   , which depicts a schematic diagram of a virtual camera VC according to one embodiment of the present disclosure. It is noted that the virtual camera VC in  FIG.  14    is used to illustrate the concept of the present disclosure. The spatial parameter of the virtual camera VC may include kinds of position and/or orientation Information such as but not limited to vectors. Both of the registered virtual camera and the unregistered virtual camera can be illustrated by  FIG.  14   , for example, each of the spatial parameter of the registered virtual camera and the unregistered virtual camera may include a vector of axis Z and an axis Y and also a focal point FP, respectively, defined in the coordination system of the three-dimensional subject generated by the three-dimensional image data set. Alternatively, the focal point FP may be accessed by the processor  1120  from the database  1200  separately instead of included in the spatial parameter. For identification purpose, the registered virtual camera will be labeled as VC 1 , and its axes and focal point will be labeled as Z 1 , Y 1  and FP 1  in the following description. Besides, the unregistered virtual camera will be labeled as VC 2 , and its axes and focal point will be labeled as Z 2 , Y 2  and FP 2  in the following description. 
     Referring to  FIG.  2   ,  FIG.  13   , and  FIG.  14   , in operation, the step  6100  is performed by the processor  1120  to obtain a first vector from a spatial parameter of a registered virtual camera in the coordinate system of the three-dimensional image data set. For example, the processor  1120  may obtain the axis Z 1  from the spatial parameter of the registered virtual camera VC 1  in a coordinate system of the three-dimensional image data set pre-stored in the database  1200 . 
     The step  6200  is performed by the processor  1120  to obtain a first transformed vector from a spatial parameter of an unregistered virtual camera in the coordinate system of the three-dimensional image data set by transforming the first vector of the registered virtual camera through at least one transforming matrix. For example, the processor  1120  may obtain the axis Z 2  from the spatial parameter of the unregistered virtual camera VC 2  in the coordinate system of the three-dimensional image data set by transforming the axis Z 1  of the registered virtual camera VC 1  through a programmed or pre-stored transforming matrix which is established by the processor  1120  according to the spatial relation of the particular components in the navigation system  1000 . 
     The step  6300  is performed by the processor  1120  to obtain a focal point of the unregistered virtual camera at a reference point of the unregistered LA X-ray image, which is the unregistered two-dimensional image of the two-dimensional image data set, in the coordinate system of the three-dimensional image data set. For example, the processor  1120  may obtain a focal point FP 2  of the unregistered virtual camera VC 2  at a central point of calibrators of the two-dimensional image in the coordinate system of the three-dimensional image data set according to the previously performed unsuccessful registration. 
     The step  6400  is performed by the processor  1120  to reposition the unregistered virtual camera according to the first transformed vector and the focal point of the unregistered virtual camera for generating an update reconstructed image based on reposition of the unregistered virtual camera. For example, the unregistered virtual camera VC 2  may be simulatively moved from its original position to the position calculated by the processor  1120  according to the axis Z 2  of the unregistered virtual camera VC 2  and the focal point FP 2  of the unregistered virtual camera VC 2 . 
     In some embodiments, the first vector of the registered virtual camera is from the position of the registered virtual camera to the focal point of the registered virtual camera. For example, as shown In  FIG.  14   , the axis Z 1  of the registered virtual camera VC 1  is from the position of the registered virtual camera VC 1  to the focal point FP 1  of the registered virtual camera VC 1 . 
     In some embodiments, the first vector is defined as the Z axis (e.g., the axis Z 1  in  FIG.  14   ) of the registered virtual camera (e.g., the registered virtual camera VC 1  in  FIG.  14   ) in a coordinate system of the three-dimensional image data set. 
     In some embodiments, the processor  1120  is configured to obtain the plurality of commands from the memory  1110  to perform following steps: obtaining a second vector from a spatial parameter of the registered virtual camera in the coordinate system of the three-dimensional image data set; and obtaining a second transformed vector from a spatial parameter of the unregistered virtual camera in the coordinate system of the three-dimensional image data set according to the second vector of the registered virtual camera. 
     For example, the processor  1120  may obtain the axis Y 1  from the spatial parameter of the registered virtual camera VC 1  in a coordinate system of the three-dimensional image data set. The processor  1120  may obtain the axis Y 2  three-dimensional of the unregistered virtual camera VC 2  in the coordinate system of the three-dimensional image data set according to the axis Y 1  from the spatial parameter of the registered virtual camera VC 1 . 
     In some embodiments, the second vector Is from the central point (e.g., the point FP in  FIG.  14   ) to the top edge (e.g., the top edge in  FIG.  14   ) of a reconstructed image obtained by the registered virtual camera (e.g., the registered virtual camera VC 1  in  FIG.  14   ) parallel to the reconstructed image. 
     In some embodiments, the second vector is defined as the Y axis (e.g., the axis Y 1  in  FIG.  14   ) from the spatial parameter of the registered virtual camera (e.g., the registered virtual camera VC 1  in  FIG.  14   ) in a coordinate system of the three-dimensional image data set. 
     It is noted that, the present disclosure is not limited to the structures and the operations as shown in  FIG.  13    and  FIG.  14   , and it is merely an example for illustrating one of the implements of the present disclosure. 
     In some embodiments, the two-dimensional image data set comprises a first and second two-dimensional images, and the at least one transforming matrix similar or identical to the previously disclosed herein comprises a first matrix which functions to transform the coordinate system of the first two-dimensional image to the coordinate system of the second two-dimensional image. For example, the two-dimensional image data set includes an AP two-dimensional image and a LA two-dimensional image, and the transforming matrix includes a first matrix which functions to transform the coordinate system of the AP two-dimensional image to the coordinate system of the LA two-dimensional image. 
     In some embodiments, the reference point is at the central point of a calibrator module in the two-dimensional image data set in the coordinate system of the three-dimensional image data set. For example, the reference point is at the central point, which is also called the origin, of a calibrator module which is shown on the unregistered AP or LA X-ray two-dimensional image included in the two-dimensional image data set. The reference point is simulatively positioned and orientated in the coordinate system of the three-dimensional image data set for further function by the program of the navigation system  1000 . 
     In some embodiments, the at least one transforming matrix comprises a second matrix and a third matrix, wherein the second matrix which functions to transform the coordinate system of a reference mark to the coordinate system of the three-dimensional image data set and the third matrix which functions to transform the coordinate system of the reference mark to the coordinate system of a tracker module. For example, the at least one transforming matrix includes a second matrix and a third matrix. The second matrix which functions to transform the coordinate system of the calibrators  1510 ,  1530  and the dynamic reference frames  1520 A in  FIG.  1    to the coordinate system of the 3D image data set stored in the database  1200  in  FIG.  1   . The third matrix which functions to transform the coordinate system of the calibrators  1510 ,  1530  and the dynamic reference frames  1520 A in  FIG.  1    to the coordinate system of the tracker  1400  in  FIG.  1   . The transforming matrix and the transformation of coordinate systems are well-known in the state of art. More information can be found in L. Dorst, etc., Geometric Algebra For Computer Science, published by Morgan Kaufmann Publishers and M. N. Oosterom, etc., Navigation of a robot-integrated fluorescence laparoscope in preoperative SPECT/CT and intraoperative freehand SPECT imaging data: A phantom study, August 2016. Journal of Biomedical Optics 21(8):086008, which are incorporated herein by reference. 
     The step  5600  for realignment in the method  5000  in  FIG.  12    will be described in the following  FIG.  15   .  FIG.  15    depicts a flow diagram of a method  7000  for realignment according to one embodiment of the present disclosure. Referring to  FIG.  2    and  FIG.  15   , if an unregistered virtual camera corresponding to the vertebra V 1  as shown in  FIG.  5    or  FIG.  7    needs realignment, the processor  1120  may find a registered virtual camera corresponding to the vertebra V 0  or V 2  as shown in  FIG.  5    or  FIG.  7   . 
     Referring to  FIG.  2    and  FIG.  15   , in operation, the step  7100  is performed by the processor  1120  to obtain a first spatial parameter of a first registered virtual camera, wherein the first registered virtual camera is positioned corresponding to a first two-dimensional image of the two-dimensional image data set. For example, the processor  1120  may obtain the first spatial parameter of the registered virtual camera corresponding to the vertebra V 0  or V 2  as shown in  FIG.  5    or  FIG.  7   . The registered virtual camera is positioned corresponding to the two-dimensional image related to the vertebra V 0  or V 2  as shown in  FIG.  4    or  FIG.  6   . 
     Referring to  FIG.  2    and  FIG.  15   , in operation, the step  7200  is performed by the processor  1120  to adjust a second spatial parameter of the first unregistered virtual camera with the first spatial parameter of the first registered virtual camera for generating an update reconstructed image based on reposition of the first unregistered virtual camera, wherein the first unregistered virtual camera is failed to be positioned corresponding to the first two-dimensional image of the two-dimensional image data set. For example, the processor  1120  may adjust the second spatial parameter of the unregistered virtual camera corresponding to the vertebra V 1  as shown in  FIG.  5    or  FIG.  7    with the first spatial parameter of the registered virtual camera corresponding to the vertebra V 0  or V 2  as shown in  FIG.  5    or  FIG.  7   . The unregistered virtual camera is failed to be positioned corresponding to the two-dimensional image related to the vertebra V 1  as shown in  FIG.  4    or  FIG.  6   . 
     In some embodiments, a first part of the body of interest is included in the first two-dimensional image, a second part of the body of interest is included in the first two-dimensional image, and the first part and the second part of the body of interest are adjacent. For example, the object  9000  is a patient under vertebral disorder which needs an operation for stabilizing three vertebral levels. The three vertebral levels are together considered as the body of interest and shown in  FIG.  4    and  FIG.  6   . According to the success or failure of the alignment with the three-dimensional image data set, the vertebral levels can be categorized into two parts. 
     The first part includes the vertebra V 0  or V 2 , and the second part includes the vertebra V 1 . In more detail, the first part of the body of interest in  FIG.  1    is included in the first two-dimensional images corresponding to the vertebra V 0  or V 2 . The first two-dimensional images are  FIG.  4    as the AP X-ray image and  FIG.  6    as the LA X-ray image. The second part of the body of interest in  FIG.  1    is included in the first two-dimensional images corresponding to the vertebra V 1 . The first two-dimensional images are  FIG.  4    and  FIG.  6   . As can be seen in  FIG.  4    and  FIG.  6   , the vertebra V 0  or V 2  included in the first part of the object  9000  is adjacent to the vertebra V 1  included in the second part of the object  9000  corresponding to the vertebra V 1 . 
     In some embodiments, the first part of the body of interest is defined according to a first marker in the first two-dimensional image of the two-dimensional image data set, and the second part of the body of interest is defined according to a second marker in the first two-dimensional image of the two-dimensional image data set. For example, the first part of the body of interest of the object  9000  in  FIG.  1    is defined by the program of the navigation system  1000  to automatically recognize the image boundary of the vertebra which is mark as V 0  or V 2  on the two-dimensional images in  FIG.  4    and  FIG.  6   . The second part of the body of interest of the object  9000  in  FIG.  1    is defined by the program of the navigation system  1000  to automatically recognize the image boundary of the vertebra which is mark as V 1  on the two-dimensional image in  FIG.  4    and  FIG.  6    by the same measure as the first part. 
     In some embodiments, the first spatial parameter of the first registered virtual camera comprises a position and/or an orientation data which are used to define a position and/or an orientation of the first registered virtual camera corresponding to the three-dimensional subject or the three-dimensional subject corresponding to the first registered virtual camera. For example, the first spatial parameter of the registered virtual camera corresponding to the vertebra V 0  or V 2  as shown in  FIG.  5    or  FIG.  7    includes a position and/or an orientation data which are used to define a position and/or an orientation of the registered virtual camera corresponding to the three-dimensional object generated from the three-dimensional image data set or the three-dimensional object corresponding to the registered virtual camera. 
     In some embodiments, the second spatial parameter of the first unregistered virtual camera comprises a position and/or an orientation data which are used to define a position and/or an orientation of the first unregistered virtual camera corresponding to the three-dimensional subject or the three-dimensional subject corresponding to the first registered virtual camera. For example, the second spatial parameter of the unregistered virtual camera corresponding to the vertebra V 1  as shown in  FIG.  5    or  FIG.  7    includes a position and/or an orientation data which are used to define a position and/or an orientation of the unregistered virtual camera corresponding to the three-dimensional object generated from the three-dimensional image data set or the three-dimensional object corresponding to the registered virtual camera. 
     In some embodiments, the first registered virtual camera is positioned according to comparison of the similarity values calculated according to different reconstructed images obtained from the three-dimensional image data set and the first two-dimensional image of the two-dimensional image data. For example, the registered virtual camera is positioned according to comparison of the similarity values calculated according to different DRR images obtained from the three-dimensional image data set and the two-dimensional image related to the vertebra V 0  or V 2  as shown in  FIG.  4    or  FIG.  6   . 
     In some embodiments, each of the similarity values is calculated by local normalized correlation (LNC), sum of squared differences (SSD), normalized cross-correlation (NCC), or correlation ratio (CR). 
     In some embodiments, the processor  1120  is further used to perform the following steps: defining the second spatial parameter of the first unregistered virtual camera to be a N spatial parameter; determining whether a N-M spatial parameter of the first registered virtual camera is positioned corresponding to the first two-dimensional image of the two-dimensional image data set, wherein N and M are integers, and M is less than N; and if the N-M spatial parameter of the first registered virtual camera is positioned corresponding to the first two-dimensional image of the two-dimensional image data set, defining the N-M spatial parameter to be the first spatial parameter of the first registered virtual camera. 
     For example, the processor  1120  of the calculating device  1100  may define the second spatial parameter of the unregistered virtual camera to be a N spatial parameter. The processor  1120  of the calculating device  1100  may determine whether a N-M spatial parameter of the registered virtual camera is positioned corresponding to the two-dimensional image related to the vertebra V 0  or V 2  as shown in  FIG.  4    or  FIG.  6   , wherein N and M are integers, and M is less than N. The processor  1120  of the calculating device  1100  may define the N-M spatial parameter to be the first spatial parameter of the registered virtual camera if the N-M spatial parameter of the registered virtual camera is positioned corresponding to the two-dimensional image related to the vertebra V 0  or V 2  as shown in  FIG.  4    or  FIG.  6   . Specifically, the N spatial parameter is corresponding to the unregistered virtual camera. The navigation system  1000  may find the N-M spatial parameter which is corresponding to the registered virtual camera, and the N-M spatial parameter will be used in the unregistered virtual camera for facilitating the process. 
     In some embodiments, the processor  1120  is further used to perform the following steps: defining the second spatial parameter of the first unregistered virtual camera to be a N spatial parameter; determining whether a N+M spatial parameter of the first registered virtual camera is positioned corresponding to the first two-dimensional image of the two-dimensional image data set, wherein N and M are integers, and M is less than N; and if the N+M spatial parameter of the first registered virtual camera is positioned corresponding to the first two-dimensional image of the two-dimensional image data set, defining the N+M spatial parameter to be the first spatial parameter of the first registered virtual camera. 
     For example, the processor  1120  of the calculating device  1100  may defining the second spatial parameter of the unregistered virtual camera to be a N spatial parameter. The processor  1120  of the calculating device  1100  may determine whether a N+M spatial parameter of the registered virtual camera is positioned corresponding to the two-dimensional image related to the vertebra V 0  or V 2  as shown in  FIG.  4    or  FIG.  6   , wherein N and M are integers, and M is less than N. The processor  1120  of the calculating device  1100  may define the N+M spatial parameter to be the first spatial parameter of the registered virtual camera if the N+M spatial parameter of the first registered virtual camera is positioned corresponding to the two-dimensional image related to the vertebra V 0  or V 2  as shown in  FIG.  4    or  FIG.  6   . 
     It is noted that, the present disclosure is not limited to the operations as shown in  FIG.  15   , and it is merely an example for illustrating one of the implements of the present disclosure. 
     As discussed above, the step  5600  for realignment in the method  5000  in  FIG.  12    includes but not limited to two realignment processes in  FIG.  13    and  FIG.  15   . For facilitating the understanding regarding the realignment processes in  FIG.  13    and  FIG.  15   , reference is made to  FIG.  16   , which depicts a schematic diagram of a flow diagram of a method  8000  for realignment according to one embodiment of the present disclosure. 
     Reference is now made to both  FIG.  2    and  FIG.  16   . In operation, the step  8200  is performed by the processor  1120  to determine whether one of the AP DRR image acquired by the AP virtual camera and the LA DRR image acquired by the LA virtual camera is not registered. If it is determined that one of the DRRs acquired by the AP virtual camera or the LA virtual camera is not registered, the method  8000  proceeds to step  8300 . Specifically, if the AP virtual camera is not registered, the step  8300  is performed by the processor  1120  to reset the AP virtual camera which is not registered according to the LA virtual camera which is registered. The method  6000  in  FIG.  13    is similar to the step  8300  in method  8000 . When the DRR image acquired by the AP virtual camera or the LA virtual camera is not registered, the method  6000  will find out and use a registered virtual camera to reset the unregistered virtual camera. Subsequently, the step  8700  is performed by the processor  1120  to execute the original drawing alignment by using the reset virtual camera. In addition, the step  8400  is performed by the processor  1120  to adjust the ROI region for avoiding the interference. 
     After the step  8200  is performed, if it is determined that none of the DRR images acquired by the AP virtual camera and the LA virtual camera is registered, the method  8000  proceeds to step  8500 . Specifically, if the AP virtual camera and the LA virtual camera are not registered, it means the AP and LA DRR images corresponding to a first vertebra are all failed to be registered. The step  8500  is performed by the processor  1120  to find out another AP virtual camera and another LA virtual camera corresponding to a second vertebra, wherein the DRRs of the virtual cameras are successfully registered with the three-dimensional image data set. Thereafter, the processor  1120  may reset the unregistered AP virtual camera and the unregistered LA virtual camera corresponding to the first vertebra according to the spatial parameter or data of the registered AP virtual camera and the registered LA virtual camera corresponding to the second vertebra. The method  7000  in  FIG.  15    is similar to the step  8500  in method  8000 . When the DRR images acquired by the AP virtual camera and the LA virtual camera corresponding to the first vertebra are all failed to be registered, the method  7000  will find out and use the spatial parameter or data of the registered AP virtual camera and the registered LA virtual camera corresponding to the second vertebra to reset the unregistered AP virtual camera and the unregistered LA virtual camera corresponding to the first vertebra. Subsequently, the step  8700  is performed by the processor  1120  to execute the original drawing alignment by using the reset virtual camera. In addition, the step  8600  is performed by the processor  1120  to adjust the ROI region for avoiding the interference. 
     It can be understood from the embodiments of the present disclosure that application of the present disclosure has the following advantages. The method and the navigation system for registering a two-dimensional image data set with a three-dimensional image data set of a body of interest of the present disclosure can pre-store three-dimensional image data set of the body of interest in the database, and then take merely two X-ray images (two-dimensional images) of the patient (the body of interest) during the surgery so as to establish the relation between the two-dimensional image data set and the three-dimensional image data set. Thereafter, the method and the navigation system of the present disclosure may provide an accurate navigation during the surgery by using the pre-store three-dimensional image data set. Since the method and the navigation system of the present disclosure merely take two X-ray images (two-dimensional images) of the body of interest, the radiation exposure to the patient (the body of interest) is reduced by over 98%. In view of the above, the present disclosure may provide the method and the navigation system for executing the two-dimensional to three-dimensional registration in a more accurate and efficient way. 
     Although the present invention has been described in considerable detail with reference to certain embodiments thereof, other embodiments are possible. Therefore, the spirit and scope of the appended claims should not be limited to the description of the embodiments contained herein. 
     It will be apparent to those skilled In the art that various modifications and variations can be made to the structure of the present invention without departing from the scope or spirit of the invention. In view of the foregoing, it is intended that the present invention cover modifications and variations of this invention provided they fall within the scope of the following claims and their equivalents.