Frame Coordinate System Research Articles

An Introduction to Isomorphic Mathematical Analysis System

This paper is to build a primitive framework for a new possible extended system of real mathematical analysis - the Isomorphic Mathematical Analysis System (IMAS). It is based on some new concepts: e.g. isomorphic frame, dualvariable-isomorphic function, and isomorphic coordinate system. More concepts are introduced to constitute the whole IMAS framework. This IMAS attempts to provide current MA with new implements, which include isomorphic frame, thereby effectively putting the MA to work as well in some unevenly distributed coordinate spaces, realized by the isomorphic coordinate system. With these implements, many existing MA concepts are extended and incorporated into the new IMAS.

An Acoustic Source Localization Method Using a Drone-Mounted Phased Microphone Array

Currently, the detection of targets using drone-mounted imaging equipment is a very useful technique and is being utilized in many areas. In this study, we focus on acoustic signal detection with a drone detecting targets where sounds occur, unlike image-based detection. We implement a system in which a drone detects acoustic sources above the ground by applying a phase difference microphone array technique. Localization methods of acoustic sources are based on beamforming methods. The background and self-induced noise that is generated when a drone flies reduces the signal-to-noise ratio for detecting acoustic signals of interest, making it difficult to analyze signal characteristics. Furthermore, the strongly correlated noise, generated when a propeller rotates, acts as a factor that degrades the noise source direction of arrival estimation performance of the beamforming method. Spectral reduction methods have been effective in reducing noise by adjusting to specific frequencies in acoustically very harsh situations where drones are always exposed to their own noise. Since the direction of arrival of acoustic sources estimated from the beamforming method is based on the drone’s body frame coordinate system, we implement a method to estimate acoustic sources above the ground by fusing flight information output from the drone’s flight navigation system. The proposed method for estimating acoustic sources above the ground is experimentally validated by a drone equipped with a 32-channel time-synchronized MEMS microphone array. Additionally, the verification of the sound source location detection method was limited to the explosion sound generated from the fireworks. We confirm that the acoustic source location can be detected with an error performance of approximately 10 degrees of azimuth and elevation at the ground distance of about 150 m between the drone and the explosion location.

Two-step calibration method for extrinsic parameters of an airborne camera.

In order to meet the accuracy requirements of target geo-location of a wide-area reconnaissance camera, it is necessary to calibrate the extrinsic parameters of the camera. A novel calibration method is proposed for the orientation relationship between the camera coordinate system (CCS) and the frame coordinate system (FCS). First, the calibration between the roll axis of the FCS and the CCS is carried out based on the method of the extended Kalman filter. Second, the calibration between the pitch axis of the FCS and the CCS is deduced based on the least mean square combined with the particle swarm optimization method. Then, the calibration accuracy of the proposed method is quantitatively analyzed by numerical simulation. Finally, a calibration experiment is conducted on verifying the effectiveness of the method.

User-Friendly InSAR Data Products: Fast and Simple Timeseries Processing

Interferometric synthetic aperture radar (InSAR) methods provide high-resolution maps of surface deformation applicable to many scientific, engineering, and management studies. Despite its utility, the specialized skills and computer resources required for InSAR analysis remain as barriers for truly widespread use of the technique. Reduction of radar scenes to maps of temporal deformation evolution requires not only detailed metadata describing the exact radar and surface acquisition geometries, but also a software package that can combine these for the specific scenes of interest. Furthermore, the range-Doppler reference frame and radar coordinate system itself are confusing, so that many users find it hard to incorporate even useful products in their customary analyses. Finally, the sheer data volume needed for interferogram time series makes InSAR analysis challenging for many analysis systems. We show here that it is possible to deliver radar data products to users that address all of these difficulties, so that the data acquired by large, modern satellite systems are ready to use in more natural coordinates, without requiring further processing, and in as small volume as possible.

CCD Camera Calibration Technology Based on the Translation of Coordinate Measuring Machine

A new CCD camera calibration method based on the translation of Coordinate Measuring Machine (CMM) is proposed. The CMM brings the CCD camera to produce the relative translation with respect to the center of the white ceramic standard sphere along the X, Y, Z axis, and the coordinates of the different positions of the calibration characteristic point in the probe coordinate system can be generated. Meanwhile, the camera captures the image of the white ceramic standard sphere at every position, and the coordinates of the calibration characteristic point in the computer frame coordinate system can be registered. The calibration mathematic model was established, and the calibration steps were given and the calibration system was set up. The comparing calibration result shows that precision of this method is equivalent to that of the special calibration method, and the difference between the calibrating data of these two methods is within ±1μm.

Diagrams for the Leksell Gamma Knife 4C automatic positioning system accessible shot coordinates

We have developed a graphic representation (APS shot-range diagrams) of achievable shot coordinates with the automatic positioning system (APS) for Gamma Knife stereotactic radiosurgery. We formulated a mathematical relationship between the APS coordinate system and the Leksell frame coordinate system (frame-system) by considering the relative translation and rotation. Using the transformation equations, we calculated the Y-Z coordinate domain in the frame-system (domain B), which corresponds to the known coordinate domain achievable in the APS coordinate system (domain A). APS shot-range diagrams were presented by overlaying of domain B over domain A so that one can easily visualize the achievable shot coordinates with APS for various gamma angles. Domains A and B are identical for a 90° gamma angle, but they are different for other gamma angles. Applications of the diagrams to clinical cases, in which Leksell GammaPlan treatment planning software automatically set some of the shots in a treatment plan as trunnion shots because of the APS coordinate limit, enabled us to avoid the trunnion shots, and consequently to achieve much faster treatment delivery. In conclusion, APS shot-range diagrams can be used for achieving more efficient treatment delivery by avoiding unnecessary trunnion shots with a Gamma Knife unit equipped with the APS.

SU‐C‐BRB‐06: High‐Precision Volume‐Staged Treatments with Stereotactic Radiosurgery

Purpose: The purpose of the study was to develop a procedure using selective region mutual information image registration and anatomic landmarks transformation to improve the treatment accuracy of volume‐staged Gamma Knife (GK) radiosurgery for large arteriovenous malformations (AVMs). Methods: The procedure was implemented via Leksell Gamma Plan (LGP version 9.0) and an in‐house point registration program for multiple session staged GK treatments. A requirement of such treatments was to match the partial‐volume dose distribution of a previously delivered treatment with the current treatment. In our procedure, MR images of the current treatment plan were first imported and co‐registered with the initial reference MR studies via selective region mutual information algorithm in LGP. Then the current MR studies were re‐imported and defined for its stereotactic frame. Based on these two MR studies (one registered and one defined), four or more anatomic landmarks surrounding the target region were selected, and then a rigid‐body transformation matrix was calculated from these points to map the original treatment plan onto the current treatment plan for the existing frame coordinate system. We analyzed the accuracy of such procedures performed for a group of 12 patients with 14 staged treatments at our institution since 2007. Results: The average discrepancy in the landmark vector distance between the original treatment plan and the transformed treatment plan was 0.25±0.09 mm. This value was 3–4 times smaller than previously published results. Additional studies on the accuracy of mutual information registration of MR‐MR images of the same objects/patients on our LGP system yielded a mean standard deviation of 0.16±0.07 mm, where the largest deviation was generally observed along the image scanning direction Conclusions: Volume‐staged GK treatments can be delivered to the same level of accuracy as single fraction GK treatments.

Radiosurgery Treatment Planning.

The Gamma Knife (Leksell Gamma Unit; Elekta Radiosurgery, Inc, Atlanta, GA) and specially adapted linear accelerators are the systems most commonly used for intracranial stereotactic external beam irradiation. Both systems deliver collimated radiation to a treatment isocenter and a stereotactic head frame is required to align each target or portion of the target with this isocenter. Image acquisition and treatment planning define how the target is to be treated using one or more treatment positions. Diagnostic images are required to link the target volume with the stereotactic frame coordinate system. The number of diagnostic imaging modalities and the corresponding diagnostic technique(s) selected for optimum target localization are determined by the nature of the target and surrounding structures. The diagnostic modalities presented in this article include magnetic resonance imaging, magnetic resonance angiography, computerized tomography, and x-ray angiography. This review covers the fundamentals of radiosurgical treatment planning using the Gamma Knife as the system of reference.

An algorithm for stereotactic localization by computed tomography ormagnetic resonance imaging

Stereotactic localization of an intracranial lesion by computed tomography ormagnetic resonance imaging requires the use of a head frame that is fixed tothe skull of the patient. To such head frames are attached either N-shaped orV-shaped localization rods. Because of patient positioning, the transverseimaging slices may not be parallel to the frame base; a coordinatetransformation algorithm that takes this possibility into consideration iscrucial. Here we propose such an algorithm for a head frame with V-shapedlocalization rods. Our algorithm determines the transformation matrix betweenthe image coordinate system of a transverse image and the frame coordinatesystem. The determining procedure has three steps: (a) calculation of theoblique angles of a transverse image relative to the head frame andcalculation of the image magnification factor; (b) determination of thecoordinates of four central markers in both coordinate systems; and(c) determination of the 3×3 transformation matrix by using thecoordinates of the four markers. This algorithm is robust in principle and isuseful for improving the accuracy of localization.

Radiosurgery treatment planning

The Gamma Knife (Leksell Gamma Unit; Elekta Radiosurgery, Inc, Atlanta, GA) and specially adapted linear accelerators are the systems most commonly used for intracranialstereotactic external beam irradiation. Both systems deliver collimated radiation to a treatment isocenter and a stereotactic head frame is required to align each target or portion of the target with this isocenter. Image acquisition and treatment planning define how the target is to be treated using one or more treatment positions. Diagnostic images are required to link the target volume with the stereotactic frame coordinate system. The number of diagnostic imaging modalities and the corresponding diagnostic technique(s) selected for optimum target localization are determined by the nature of the target and surrounding structures. The diagnostic modalities presented in this article include magnetic resonance imaging, magnetic resonance angiography, computerized tomography, and x-ray angiography. This review covers the fundamentals of radiosurgical treatment planning using the Gamma Knife as the system of reference.

Target point calculation in the computerized tomography. Comparison of different stereotactic methods

The adaptation of computerized tomography for stereotactic operations requires the transformation of the coordinates of the target point from the CT image space into the stereotactic frame space. Two basic solutions for this transformation are realized in the most of the contemporary stereotactical systems. The indirect geometric method adjusts the frame coordinate system mechanically and identifies its origin in the CT image. There are 6 degrees of freedom: 3 of rotation and 3 of translation which have to be taken into consideration. The second method is a based on direct algebraic coordinate transformation and is independent of the explicite knowledge of the relationship between the image and the frame space. A localization frame serves to determine a transformation matrix which, applied to any point in the image, transforms the coordinates directly into the frame coordinate system. Only the algebraic method is independent of the position of the patient in the gantry. All other methods require high mechanical precision of the alignment and stability for the CT table.

Stereotactic γ-Thalamotomy with a Computerized Brain Atlas

Radiosurgical stereotactic thalamotomy was performed in a patient with parkinsonian tremor with a computerized stereotactic brain atlas, which was transformed to fit the patient's thin-sliced magnetic resonance image to select an optimal target in the nucleus ventralis intermedius of the thalamus. The patient's tremor and rigidity disappeared and have not appeared again for more than 1 year since the eighth postoperative month. A method for converting the presurgically planned stereotactic coordinates in the atlas coordinate system to the coordinates in the frame coordinate system is described.

A CT-based computerized treatment planning system for I-125 stereotactic brain implants

A computer program has been developed at the University of California, San Francisco, as an aid in planning and evaluating stereotactic brain implants made with 125I seeds. The program allows images of seeds and catheters to be positioned in the target volume revealed by CT. It then generates and displays the resulting isodose distributions. Catheters may be changed interactively until an optimum implant is achieved. From the geometry of a stereotactic implant frame as measured by CT, the program calculates the approach angles of the catheters in the frame coordinate system. After the seeds are implanted, films made with a fiducial marker box can be used to generate true seed positions and hence true isodoses. This paper describe's mathematically the geometrical transformations used by the program, and also outlines its many features and options. In its first 2 years of use the program has proved to be a valuable contributor to improved patient care.

The role of computed tomographic and digital radiographic techniques in stereotactic procedures for electrode implantation and mapping, and lesion localization.

This paper describes a computer-based system for analyzing stereotactic CT scans and angiograms. Simple Plexiglas frames containing metallic marker pellets and rods are affixed to the sides of the frame during CT scanning and angiography. The images of these markers are recognized by the computer program and used to compute the frame coordinate system. Coordinates of a lesion on CT and angiogram images may be readily computed and coordinate sets specified by the operator may be displayed on the imager, along with positions of implanted electrodes and a numerical indication of recorded activity for each site.