Figure 6. Parameter Calculation. Parameters R, T, f, and c are found from m ij. Patient f : camera focal vector along optical axis c : camera center offset Calculate Parameters Trucco & Verri, “Intro Techniques for 3-D Comp Vision”, PROJ_MAT_CALIB Write world  image transformation equations 2 equations in 12 unknowns/point pair Use enough point pairs to determine Solve system of equations using SVD Extract parameters from SVD solution Coordinate systems Gamma camera / World coordinates x w Optical camera coordinates x c is rotation & translation from world x w Image coordinates x i is projection from camera x c Equations World point x w =(x w,y w,z w ) projects to x i =(x i,y i ) where Rewrite to be linear in m ij as Each world / image point pair gives N point pairs yield 2 N equations, so need  6 point pairs to compute m ij Solve Am=0 where Find m in A’ s nullspace using Singular Value Decomposition 2. Procedure We designed a calibration phantom, comprising a set of Lucite disks, that can be imaged by an optical camera and a gamma camera. The disk arrangement is non-coplanar and asymmetric, guaranteeing a unique solution for the calibration parameter equations. Abstract Objectives: One approach to motion detection in SPECT is to observe the patient using optical cameras. Patient motion is estimated from changes in the images and is used to modify the reconstruction algorithm. An important subproblem is calibrating the optical cameras and the gamma camera. That is, it is necessary to determine the transformation from the gamma camera coordinate system to the optical camera coordinate system such that given a gamma camera point, one may compute the corresponding optical camera point. Conversely, given an optical camera point, one may compute the corresponding patient ray. Methods: We have devised a calibration phantom that can be imaged using both optical and gamma cameras. The phantom comprises a set of Lucite disks; each disk supports 2 low-intensity light bulbs and a 0.8mm diameter hole centered between the bulbs to hold a 99m Tc point source. The radioactive source location for each disk in image coordinates is taken to be the midpoint of the bulbs. The radioactive source location in gamma camera coordinates is found by segmenting the reconstructed source distribution and computing the centroid of the activity of each source. At least 6 such point pairs are needed, although 7 are used in practice to provide increased accuracy. Using procedure PROJ_MAT_CALIB of Trucco & Verri Introductory Techniques for Computer Vision, we compute the 11 parameters of the coordinate transformation and the residual error. Because we do not know in advance which optical camera points match which gamma camera points, an exhaustive search is used to find lowest-error matches. Results: We have been able to match optical and gamma camera points and determine the transformation. Tomographic reconstruction and segmentation take up most of the processing time; point matching and parameter calculation take less than 14 seconds of processor time on a Digital Alpha 433au workstation. Conclusions: A calibration phantom can be imaged simultaneously to calibrate optical and gamma cameras and the transformation computed with no other input required. 1. Introduction One approach to motion detection in SPECT is to observe the patient using optical cameras. Patient motion is estimated from changes in the images and is used to modify the reconstruction algorithm. In order to relate changes in patient position as observed by the optical cameras, to SPECT data as observed by the gamma camera, it is necessary to determine the camera parameters. This is the calibration problem— determining the transformation from the gamma camera coordinate system to an optical camera coordinate system and vice versa. 99m Tc well (approx 0.1 mCi) Light bulbs Figure 2. Calibration Phantom comprising 7 Lucite disks (left), each holding 2 light bulbs and a 99m Tc source. Complete phantom is shown at right. Figure 3. Optical (left) and gamma (right) images of the phantom. The 7 pairs of light bulbs are clearly visible in the optical image. The reconstructed gamma image shows 64 out of 128 slices, with 5 out of 7 gamma source blobs. Optical Blobs X Centroid Y Centroid Gamma Blobs X Centroid Y Centroid Z Centroid Figure 4. Blob Detection. Processing is similar for optical and gamma blob detection. For optical blobs, final centroids are computed by taking midpoints of pairs of closest blobs. Algorithm Read image Threshold Segment Select regions Optical: manually Gamma: largest regions Compute centroids Match Generation Generate all possible image  world point matches If N points, generate N! permutations Compute camera parameters for each possible match For each parameter set, calculate residual error defined as Select parameter set with lowest residual error Figure 5. Match Generation. Best match is found by exhaustive search. Image camera parameters Calculate Parameters Acquire Optical Image Detect Blobs Generate Matches possible matches Select Best image point list Acquire Gamma Image Detect Blobs Image world point list Figure 1. Calibration Processing Flow. Figures 2–7 show module details. Calibration Phantom 3. Conclusions We have successfully calibrated optical and gamma cameras. The best match residual error is 1000 pixel 2, giving confidence that the best match of optical and gamma points has been found. Figure 7. Sample Output showing image points and world points in correct correspondence, with residual error=9.05. Camera parameters are computed from matrix entries m ij. For a 640x480 image the expected camera center offset is [319.5,239.5]. Note the close agreement with image center IC=[317.2,238.6]. Sample Output IPL = ImagePointList[ ImagePoint(177.5, 82.0), ImagePoint(222.5, 211.0), ImagePoint(193.5, 349.0), ImagePoint(293.5, 289.5), ImagePoint(359.0, 83.5), ImagePoint(312.0, 347.0), ImagePoint(269.5, 437.0)] WPL = WorldPointList[ WorldPoint[88.3, 39.7, 62.2], WorldPoint[66.9, 87.3, 79.6], WorldPoint[82.4, 87.1, 31.0], WorldPoint[53.8, 87.5, 48.3], WorldPoint[42.0, 40.2, 71.6], WorldPoint[53.7, 86.8, 29.7], WorldPoint[70.5, 86.4, 6.8]] Res = 9.05 CPs = Camera Parameters[ T:[79.8, -19.6, 104.2], R:[[-0.923, , ], [-0.010, 0.747, ], [-0.383, 0.610, 0.692]], IC:[[317.2], [238.6]], fx:650.7, fy:672.4] Calibrating Optical Images and Gamma Camera Images for Motion Detection Michael A. Gennert 1,2, Philippe P. Bruyant 1, Manoj V. Narayanan 1, Michael A. King 1 1 University of Massachusetts Medical School, Worcester, MA 2 Worcester Polytechnic Institute, Worcester, MA