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Panorama
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Ariel "Panorama" Panning Head OperationINTRODUCTION The Direct Linear Transformation (DLT) is a technique commonly used to locate spatial points filmed with two or more stationary cameras. The DLT does not necessarily yield coefficients which correspond to an orthogonal orientation matrix of the image to object coordinate system. It has been demonstrated that increase accuracy for the reconstruction of points is achieved by imposing an orthogonality constraint upon the optimization procedure used to obtain the DLT coefficients. This DLT with orthogonality constraint is called the modified DLT (MDLT). Ariel Dynamics, Inc. has developed a technique called physical parameter transformation (PPT) which allows the use of panning cameras. The PPT is built upon the colinearity photogrammetric relations from which the DLT is derived. Like the MDLT, PPT is implemented such that orthogonality of the orientation matrix of the image to object coordinate system is guaranteed. PPT with panning will be demonstrated to have greater accuracy than the DLT. PANORAMA is an option of the Ariel Performance Analysis System that allows spatial coordinate reconstruction from panoramic or still camera views in any combination. PANORAMA consists of the panning angle measurement hardware and sophisticated software for data transformation after the digitizing process in the APAS. EQUIPMENT SET-UP
DATA COLLECTION FILMING AN ACTIVITY These rules must be followed to ensure that subsequent analysis will be correct and accurate:
Bar position in the image and bar width should be selected by selecting the Bar Width switches (3 & 4) and the Bar Position Switches (5 & 6) located on the rear panel of the Ariel Panning Head. CALIBRATION OF THE PANNING CAMERA For the panning views, it is recommended to position Two Calibration Objects; one at the left side of the panning range, the other at the right side of the panning range. There should be a minimum of 6 control points on each calibration object with known X, Y, and Z coordinates from a single reference point. In order to have the calibration objects proportional to the bar scale, the camera should be directed to the center of the panning angle and then push the Reset Button on the panning head. Then film the left and right calibration objects. It is recommended that the control points be filmed before and after the activity is recorded. However, one frame for calibration is often enough if the user is certain about the control points in the procedure.
DIGITIZING A PANNING VIEW As with normal Ariel Performance Analysis System (APAS) sequences, data collection begins with the videotaping process. Most sequences can be recorded in their entirety with one side panning camera and one front/back stationary camera. The panning angle is provided by an optical encoder yielding 10 minutes of resolution. Panning axis location and direction were determined by performing 2 normal PPT calibrations corresponding to different panning angles. The two calibrations yield positions of the camera which only differ by a rotational displacement about the panning axis; thus, the calibrations provide enough information to determine panning axis location and direction. Since the displacement may be expressed as a function of panning angle, axis direction, and axis location, the PPT coefficients corresponding to any panning angle about a single axis is determinable. DIGITIZING Digitizing is the process of converting film or video image sequences to computer image sequences (stick figures). To produce computer images from film or video images one must convert the recorded patterns to numbers or digits, hence the term digitizing. Each frame of film or video is a picture and contains a great deal of information. Usually the information is far more than is needed to analyze the motion of the subject. Therefore, the digitizing process becomes one of digitizing the subject rather than the entire frame. Human subjects consist of various body segment (limbs) connected at body joints. If the location and identity of each of the body joints are known then the location and orientation of each of the body segments (therefore the complete subject) can be easily determined. The APAS takes this approach to the digitizing and saving of images of subject motion; namely the determination of joint location for each body joint in each frame of the film or video recording. Digitizing a panning view is exactly the same as with stationary cameras up to the point of entering the View Information. The Ariel Digitizing module has been enhanced to allow for use of the panning camera using the custom panning head. The PAN option should be toggled to YES to indicate a panning camera. When the PAN option is turned on (YES) and F10 is pressed to proceed, you will then be required to enter the Panning Options.
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 | "PanRange" is used to set the panning camera range. This is determined by the DIP switches #5 and #6 on the panning head hardware. Select the appropriate range using the up/down arrow keys.
| "#Points[Right & Left]" is used to specify the number of control points in the left and right control fixtures for the panning camera.
| "ID[Right & Left]" is used to specify an identification label with the corresponding control points.
| "F10-Done" is selected to proceed with the digitizing process.
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When "Consistency Tests" is selected, a different report is generated depending on whether view is DLT, PPT or PAN. "Residuals" are always reported in digitizer units with a range 0->9000 full range. Since the screen is of resolution 640x480 one converts to pixels as follows:
1 "x" pixel = 9000/640= 14 digitizer units 1 "y" pixel = 9000/480= 19 digitizer units
ChiSq= SUM[(u-u0)**2 +(v-v0)**2) Residual=Sqrt(ChiSq) ChiSq/DOF=ChiSq/(2*#CTLPTS-11) Residual/DOF=Sqrt(ChiSq/DOF) where [u,v] is observed image location [0->9000 range] & [u0,v0] is the expected image locationThe #degrees of freedom [DOF] when fitting parameters to data is the # of measurements [2*#CTLPTS] minus the # parameters in the fit [11].
A1/A2/A3- Successive rotations about z/x/y needed to specify camera orientation in lab frame R1/R2/R3- [x,y,z] Location of camera projection point in the lab frame. g1/g2- Projection plane origin in digitizer units h1/h2- distance from projection point to projection plane in digitizer units [u/v separately].
A1/A2/A3- Successive rotations, A1/A2 about y/z to locate panning axis, then A3 about Y [pan angle]. R1/R2/R3- Pan Axis location in lab.Residual is reported for pan left calculated directly from pan left calibration data and transformation using right pan calibration transformed according to "pan" solution. "Direct" will always be smaller [better]. The closeness of the two measurements indicates the "goodness" of the panning solution.
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