On the accuracy of videometry

For accurate computer vision based on standard video signals, the term Videometry is introduced (PLATZER 87). Some geometrical, optical and electrical properties of CCD-cameras in conjunction with analog/digital-converters and frame buffers are investigated: Lens distortion, sensor distortion, anisotropic modulation transfer function, space variant impulse response due to discrete sensor elements and insufficient optical low-pass filtering, horizontal line jitter and scaling factor due to mismatch of sensor-shiftand A/Dconversion-clock, noise etc .. Based on these results, a very simple camera model with a special radial lens distortion equation is proposed. This allows for a fast, fully linear calibration algorithm (15msec calibration time for 36 coplanar calibration points) with good accuracy (1130 of a frame buffer pixel residual error). It requires independent pre-calibration of the principal point and the horizontal scale factor. The latter is performed by Fourier analysis of the aliasing patterns produced by interference of cameraand ND-converter clock. Only small improvements (3% average error, 30% maximum error) were obtained by subsequent non-linear optimization (self-calibration with bundle adjustment) using the results from the linear approach as initial guess. In order to obtain a feature localization error well below sensor element resolution, rather large calibration points for boundary averaging and a special chain code operating in greyvalue images are used (LENZ 87a). Introduction; This paper is concerned with the accuracy of imaging with solid-state, discrete-array sensors (short: CCD-sensors). The interface between camera and digitizer/computer is assumed to be the standard, B/W video signal (RS170 or CCIR). Theoretical predictions are compared with actual measurements on a modem, well designed camera (Panasonic WV -CD50) with a Sony interline transfer 2/3" CCD-Sensor (500 Sensor Elements (Sels) horizontally, pitch 17J.lm and 582Sels vertically, spaced at 11Ilm), digitized with several frame grabbers (Imaging Technologies AP512, Kontron IBAS II and Matrox PIP-l024A, all with 512x512 Picture Elements (Pels». In detail, the following was investigated: Geometrical Camera Model Exterior Parameters: Rotation, Translation Inner Parameters: Principal Distance, Lens Distortion, Principal Point, Scaling Factors Analyzed Model Errors: Line Jitter, Spatial Quantization, Center Offset caused by Perspective Imaging & Lens Distortion, Sensor distortion Neglected Model Errors: 5th Order Radial Lens Distortion, Tangential Lens Distortion, Thermic Camera Instability Signal Transfer Model Optical Transfer Function: Diffraction, Defocussing, Phase Errors of Lens Surface Sensor Transfer Function: Local Integration, Sampling, Linearity Electrical Transfer Function (x-direction only): Sample & Hold, Lowpass-Filtering, Sampling Random Noise: Photon Noise, Amplifier Noise, Quantization Noise Fixed Noise: Sensor Noise, AID-Converter Noise, Computer Noise Analyzed Errors: Periodically Space-Variant & Asymmetrical Impulse Response The Geometrical Camera Model Calibration of the geometrical camera model: First, the model in Fig. 1 will be briefly described. It originates in work from TSAI 85 and was modified by LENZ 87b to allow for a fully linear calibration algorithm capable of real-time perlormance. The geometrical imaging process may be subdivided into four steps (here, parameters are printed bold): 1.) Rigid body transformation (object coordinate system (CS) to camera-CS): ( ;~J ::::: (~;~ ~;~ ~;~J (;:J + (~J (1) Zc rzx rzy rzz Zw tz 2.) Perspective transformation with principal distance b (camera-CS to undistorted sensor-CS):