To the Graduate Council: I am submitting herewith a thesis written by ...

Chapter 3: Data Collection and Modeling 30αCameraRangeExtractionProfileAccumulationFigure 3.2: Triangulation and range image acquisition.The differential of the range equation in Equation 3.2 is the resolution of the sensor asshown in Equation 3.3− Bb0∆ r = ∆s2( b cosα + s sinα)0(3.3)The maximum range that a particular sensor arrangement with a baseline B and angleα (Equation 3.4) can measure is obtained by maximizing the function for range(Equation 3.2) in terms of the sensor size N and resolving capability ∆x.RT4BbN∆x(1+tanα)20=224bo−(N∆xtanα)24BfN∆x(1+tanα)=4 f −(N∆xtanα)(3.4)These equations are important when the decision between field of view and resolutionhas to be made. We make use of these equations for the design of our scanningmechanism but not for range measurements. We follow a much more robustcalibration procedure that models the world to sensor coordinate transformation as acombination of translation (of the world coordinate system to the optical coordinatesystem), a rotation (to align optical axis with real world axis) and a projection fromworld to sensor coordinate system. Equation 3.5 is the transformation from the worldto the sensor coordinate system where w p is the sensor coordinate system scale factorproportional to the baseline distance B, (u, v) refers to the position in the sensorcoordinates; (X, Y, Z) are the real world position coordinates, f is the focal length ofthe optics. (u 0 , v o ) is the position where the optical axis meets the sensor, and k v , k u