Geometric, Kinematic and Radiometric Aspects of Image-Based Measurements

This paper discusses theoretical foundations of quantitative image-based measurements for extracting and reconstructing geometric, kinematic and dynamic properties of observed objects. New results are obtained by using a combination of methods in perspective geometry, differential geometry, radiometry, kinematics and dynamics. Specific topics include perspective projection transformation, perspective developable conical surface, perspective projection under surface constraint, perspective invariants, the point correspondence problem, motion fields of curves and surfaces, and motion equations of image intensity. The methods given in this paper are useful for determining morphology and motion fields of deformable bodies such as elastic bodies, viscoelastic mediums and fluids.