This thesis deals with topics central to metric vision, i.e. the use of digital image processing techniques to gain quantitative information about position, orientation, dimensions and shape of objects. Measurements are based on extraction of points from images and fitting of geometric models to these noisy data points. An analytic and a stochastic approach to estimate the uncertainty of measurement results are presented. The error propagation in line and circle fitting algorithms and in the derivation of results from the fitted parameters is quantified. All investigations consider the correlations between fitting parameters. A special issue of research is the reconstruction of convex Jordan curves from curvature data. Two algorithms based on differential geometry are designed and tested for specific parameterizations of the curvatures. Based on this reconstruction, a profile measurement system for rotating objects is implemented as a quality control system for seamless pipes. The eccentricity of a rotating pipe is used as a measure of its straightness. The circularity of the pipe is determined by reconstructing its cross sectional profile. A video extensometer developed for strain measurement of hot glowing material enables the determination of properties of refractory material at temperatures up to 1400°C. Specific influence factors on the measurement uncertainty are identified.