Many different approaches to the geometric and statistical analysis of document layouts have been proposed in the literature. The development of practical branchand- bound algorithms for solving geometric matching problems under noise and uncertainty has enabled the formulation of new classes of geometric layout analysis methods based on globally optimal maximum likelihood interpretations for well-defined models of the spatial statistics of document images. I review this approach to geometric layout analysis using text line finding and column finding in the presence of noise and uncertainty as examples and compare the approach with selected other statistical and geometric layout analysis methods.