We propose an on-line handwriting recognition approach that integrates local bottom-up constructs with a global top-down measure into a modular recognition engine. The bottom-up process uses local point features for hypothesizing character segmentations and the top-down part performs shape matching for evaluating the segmentations. The shape comparison, called Fisher segmental matching, is based on Fisher's linear discriminant analysis. Along with an efficient ligature modeling, the segmentations and their matching scores are integrated into a recognition engine termed Hypotheses Propagation Network, which runs a variant of topological sort algorithm of graph search. The result is a system that is more shape-oriented, less dependent on local and temporal features, modular in construction and has a rich range of opportunities for further extensions. Our system currently performs at 95% of recognition rate on cursive scripts with a 460-words dictionary.