This paper presents a class of nonlinear hierarchical algorithms for the fusion of multiresolution image data in low-level vision. The approach combines nonlinear causal Markov models defined on hierarchical graph structures, with standard bayesian estimation theory. Two random processes defined on simple hierarchical graphs (quadtrees or "ternary graphs") are introduced to represent the multiresolution observations at hand and the hidden labels to be estimated. An optimal algorithm (inspired from the Viterbi algorithm) is developed to compute the bayesian estimates on the hierarchical graph structures. Estimates are obtained within two passes on the graph structure. This algorithm is non-iterative and yields a per pixel computational complexity which is independent of image size. This approach is compared to the multiscale algorithm proposed by (Bouman et al., 1994) for single-resolution image segmentation (that we have extended for multiresolution data fusion).