We explore the principles of quaternion wavelet construction for achieving multiscale analysis of geometric image features. Then the quaternion wavelets are applied to propose a cooperative stereo matching algorithm using top-down segmentation-based disparity propagation. Without bidirectional matching to remove ambiguous outliers, uniqueness constraint is enforced on cost function by inhibiting the matches along similar sightlines. To produce smooth disparity maps with the discontinuities well-preserved, cost aggregation is performed in segmentation-based local support and high confidence matches serve as heavyweight seeds for disparity propagation in the supports. Compared with the current matching methods based on quaternion wavelets, the main merit of the proposed algorithm is that the matching results are encouraging in extensive comparison data, ranging from calibrated images to uncalibrated images, indoor images to aerial images.