The typical local stereo matching for disparity estimation can deliver accurate disparity maps by a well-designed cost aggregation method, but usually suffers from natively high computational complexity due to its dense processing. To address it, we propose a fast algorithm with search point reduction on spatial and disparity domains to generate a sparse search map. The sparse search map guides the local stereo matching to produce a sparse disparity map, and then it is recovered to a dense disparity map. The experimental results show the proposed fast algorithm could reduce the computation time to 8.8% of original algorithm for 2-megapixel images, and only has slightly quality degradation by 0.92dB in final view synthesis images.