For the registration task of infrared and visible binocular cameras with fixed relative positions, existing algorithms do not consider the prior fixed relative positions of the two cameras, resulting in problems, such as low registration accuracy, large differences in geometric positioning, and poor applicability. An infrared and visible binocular image registration method based on region search under geometric constraints. First, stereo correction was performed on the infrared and visible images using the calibration information of the infrared and visible binocular cameras, such that they were at the same height. Second, infrared and visible edge maps were obtained using phase congruency and feature points were extracted from the infrared edge map. Finally, a two-stage feature point search method is proposed to search for feature points with the same name in the local area of the visible edge map based on the infrared feature points. In the first stage, normalized cross-correlation (NCC) was used as a similarity metric to calculate the overall horizontal offset of the two edge maps, and the initial positions of feature points with the same name were predicted. In the second stage, a multiscale-weighted NCC was proposed as a similarity metric to accurately search for feature points with the same name around the initial location of feature points of the same name. Then, experiments were performed on the constructed real-environment dataset. The experimental results show that compared with other comparison methods, the number and accuracy of matching points and registration results in subjective vision are better.