The autocollimator is an important device for achieving precise, small-angle, non-contact measurements. It primarily obtains angular parameters of a plane target mirror indirectly by detecting the position of the imaging spot. There is limited report on the core algorithmic techniques in current commercial products and recent scientific research. This paper addresses the performance requirements of coordinate reading accuracy and operational speed in autocollimator image positioning. It proposes a cross-image center recognition scheme based on the Hough transform and another based on Zernike moments and the least squares method. Through experimental evaluation of the accuracy and speed of both schemes, the optimal image recognition scheme balancing measurement accuracy and speed for the autocollimator is determined. Among these, the center recognition method based on Zernike moments and the least squares method offers higher measurement accuracy and stability, while the Hough transform-based method provides faster measurement speed.