We propose a novel framework to simultaneously and accurately measure the three-dimensional (3-D) shape and 3-D motion of a dynamic deformable surface from a calibrated stereo image sequence. The framework mainly aims at the problems of error accumulation and local illumination change. It performs the measurement with a random gray triangle pattern marked on the object surface via the following steps: first, the triangles in all images are detected using a method we proposed; second, the matching triangles between the first, left, and right frame in the stereo image sequence are located by the proposed local triangle descriptor and an extension of the epipolar constraint to triangles; third, the spatiotemporal triangle correspondences in the subsequent frames are obtained by triangle tracking, and the tracking errors are detected and recovered by the local 3-D topology. The performance is evaluated in challenging simulated experiments, and the effectiveness is demonstrated by real surfaces. The experimental results show that the proposed framework is effective and robust to cope with error accumulation and the influence of local illumination change.