Confident adaptive algorithms are described, evaluated, and compared with other algorithms that implement the estimation of motion. A Galerkin finite element adaptive approach is described for computing optical flow, which uses an adaptive triangular mesh in which the resolution increases where motion is found to occur. The mesh facilitates a reduction in computational effort by enabling processing to focus on particular objects of interest in a scene. Compared with other state-of-the-art methods in the literature our adaptive methods show only motion where main movement is known to occur, indicating a methodological improvement. The mesh refinement, based on detected motion, gives an alternative to methods reported in the literature, where the adaptation is usually based on a gradient intensity measure. A confidence is calculated for the detected motion and if this measure passes the threshold then the motion is used in the adaptive mesh refinement process. The idea of using the reliability hypothesis test is straightforward. The incorporation of the confidence serves the purpose of increasing the optical flow determination reliability. Generally, the confident flow seems most consistent, accurate and efficient, and focuses on the main moving objects within the image. V