In order to estimate the global motion of an object, the visual system needs to segment and group local motion signals. However, it is unknown whether Gestalt grouping rules between line segments that occur in static images also operate in motion grouping. Using a computer-animated display consisting of a dynamically varying 10×10 grid of randomly oriented line segments, we investigated how well observers could detect the left or right motion of a signal column in the grid as a function of the frame rate of the animation. The signal consisted of a column of fixed line segments whose degree of co-linearity was varied by either rotating (smooth curve conditions) or displacing (offset conditions) segments in alternate rows in opposite directions by a fixed amount. In both cases the line segments in the signal could be grouped by interpolating a smooth curve between them. The goal of this study was to investigate whether the co-linearity of parallel line segments, the angle between line segments, or the distance between the ends of the segments influenced the perception of global signal motion. This global translation motion is in competition with a short-range rotation of each of the small line segments. Signal velocity (frame rate) thresholds for discriminating leftward vs. rightward signal motion were estimated using the Quest procedure to track 60,75, &90% correct. The results show that small deviations from co-linearity in both orientation and offset caused the thresholds to drop rapidly from 30 fps to 5 fps. In addition, when the distance between the ends of the signal line segments was held constant, the smooth curve condition produced poorer detection of direction than the equivalent offset condition. The results provide strong evidence for the use of co-linearity and parallelism in motion grouping. In conclusion, we have shown that mechanisms underlying grouping can be objectively investigated using the direction of apparent motion.