This thesis is concerned with the motion vector estimation and motion bound dairy detection using spatial and temporal gradient. There are two main causes to make the estimation inaccurate. The one is the erroneous measurements of spatial and temporal gradient of brightness values and the other is the blurring of motion boundaries which is caused by the smoothness constraint. In this thesis, the measurement error of spatial gradients is analyzed and it is shown that the best technique is to take the motion compensated interframe average (MCIA). The measurement error of temporal gradient is also analyzed and a new measurement technique is proposed. It is shown that this temporal gradient, called extrapolated frame difference (EFD), makes less error than the conventional technique-the frame difference (FD) in Horn & Schunck. When EFD is applied to the motion vector estimation based on the global optimization method, EFD is shown to have almost the same performance as the displaced frame difference (DFD) in Nagel & Enkelman [16] and much better performance than FD. As DFD is not a temporal gradient measure, it can not be applied to the motion boundary detection using the spatial and temporal gradient. But, in this case, EFD shows better performance than FD in some artificial and real image sequences.