Two new methods for coding image sequences in video conferencing systems are developed in this dissertation. A simple 3-D gradient operator is developed to estimate motion in an image sequence on a pixel-by-pixel basis. A stochastic 3-D gradient operator is also developed for a gradient calculation which is more robust to the noise effects of the image sequence. These gradient operators are used to estimate motion in the next frame using information from three previous frames. The concept of tangent plane, which is perpendicular to the gradient vector, is introduced to guide searching for the motion vector. The simplified 3-d gradient motion estimation (GME) technique is compared to Netravali's pixel-recursive method with scalar quantization. It was found that performance of the GME technique is very close to that of Netravali' s technique with less computational complexity. To adapt the motion estimation techniques to vector quantization, two new supplementary methods of motion estimation using the pixel motion vectors from the motion estimator were studied. The methods use either the pixel motion vectors directly on the moving block (pixel motion estimation) or calculate the block motion vector from the pixel motion vectors (block motion estimation). For both methods, the differences between the prediction block and the moving block are vector quantized. / Ph. D.