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We present and investigate methods of displacement vector estimation which can be used in predictive image coding or motion-adaptive frame interpolative coding. In both cases, a differential approach is adopted. This means that the displacement vector estimation is based on the measurement of the spatiotemporal gradient of the image sequence. In the case of predictive coding the motion estimator is composed of three parts. The first is a spatial predictor of the displacement vector, which is based on a spatial autoregressive relation of the velocity field. The coefficients of this relation are made intensity-dependent. The presence of discontinuities inherent to the motion and to the instabilities of the estimation algorithm makes necessary a stage of detection of all type of discontinuities. Finally, an a posteriori estimator achieves the task of displacement vector estimation. This last stage is of iterative form. The application of this algorithm in a very noisy image sequence has permitted to obtain a gain of about 40% in the absolute value of the difference with the predicted displacement vector and 65% with the estimated one after two iterations: The same structure of displacement field estimation can be used to make a frame interpolation motion-adaptive. We present such an estimator, which is slightly differnt from that proposed in predictive coding, knowing that a non-causal a priori estimation can be realized. We also propose a completely different algorithm, which uses a hierarchical representation of the displacement field. A dynamic hierarchical 4-trees estimation algorithm is presented. The motivation for such a proposition comes from the fact that large areas in a great number of image sequences are no-moving or have homogeneous bidimensional motion, that is to say translational. Considering this redundance in the displacement field a significant gain in complexity of calculations can be obtained, if the estimation is carried out rather over blocks than pel-by-pel. We have applied the last algorithm in the case of a sequence with moderate motion and some numerical results are given in this article.
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