Motion analysis is the most crucial part of object-based coding. A motion in 3-D environment can be analyzed better by using a 3-D motion model compared to its 2-D counterpart and hence may improve coding efficiency. Gibbs formulated joint segmentation and estimation of 2-D motion not only improves performance, but also generates robust point correspondences which are necessary for linear 3-D motion estimation algorithms. Estimated 3-D motion parameters are used to find the structure of the previously segmented objects by minimizing another Gibbs energy. Such an approach achieves error immunity compared to linear algorithms. Experimental results are promising and hence the proposed motion and structure analysis method is a candidate to be used in object-based (or even knowledge-based) video coding schemes.