Mathematical morphology for image sequences using the knowledge of dynamics

We develop a theory for morphologically processed image sequences. Instead of treating each image of the sequence one after the other in the same way, we construct the transformed sequence directly by using the dynamical information contained in the original sequence. We suppose that this dynamical information is known, i.e we know how the original sequence was constructed (how each image is obtained from the previous one). In both cases when the original sequence is constructed through an affine and bijective transformation or through a morphological operation, we give the expression (or a good approximation in few cases) of the transformed sequence directly from the first transformed image. We study this new transformation and give some interesting properties. We also present simple examples of this transformation.