Modeling and Temporal Evolution of a Family of Curves

The vector spline approximation framework is applied to the problem of spatial and temporal modeling of deformable structures in an image sequence. We show that this vector field framework is well adapted to the mathematical modeling of a family of mutually interacting curves associated to deformable structures. The tools presented in this study are applied to satellite oceanographic images, where deformable structures are vortices and temperature fronts. The curves are obtained as integral paths (or orbits) of a suitable vector field described in this work. Motion analysis is obtained with the optical flow and the mathematical notion of the transformation of a vector field by a diffeomorphism

A comparative study between Elliptic Fourier and B-spline descriptors for object contour representation

International audienceIn this work, a comparative study between Elliptic Fourier and B-spline descriptors is carried out for comparing their efficiency in characterizing the contour shape of image objects. In both cases, the goal is to obtain the least representation error using the fewest possible number of coefficients. With Fourier descriptors, different number of harmonics are used while the remaining ones are set to zero. In the B-spline case, coefficients are obtained iteratively using a least-square filter, followed by a decimation procedure. Linear and cubic B-splines are considered. In general, data will be more compressed when the lower number of coefficients is used, but the representation error also increases considerably. We use a signal/error ratio, expressed in dBs, to measure the similarity of each approximation. The signal value is obtained from the 'modulo' addition of all coordinate points, whereas the error value is computed accumulating the 'modulo' distance between original and reconstructed shape. It can be shown that for a lower compression rate, the results do not vary significantly in all three methods. For higher compression rates, Elliptic Fourier Descriptors are more efficient than linear and cubic B-splines, especially in soft contours, but B-splines have lower computational cost