In the above titled paper (ibid., vol. 27, no. 8, pp. 1045-1053, Aug. 08), the equation on p. 1052 should be corrected as presented here.

This paper deals with the problem of tracking cardiac motion and deformation using velocity-encoded magnetic resonance imaging. We expand upon an earlier described method and fit a spatiotemporal motion model to measured velocity data. We investigate several different spatial elements both qualitatively and quantitatively using phantom measurements and data from human subjects. In addition, we also use optical flow estimation by the Horn-Schunk method as complementary data in regions where the velocity measurements are noisy. Our results show that it is possible to obtain good motion tracking accuracy in phantoms with relatively few spatial elements, if the type of element is properly chosen. The use of optical flow can correct some measurement artifacts but may give an underestimation of the magnitude of the deformation. In human subjects the different spatial elements perform quantitatively in a similar way but qualitative differences exists, as shown by a semiquantitative visual scoring of the different methods.

A novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace methods and is derived from both ordinary coordinate representations and camera matrices and from a so called depth and shape analysis. Furthermore, no initial phase is needed to start up the algorithm. It starts directly with the first two images and incorporates new images as soon as new corresponding points are obtained. The performance of the algorithm is shown on simulated data. Moreover, the two different approaches, one using camera matrices and the other using the concepts of affine shape and depth, are unified into a general theory of structure and motion from image sequences.

The paper deals with the structure-motion problem for images of point configurations taken by uncalibrated cameras. Using a parametrisation by affine shape and kinetic depth, a complete and explicit characterisation of the imaging geometry is given, including the shape of the object configuration and the positions of the cameras relative to the scene. No epipolar geometry is used. It is shown that not only the projective but also the affine structure of the scene can be recovered when knowing the relative placement of five of the camera centres (four if they are coplanar). Variational algorithms for reconstruction and motion are presented, thus avoiding numerically unstable solving of algebraic equations. Any number of points in any number of images can be treated simultaneously and uniformly, without preselection of reference points. The performances of the algorithms are illustrated on simulations and experiments.