Artificial neural networks for 3-D motion analysis-Part II: Nonrigid motion

For pt. I see ibid., p. 1386-93 (1995). An approach applying artificial neural net techniques to 3D nonrigid motion analysis is proposed. The 3D nonrigid motion of the left ventricle of a human heart is examined using biplanar cineangiography data, consisting of 3D coordinates of 30 coronary artery bifurcation points of the left ventricle and the correspondences of these points taken over 10 time instants during the heart cardiac cycle. The motion is decomposed into global rigid motion and a set of local nonrigid deformations which are coupled with the global motion. The global rigid motion can be estimated precisely as a translation vecto and a rotation matrix. Local nonrigid deformation estimation is discussed. A set of neural nets similar in structure and dynamics but different in physical size is proposed to tackle the problem of nonrigidity. These neural networks are interconnected through feedbacks. The activation function of the output layer is selected so that a feedback is involved in the output updating. The constraints are specified to ensure stable and globally consistent estimation. The objective is to find the optimal deformation matrices that satisfy the constraints for all coronary artery bifurcation points of the left ventricle. The proposed neural networks differ from other existing neural network models in their unique structure and dynamics.