Inferring surface trace and differential structure from 3-D images

Early image understanding seeks to derive analytic representations from image intensities. This paper presents steps towards this goal by considering the inference of surfaces from three-dimensional images. We limit ourselves to smooth surfaces, and focus on the coupled problems of (i) inferring the trace points (the points through which the surface passes), and (ii) estimating the associated differential structure given by the principal curvature and direction fields over the estimated smooth surfaces. Computation of these fields is based on the determination of an atlas of local charts or parametrizations at estimated surface points. Algorithm robustness and the stability of results are essential for analysis of real images ; to this end, we present a functional minimization algorithm utilizing overlapping local charts to refine surface points and curvature estimates, and develop an implementation as an iterative constraint satisfaction procedure based on local surface smoothness properties. Examples of the recovery of local structure are presented for synthetic images degraded by noise and for clinical magnetic resonance images