VECTOR FIELD ANALYSIS AND SYNTHESIS USING 3-DIMENSIONAL PHASE PORTRAITS

Tools from dynamical systems theory are used to decompose 3-D vector f ields into simpler building blocks consisting of critical points and p hase portraits, A robust critical point detectors is developed for thr ee dimensions. Samples from the vector field surrounding each critical point are then used to estimate the associated linear phase portrait, which is written as a 3 x 3 matrix. The estimated matrix may be categ orized into one of seven canonical forms by its eigenvalues, which rem ain consistent under an arbitrary differentiable mapping of the region , The original vector field behavior is estimated using two methods. I n one technique, the global behavior is reconstructed using a weighted superposition of phase portraits. For more complex field patterns, a regular partition is imposed prior to phase portrait representation, a nd each individual partition is decomposed into a separate phase portr ait. These methods provide a means of extracting the relevant features and information from the vector field in the form of a higher lever d escriptor and provide a means of reconstructing the field qualitativel y from those descriptors, The method is demonstrated on fluid flow dat a. (C) 1997 Academic Press.