Image models for flow field analysis, representation, and compression: A dynamical systems approach

Abstract

Pattern models for analyzing, representing, and compressing experimental 2D fluid flow imagery are developed. The approach is to represent flow fields using the tools of dynamical systems theory. Complex flow fields are decomposed into simple components based on the observed critical point behavior. A critical point detector based on the vector field index is developed, and its performance is analyzed. The critical point behavior is modeled by the linear phase portrait, which is a compact representation specified by a 2 x 2 A matrix. The eigenvalues of A provide a symbolic descriptor, and this allows the qualitative behavior of the critical points to be classified into one of six canonical forms. The global flow field behavior is represented using the linear phase portrait estimates as a basis. First, a linear superposition approach is considered, where the flow field is modeled using the tools of potential theory. This technique is appropriate for the representation of incompressible flows with negligible friction effects. A second approach is considered in which complex flows are modeled by nonlinear dynamical systems. A Taylor series model is assumed for the velocity components, and the model coefficients are computed by considering both local critical point and global flow field behavior. A merge and split procedure for complex flows is presented, in which patterns of neighboring critical point regions are combined and modeled. The computed models are then employed to compress scalar flow images that exhibit little or gradual variation along the flow streamlines. The model serves as a guide for removing this redundancy, and compression ratios on the order of 100:1 are achieved. Finally, the compression of vector field data using orthogonal polynomials derived from the Taylor series model is considered. A critical point scheme and a block transform are presented. They are applied to velocity fields measured in particle image velocimetry experiments and generated by computer simulations, and compression ratios ranging from 15:1 to 100:1 are achieved.