Abstract
An approach to the solution of signal-to-symbol transformation in the domain of flow fields, such as oriented texture fields and velocity vector fields, is discussed. The authors use the geometric theory of differential equations to derive a symbol set based on the visual appearance of phase portraits which are a geometric representation of the solution curves of a system of differential equations. They also provide the computational framework to start with a given flow field and derive its symbolic representation. Specifically, they segment the given texture, derive its symbolic representation, and perform a quantitative reconstruction of the salient features of the original texture based on the symbolic descriptors. Results of applying this technique to several real texture images are presented. This technique is useful in describing complex flow visualization pictures, defects in lumber processing, defects in semiconductor wafer inspection, and optical flow fields.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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