Segmentation of a Vector Field: Dominant Parameter and Shape Optimization

Abstract

Vector field segmentation methods usually belong to either of three classes: methods which segment regions homogeneous in direction and/or norm, methods which detect discontinuities in the vector field, and region growing or classification methods. The first two classes of method do not allow segmentation of complex vector fields and control of the type of fields to be segmented, respectively. The third class does not directly allow a smooth representation of the segmentation boundaries. In the particular case where the vector field actually represents an optical flow, a fourth class of methods acts as a detector of main motion. The proposed method combines a vector field model and a theoretically founded minimization approach. Compared to existing methods following the same philosophy, it relies on an intuitive, geometric way to define the model while preserving a general point of view adapted to the segmentation of potentially complex vector fields with the condition that they can be described by a finite number of parameters. The energy to be minimized is deduced from the choice of a specific class of field lines, e.g. straight lines or circles, described by the general form of their parametric equations. In that sense, the proposed method is a principled approach for segmenting parametric vector fields. The minimization problem was rewritten into a shape optimization and implemented by spline-based active contours. The algorithm was applied to the segmentation of precomputed optical flow fields given by an external, independent algorithm.