Q-Warping: Direct Computation of Quadratic Reference Surfaces

We consider the problem of wrapping around an object, of which two views are available, a reference surface and recovering the resulting parametric ow using direct computations (via spatio-temporal derivatives). The well known examples are a ne ow models and 8-parameter ow models | both describing a ow eld of a planar reference surface. We extend those classic ow models to deal with a Quadric reference surface and work out the explicit parametric form of the ow eld. As a result we derive a simple warping algorithm that maps between two views and leaves a residual ow proportional to the 3D deviation of the surface from a virtual quadric surface. The applications include image morphing, model building, image stabilization, and disparate view correspondence.