Synthesis using example sets

We generate new views using sets of examples: interpolation is restricted to only occur inside the convex hull of an example set found as above for which $E_I(s) \leq \epsilon$. Given a new parameter vector x, we test whether it is in the convex hull of parameters in any example set. If the point does not lie in the convex hull of any example set, we find the nearest point on the convex hull of one of the example sets, and use that instead. This prevents erroneous extrapolation.

If a new parameter is in the convex hull of more than one example set, we first select the set whose median example parameter is closest to the desired example parameter. Once a set has been selected, we interpolate a new function value from examples using the RBF method summarized above. To enforce temporal consistency of rendered images over time, we can use a simple additional constraint on subsequent frames. Once we have selected an example set, we keep using it until the desired parameter value leaves the valid region (convex hull) of that set. When this occurs, we allow transitions only to ``adjacent'' example sets; adjacency is defined as those pairs of sets for which at least one example on each convex hull are sufficiently close ($\vert\vert y_i - y_j\vert\vert<\epsilon$) in appearance space.