  We show that the boundary curves (profiles) in $\R^2$ of the generalized
projections of a body in $\R^3$ uniquely determine a large class of shapes, and
that sparse profile data, combined with projection volume (brightness) data,
can be used to reconstruct the shape and the spin state of a body. We also
present an optimal strategy for the relative weighting of the data modes in the
inverse problem, and derive the maximum compatibility estimate (MCE) that
corresponds to the maximum likelihood or maximum a posteriori estimates in the
case of a single data mode. MCE is not explicitly dependent on the noise
levels, scale factors or numbers of data points of the complementary data
modes, and can be determined without the mode weight parameters. We present a
solution method well suitable for adaptive optics images in particular, and
discuss various choices of regularization functions.
