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

Maximum compatibility estimates and shape reconstruction with boundary curves and volumes of generalized projections