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Utilization of an acoustic camera for range measurements is a significant advantage for 3D shape recovery of underwater targets by opti-acoustic stereo imaging, where the associated epipolar geometry of visual and acoustic image correspondences is described in terms of conic sections and trigonometric functions. In this paper, we propose and analyze a number of methods based on direct and indirect approaches that provide insight on the merits of the new imaging and 3D object reconstruction paradigm. We have devised certain indirect methods, built on a regularization formulation, to first compute from noisy correspondences maximum likelihood estimates that satisfy the epipolar geometry. The 3D target points can then be determined from a number of closed-form solutions applied to these ML estimates. An alternative direct approach is also presented for 3D reconstruction directly from noisy correspondences. Computer simulations verify consistency between the analytical and experimental reconstruction SNRs - the criterion applied in performance assessment of these various solutions.