Transmitting compactly represented geometry of a dynamic scene from a sender can enable a multitude of 3D imaging functionalities at a receiver, such as synthesis of virtual images from freely chosen viewpoints via depth-image-based rendering (DIBR).While depth maps can now be readily captured using inexpensive depth sensors, they are often corrupted by non-negligible acquisition noise. In this paper, we derive 3D surfaces of a dynamic scene from noise-corrupted depth maps in a rate-distortion (RD) optimal manner. Specifically, unlike previous work that finds the most likely (e.g., maximum likelihood) 3D surface from noisy observations regardless of representation size, we judiciously search for the best fitting (i.e., minimum distortion) 3D surface subject to a bitrate constraint. Our RD-optimal solution reduces to the maximum likelihood solution as the rate constraint is loosened. Using the MVC codec for compression of multiview depth video and MPEG free viewpoint test sequences as input, experimental results show that RD-optimized 3D reconstructions computed by our algorithm outperform unprocessed depth maps by up to 2.42dB in PSNR of synthesized virtual views at the decoder for the same bitrate.