The depth modality of the multiview video plus depth (MVD) format is an active research area, whose main objective is to develop depth image based rendering friendly efficient compression methods. As a part of this research, a novel 3D planar-based depth representation is proposed. The planar approximation of multiple depth images are formulated as an energy-based co-segmentation problem by a Markov random field model. The energy terms of this problem are designed to mimic the rate-distortion tradeoff for a depth compression application. A novel algorithm is developed for practical utilization of the proposed planar approximations in stereo depth compression. The co-segmented regions are also represented as layered planar structures forming a novel single-reference MVD format. The ability of the proposed layered planar MVD representation in decoupling the texture and geometric distortions make it a promising approach. Proposed 3D planar depth compression approaches are compared against the state-of-the-art image/video coding standards by objective and visual evaluation and yielded competitive performance.