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To build a compact and photorealistic representation of a 3-D object without using polygonal mesh, 3-D representations of an object based on images accompanied by depth values were developed. In this letter, we propose a new compression system for the depth component of layered depth image (LDI), one of these representations, which represents a 3-D object. In order to achieve a high compression performance, it is necessary to group more correlated depth data. For this purpose we introduce the concept of partial surfaces from depth point cloud in LDI and derive a depth compression algorithm based on them generated from LDI. Neighboring depth points on the generated partial surface are likely to have high correlation, since it is a curved surface composed of surface points of the object. From experimental results, our proposed compression method outperforms other previous methods in terms of compression efficiency.