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A system is proposed for robust and efficient search for solid objects in a cluttered depth scene. Since the system is designed for obtaining robustness in real industry applications, it utilizes only depth information without color or texture on the object surfaces. The search is based on image matching of our novel surface representation called depth aspect image (DAI). The representation defined as a basic cue for the search is a two-dimensional orthographic image of local depth distribution and it is created through voxel framing, which gives effective references for definition of various aspects without any prominent features on the surfaces such as vertices or edges. For local coordinates of DAIs, the aspect coordinate frame is defined by 3-tuples of voxels and five constraint conditions on the 3-tuples can be formalized for the efficient selection. These can contribute to a reduction of the number of possible voxel sets. A robust statistical estimator called least quantile of residuals is furthermore introduced for robust matching even in the presence of occlusion and/or lack of data. The estimator can be utilized for both depth matching and model verification. Since the proposed system is following a model-based approach with possible views of local depth distributions, the computation cost for matching has to be reduced by introducing random sampling and an effective hashing. The sufficient number of trial samplings is derived through investigation and modeling of voxel arrangement. Experiments with real scenes show the effectiveness of the proposed method.