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Object recognition systems that use 3D point cloud as the input data are potentially subjected to the problems of signal attenuation at a local level, or occlusions in cluttered scenes. In an attempt to develop more robust methods in handling these problems, the present paper introduces the notion of repeatable regions through a 3D region segmentation algorithm based on the extraction of repeatable interest points. A segmentation method presented is presented which is capable of segmenting 3D images of free-form objects using piece-wise boundary curves and regions reconstructed from extracted interest points. An experimental evaluation was devised to confirm the repeatability of segments in various realistic scenes, including cluttered and partially occluded scene. Three different 3D free-form objects in seven 2.5D scenes were tested in the experiment, with results showing that out of the top 15 selected regions from each 3D model, an average of six repeatable segmented regions with at least one correctly segmented region were recorded for each scene. This shows that highly repeatable regions can be localized and used to drive robust object recognition in 3D data.