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The issue of achieving an appropriate segmentation for indoor point cloud scenes remains difficult. Although available methods continue to improve the benchmark performance, more attentions need to be paid to deal with the drawbacks of inaccurate or incomplete segments in division. To push the research to the next level, this work proposes an learning-free algorithm for the segmentation of indoor point clouds which consists of two stages. The first stage extracts edges of RGBD point clouds and applies them in the voxel clustering process to avoid generating supervoxels which are situated across object boundaries. After this pre-segmentation, a two-phase merging procedure is presented in the second part. By conducting region growing on optimized supervoxels, a set of local regions is obtained. Then we propose to define the convexity-concavity of adjacent regions based on the observations of object structures and merge the convexly connected regions to achieve object-level segmentation. This algorithm is straightforward to implement and requires no training data. Experimental results show that it produces supervoxels with plausible boundaries and arrives at better object-level segmentation.