Seite - 171 - in Proceedings of the OAGM&ARW Joint Workshop - Vision, Automation and Robotics

Fig. 7: Segmentation strategy for patches. Every valid patch (blue) is a cluster of points e.g. 10×10pixel and will be connected to an neighboring (green) existing collection of patches if it fits to one of the existing plane hypothesis. If it can not be added to an existing hypothesis it will become the starting point for a new hypothesis. approximated plane. For this the distance d= |ax+by+cz−1|√ a2+b2+c2 <dth (18) has to be below a threshold (e.g. 1cm). 2) Segmentation: These patches can easily be grouped by any clustering algorithm that supports 4 or 8 connectivity. Neighboring planes or patches can be combined by meeting the criteria of pointing roughly in the same direction e.g. +-15◦. In this implementation it was sufficient to run one pass with the following strategy (see Figure 7): 1) If the current patch (blue) is not already assigned to a plane, create a new plane with this patch as first member. 2) If the neighboring (green) patch to the right has the samenormaldirectionas theplaneof thecurrentpatch, add the patch (green) to this plane. If the patch to the right is already assigned to a plane, and both plane normals are similar, merge the planes. 3) Merge the patch to the bottom with the current plane if the normal direction is similar. 3) Post-processing: The segmentation of the bigger patches are by far not satisfying because they leave a lot of pixel unassigned. In the last step the filter is running from top left to bottom right and vice versa (see Figure 8) to assign pixel to the most fitting plane. To assign a pixel to a plane it must meet one of the following criteria, otherwise it stays unassigned or assigned to its current plane. • The considered point is unassigned and fits inside the neighboring plane. • If the point is already assigned to a plane, which size is a lot smaller (e.g. factor of 10) than the new plane, the point simply has to be close enough (d<dth to get reassigned. • If the point is already assigned to a plane, which is of similar size (|Pnew|f> |Pcurrent|> |Pnew|1f ) the point has to be closer to the new plane, than to the old plane (dPnew<dPcurrent). Note that small planes can’t take away points from bigger planes but bigger planes sure can do this to smaller ones. Fig. 8: The bottom up and top down processing steps follow- ing the same pattern: The center point (blue) is traversing the image pixelwise in the directions top-down (left) or bottom- up (right). When one of the center points neighboring pixels (green) is a suitable candidate for the center points plane hypothesis, it will get added to this plane. (a) Original image. (b) Raw patch clustering. (c) The top-down post- processing step. (d) The bottom-up post- processing step. Fig. 9: Synopsis of the segmentation process. This is a strategy to eliminate smaller planes, that might be created in the first step due to oversegmentation. One might replace this strategy by a more sophisticated one. An other parameter that could additionally be taken into account is the normal vector of each point, which should show into the same direction as the plane it is added to. VI. RESULTS OF SEGMENTATION The simple plane segmentation algorithm provides useable results for indoor scenarios as seen in Figure 9. It is notable that the depthmap quality degrades in the image corners. As a result the algorithm wrongly creates another plane in this region (bottom right corner). Besides this, the algorithm shows the desired behavior. The cylindrical regions around thecansandboxesareapproximatedbysmallerplanes,while smaller planar surface patches of boxes get detected as such. In terms of frame rate our algorithm is competitive as it runs at 22Hz while processing a 640×480 pixel depth map. The algorithms described by Holz [5] (7Hz) and Wang 171