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This slide illustrates how the method can automatically get rid of some outliers in noisy data.
There are several noisy data points in the view from the yellow camera. However, the outliers lie between the surface and the red camera. The red camera is able to claim that a cube containing the points is in free space, carving away both the cube and the data within it. Similar thing happens with the other outliers and the green camera.
[I removed this slide to keep the talk short.]