Visibility of Point Clouds and Mapping of Unknown Environments

13 years 10 months ago

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Abstract. We present an algorithm for interpolating the visible portions of a point cloud that are sampled from opaque objects in the environment. Our algorithm projects point clouds onto a sphere centered at the observing locations and performs essentially non-oscillatory (ENO) interpolation to the projected data. Curvatures of the occluding objects can be approximated and used in many ways. We show how this algorithm can be incorporated into novel algorithms for mapping an unknown environment. 1 Visibility The problem of visibility involves the determination of regions in space visible to a given observer when obstacles to that sight are present. When the observer is replaced by a light source in the simpliﬁed geometrical optics setting with perfectly absorbing boundary condition at the obstacles, the problem translates to that of ﬁnding illuminated regions. In this regard, the visibility problem is highly related to the high frequency wave propagation problems and is needed in m...

Yanina Landa, Richard Tsai, Li-Tien Cheng

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