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Range data provide an important source of 3-D shape information. This information can be used to extract jump boundaries which correspond to occluding boundaries of objects in a scene and ``edges'' which correspond to points lying between significantly different regions on the surface of objects. We are mainly interested in range data obtained from sensors such as lasers. The main problem with this type of range finder is the fact that the accuracy of the measurements depends on the power of the signal that reaches the receiver. This study describes how a range edge detection procedure can be designed that has low sensitivity to noise and imbeds all the knowledge available on the range measurement accuracy.