  We present an adaptive sampling approach to 3D reconstruction of the welding
joint using the point cloud that is generated by a laser sensor. We start with
a randomized strategy to approximate the surface of the volume of interest
through selection of a number of pivotal candidates. Furthermore, we introduce
three proposal distributions over the neighborhood of each of these pivots to
adaptively sample from their neighbors to refine the original randomized
approximation to incrementally reconstruct this welding space. We prevent our
algorithm from being trapped in a neighborhood via permanently labeling the
visited samples. In addition, we accumulate the accepted candidates along with
their selected neighbors in a queue structure to allow every selected sample to
contribute to the evolution of the reconstructed welding space as the algorithm
progresses. We analyze the performance of our adaptive sampling algorithm in
contrast to the random sampling, with and without replacement, to show a
significant improvement in total number of samples that are drawn to identify
the region of interest, thereby expanding upon neighboring samples to extract
the entire region in a fewer iterations and a shorter computation time.
