  The rigid registration of two 3D point sets is a fundamental problem in
computer vision. The current trend is to solve this problem globally using the
BnB optimization framework. However, the existing global methods are slow for
two main reasons: the computational complexity of BnB is exponential to the
problem dimensionality (which is six for 3D rigid registration), and the bound
evaluation used in BnB is inefficient. In this paper, we propose two techniques
to address these problems. First, we introduce the idea of translation
invariant vectors, which allows us to decompose the search of a 6D rigid
transformation into a search of 3D rotation followed by a search of 3D
translation, each of which is solved by a separate BnB algorithm. This
transformation decomposition reduces the problem dimensionality of BnB
algorithms and substantially improves its efficiency. Then, we propose a new
data structure, named 3D Integral Volume, to accelerate the bound evaluation in
both BnB algorithms. By combining these two techniques, we implement an
efficient algorithm for rigid registration of 3D point sets. Extensive
experiments on both synthetic and real data show that the proposed algorithm is
three orders of magnitude faster than the existing state-of-the-art global
methods.
