Alignment methods which can handle partially overlapping point sets and are invariant to the corresponding transformations are desirable in computer vision, with applications such as providing initial transformation configuration for local search based methods like ICP. To this end, we first show that the objective of the robust point matching (RPM) algorithm is a cubic polynomial. We then utilize the convex envelopes of trilinear and bilinear monomials to develop its lower bounding function. The resulting lower bounding problem can be efficiently solved via linear assignment and low dimensional convex quadratic programming. We next develop a branch-and-bound (BnB) algorithm which only branches over the transformation parameters and converges quickly. Experimental results demonstrated favorable performance of the proposed method over the state-of-the-art methods in terms of robustness and speed.
翻译:对齐方法可以处理部分重叠的点数组,并且与相应的变异性不相容,这些对齐方法在计算机视觉中是可取的,其应用软件,例如为比较方案等以本地搜索为基础的方法提供初始变换配置。为此,我们首先显示,稳健的点匹配(RPM)算法的目标是一个立方数的多式算法。然后,我们利用三线和双线单线的圆形封套件来开发其下线连接功能。由此产生的下线绑定问题可以通过线性指派和低维度的锥形二次方形编程来有效解决。我们接下来将开发一个分支和直线(BnB)算法,该算法仅对转换参数进行分支,并快速聚合。实验结果显示,在稳健性和速度方面,拟议方法在最先进的方法上表现良好。