3D-3D alignment using particle swarm optimization

Three-dimensional datasets of unique, complex objects are readily available from the tomographic modalities, and fusion of these data sets leads to new understanding of the data and their relationships. In many cases, automatic alignment of the objects is difficult or time consuming when substantial misalignments are present or point correspondences cannot be established, or the solution space is non-convex. These issues effectively exclude most optimization algorithms used in conventional data alignment. Here, we present the particle swarm optimization (PSO) approach which is not sensitive to initial conditions, local minima or non-convex solution space. Intercommunicating particle swarms are randomly placed in the solution space (representing the parameters of the rigid transformations). Each member of each swarm traverses the solution space, constantly evaluating the objective function at its own position and communicating with other members of the swarm about theirs. In addition, the swarms communicate between themselves. Through this information sharing between swarm members and the swarms, the space is searched completely and efficiently, and as a result all swarms converge near the globally optimal rigid transformation. To evaluate the technique, high-resolution micro-CT data sets of single mouse heads were acquired with large initial misalignments. Using two communicating particle swarms in the same solution space, six distinct mouse head objects were aligned finding the approximate global minima in about 25 iterations or 140 seconds on a standard PC independent of initial conditions. Faster speeds (better accuracy) can be obtained by relaxing (restricting) the convergence criteria. These results indicate that the particle swarm approach may be a valuable tool for stand-alone or hybrid alignments.