We consider the problem of defining and evaluating the distance between a three-dimensional pattern P[1..m, 1..m, 1..m] of voxels and a three-dimensional volume V[1..n, 1..n, 1..n] of voxels when rotations of P are also allowed. In particular we are interested in finding the orientation and location of P with respect of V that gives the minimum distance. We consider several distance measures. Our basic method works for all distance measures such that the voxels affect the distance between P and V only locally, that is, the distance between two voxels can be completed in unit time. The number of different orientations that P can have is analyzed. We give incremental algorithms to compute the distance, and several filtering algorithms to compute the upper and lower bounds for the distance. We conclude with experimental results on real data (three dimensional reconstruction of a biological virus).
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机译：我们考虑定义和评估voxels的三维模式P [1..M，1..M，1..M，1..M]之间的距离和三维体积V [1..N，1。当也允许P的旋转时，体素的体素。特别是我们有兴趣找到P的v的定向和位置，v v v v v v v v v v。我们考虑几个距离措施。我们的基本方法适用于所有距离测量，使得体素仅在本地影响P和V之间的距离，即，两个体素之间的距离可以在单位时间内完成。分析了P可以具有的不同方向的数量。我们提供增量算法来计算距离，以及几个过滤算法来计算距离的上限和下限。我们在真实数据（生物病毒的三维重建三维重建）的实验结果中得出结论。
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