Polyrigid and polyaffine transformations: A novel geometrical tool to deal with non-rigid deformations - Application to the registration of histological slices
Polyrigid and polyaffine transformations: A novel geometrical tool to deal with non-rigid deformations - Application to the registration of histological slices
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DOI：
10.1016/j.media.2005.04.001
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发表时间：
2005-12-01
影响因子：
10.9
通讯作者：
Ayache, N
中科院分区：
文献类型：
--
作者：
Arsigny, V;Pennec, X;Ayache, N
本文描述了一类新的几何变换--多刚体变换和多仿射变换。这些变换有效地编码局部刚性或仿射变形与少量的直观参数。它们可以描述复杂的大型刚性或仿射运动，不像大多数自由形式的变形类。该工具非常灵活，可以很容易地适应各种情况，只需调整刚性或仿射分量的数量以及描述其影响区域的参数的数量。每个空间位置的位移由一个连续的轨迹定义，该轨迹遵循一个微分方程，该微分方程平均每个刚性或仿射分量的影响。我们表明，由此产生的变换是同构，光滑的参数。我们设计了一个新的和灵活的数值方案，允许计算效率和接近理想的代数同态之间的权衡。我们的算法在Insight Toolkit中实现，其通用的编程风格提供了丰富的原型设计设施。在此背景下，我们推导出一个有效的优化策略的转换，这表明，这种新的工具是非常适合的推理。整个框架的例子与注册的组织切片成功。这种选择是具有挑战性的，因为这些数据通常会在采集过程中出现局部刚性变形，也可能会出现物质损失，这使得它们的配准更加困难。强大而灵活的新工具在非刚性3D刚性配准以及形状统计方面开辟了广阔的前景。(c)2005 Elsevier B. V.保留所有权利。
We describe in this paper a novel kind of geometrical transformations, named polyrigid and polyaffine. These transformations efficiently code for locally rigid or affine deformations with a small number of intuitive parameters. They can describe compactly large rigid or affine movements, unlike most free-form deformation classes. Very flexible, this tool can be readily adapted to a large variety of situations, simply by tuning the number of rigid or affine components and the number of parameters describing their regions of influence.The displacement of each spatial position is defined by a continuous trajectory that follows a differential equation which averages the influence of each rigid or affine component. We show that the resulting transformations are diffeomorphisms, smooth with respect to their parameters. We devise a new and flexible numerical scheme to allow a trade-off between computational efficiency and closeness to the ideal diffeomorphism. Our algorithms are implemented within the Insight Toolkit, whose generic programming style offers rich facilities for prototyping. In this context, we derive an effective optimization strategy of the transformations which demonstrates that this new tool is highly suitable for inference.The whole framework is exemplified successfully with the registration of histological slices. This choice is challenging, because these data often present locally rigid deformations added during their acquisition, and can also present a loss of matter, which makes their registration even more difficult.Powerful and flexible, this new tool opens up large perspectives, in non-rigid 3D rigid registration as well as in shape statistics. (c) 2005 Elsevier B.V. All rights reserved.