We present a convex mixed-integer programming formulation for non-rigid shape matching. To this end, we propose a novel shape deformation model based on an efficient low-dimensional discrete model, so that finding a globally optimal solution is tractable in (most) practical cases. Our approach combines several favourable properties: it is independent of the initialisation, it is much more efficient to solve to global optimality compared to analogous quadratic assignment problem formulations, and it is highly flexible in terms of the variants of matching problems it can handle. Experimentally we demonstrate that our approach outperforms existing methods for sparse shape matching, that it can be used for initialising dense shape matching methods, and we showcase its flexibility on several examples.

中文翻译：

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MINA：非刚性形状对齐的凸混合整数规划

我们提出了一种用于非刚性形状匹配的凸混合整数规划公式。为此，我们提出了一种基于高效低维离散模型的新型形状变形模型，以便在（大多数）实际情况下可以找到全局最优解。我们的方法结合了几个有利的特性：它独立于初始化，与类似的二次分配问题公式相比，它更有效地解决全局最优性，并且在它可以处理的匹配问题的变体方面非常灵活。通过实验，我们证明我们的方法优于现有的稀疏形状匹配方法，它可以用于初始化密集形状匹配方法，并且我们在几个例子中展示了它的灵活性。