In this study we present a geometric flow approach to the segmentation of three-dimensional medical images obtained from magnetic resonance imaging (MRI) or computed tomography (CT) scan methods, by minimizing a cost function. This energy term is based on the intensity of the original image and its minimum is found following a gradient descent curve in an infinite-dimensional space of diffeomorphisms (Diff) to preserve topology. The general framework is reminiscent of variational shape optimization methods, but remains closer to general developments on deformable template theory of geometric flows. In our case, the metric that provides the gradient is defined as a right invariant inner product on the tangent space (𝒱) at the identity of the group of diffeomorphisms, following the general Lie group approach suggested by Arnold [2]. To avoid local solutions of the optimization problem and to mitigate the influence of several sources of noise, a finite set of control points is defined on the boundary of the template binary images, yielding a projected gradient descent on Diff.

中文翻译：

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异形主动轮廓。

在这项研究中，我们提出了一种几何流方法，通过最小化成本函数，对从磁共振成像 (MRI) 或计算机断层扫描 (CT) 扫描方法获得的三维医学图像进行分割。该能量项基于原始图像的强度，其最小值在微分同胚 (Diff) 的无限维空间中遵循梯度下降曲线以保持拓扑结构。一般框架让人想起变分形状优化方法，但仍然更接近于几何流动的可变形模板理论的一般发展。在我们的例子中，按照 Arnold [2] 建议的一般李群方法，提供梯度的度量被定义为微分同胚群标识处的切线空间 (𝒱) 上的右不变内积。