Segmentation of Stochastic Images using Level Set Propagation with Uncertain Speed
Segmentation of Stochastic Images using Level Set Propagation with Uncertain Speed
复制标题
使用不确定速度的水平集传播对随机图像进行分割
DOI：
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发表时间：
2013
影响因子：
2
通讯作者：
T. Preußer
中科院分区：
文献类型：
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作者：
T. Pätz;T. Preußer
我们提出了一种方法的水平集的演化下的一个不确定的速度导致随机水平集。不确定的速度可以是随机变量或随机场，即空间变化的随机量，并且它可以由测量误差、噪声、未知的材料参数或其他不确定性源产生。由于零水平集不再是一条封闭的曲线，因此将随机水平集用于灰度值不确定的图像分割时，会产生随机区域。相反，我们有一个可能无限厚的带，它包含了在不确定性下零能级集的所有可能位置。因此，该方法允许对对象的分割体积和形状的概率描述。由于数值的原因，我们使用随机水平集方程，这是一个随机偏微分方程的抛物近似，并离散方程使用多项式混沌和随机有限差分格式。为了验证多项式混沌中的侵入式离散，我们进行了蒙特卡罗和随机配置模拟。我们展示了随机水平集方法的力量，通过展示从人工测试到医学图像中对象分割的各个方面的例子。
We present an approach for the evolution of level sets under an uncertain velocity leading to stochastic level sets. The uncertain velocity can either be a random variable or a random field, i.e. a spatially varying random quantity, and it may result from measurement errors, noise, unknown material parameters or other sources of uncertainty. The use of stochastic level sets for the segmentation of images with uncertain gray values leads to stochastic domains, because the zero level set is not a single closed curve anymore. Instead, we have a band of possibly infinite thickness which contains all possible locations of the zero level set under the uncertainty. Thus, the approach allows for a probabilistic description of the segmented volume and the shape of the object. Due to numerical reasons, we use a parabolic approximation of the stochastic level set equation, which is a stochastic partial differential equation, and discretized the equation using the polynomial chaos and a stochastic finite difference scheme. For the verification of the intrusive discretization in the polynomial chaos we performed Monte Carlo and Stochastic Collocation simulations. We demonstrate the power of the stochastic level set approach by showing examples ranging from artificial tests to demonstrate individual aspects to a segmentation of objects in medical images.