Abstract The integration of numerical simulation and experimental measurements in cellular materials at the sub-cellular scale is a real challenge. On the experimental side, the almost absence of texture makes displacement fields measurement tricky. On the simulation side, it requires the construction of reliable and specimen-specific geometric and mechanical models from digital images. For this purpose, high order based fictitious domain approaches have proven to be an efficient alternative to boundary conforming finite elements for the analysis of geometrically complex objects. A number of discretization parameters needs to be set by the user by making a trade-off between accuracy and computational cost. In addition to numerical errors (interpolation, integration etc.), there are additional geometric and model errors due to the pixelation of the image (e.g., quantization, sampling, noise). In the literature, discretization parameters are often analyzed without taking pixelation into account, which can lead to over-calculations. In this paper, these parameters are adjusted to obtain (a) the best possible accuracy (bounded by pixelation errors) while (b) ensuring minimal complexity (concept of fair price). In order to analyze the different sources of error, various two-dimensional synthetic experiments are generated by mimicking the image acquisition process from high-resolution numerical simulations considered as a reference. The approach leads to a modeling that outperforms conventional approaches both in terms of accuracy and complexity. Eventually, it is shown that the presented image-based models provide a unique opportunity to assist digital volume correlation and allow the measurement of relevant local kinematics within cellular materials.

中文翻译：

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为合理定价的基于图像的建模调整虚拟域参数：应用于数字图像相关性的正则化

摘要 在亚细胞尺度上对细胞材料进行数值模拟和实验测量的整合是一个真正的挑战。在实验方面，几乎没有纹理使得位移场测量变得棘手。在模拟方面，它需要从数字图像中构建可靠且特定于样本的几何和力学模型。为此，基于高阶的虚拟域方法已被证明是用于分析几何复杂对象的边界一致有限元的有效替代方法。用户需要通过在准确性和计算成本之间进行权衡来设置许多离散化参数。除了数值误差（插值、积分等），由于图像的像素化（例如量化、采样、噪声），存在额外的几何和模型误差。在文献中，经常在不考虑像素化的情况下分析离散化参数，这可能导致过度计算。在本文中，调整这些参数以获得 (a) 可能的最佳精度（受像素化误差限制），同时 (b) 确保最小的复杂性（公平价格的概念）。为了分析不同的误差来源，通过从高分辨率数值模拟中模拟图像采集过程来生成各种二维合成实验作为参考。该方法导致建模在准确性和复杂性方面均优于传统方法。最终，