In a typical optical test, a stereo camera pair is required to measure the three-dimensional motion of a test article; one camera typically only measures motions in the image plane of the camera, and measurements in the out-of-plane direction are missing. Finite element expansion techniques provide a path to estimate responses from a test at unmeasured degrees of freedom. Treating the case of a single camera as a measurement with unmeasured degrees of freedom, a finite element model is used to expand to the missing third dimension of the image data, allowing a full-field, three-dimensional measurement to be obtained from a set of images from a single camera. The key to this technique relies on the mapping of finite element deformations to image deformations, creating a set of mode shape images that are used to filter the response in the image into modal responses. These modal responses are then applied to the finite element model to estimate physical responses at all finite element model degrees of freedom. The mapping from finite element model to image is achieved using synthetic images produced by a rendering software. The technique is applied first to a synthetic deformation image, and then is validated using an experimental set of images.

中文翻译：

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从单相机光学测试数据预测 3D 运动

在典型的光学测试中，需要一对立体相机来测量测试物品的三维运动；一台相机通常只测量相机图像平面内的运动，而缺少平面外方向的测量。有限元扩展技术提供了一种在未测量的自由度下估计测试响应的途径。将单台相机的情况作为自由度未测量的测量，利用有限元模型扩展到图像数据缺失的三维，从而可以从集合中获得全场、三维的测量来自单个相机的图像。该技术的关键依赖于有限元变形到图像变形的映射，创建一组模态图像，用于将图像中的响应过滤为模态响应。然后将这些模态响应应用于有限元模型以估计所有有限元模型自由度的物理响应。从有限元模型到图像的映射是使用渲染软件生成的合成图像来实现的。该技术首先应用于合成变形图像，然后使用一组实验图像进行验证。