Inferring the 3D surface shape of a known template from 2D images captured by a monocular camera is a challenging problem. Due to the severely underconstrained nature of the problem, inferring shape accurately becomes particularly challenging when the template exhibits high curvature, resulting in the disappearance of feature points and significant differences between the inferred and actual deformations. To address this problem, this paper proposes a concise and innovative approach that utilizes a physical simulator incorporating the object’s material properties and deformation law. We utilize a view frustum space constructed from the contours of a monocular camera image to effectively restrict the physically-based free motion of the template. Additionally, we employ mesh denoising techniques to ensure the smoothness of the surface following deformation. To evaluate our shape inference results, we utilize a ground truth 3D point cloud generated from multiple viewpoint images. The results demonstrate the superior performance of our approach compared to other methods in accurately inferring deformations, particularly in scenarios where feature points are unobservable. This method carries significant practical implications across diverse domains, including virtual reality, digital modeling, and medical surgery training.

从单目相机捕获的 2D 图像推断已知模板的 3D 表面形状是一个具有挑战性的问题。由于问题的严重欠约束性质，当模板表现出高曲率时，准确推断形状变得特别具有挑战性，导致特征点消失以及推断变形与实际变形之间的显着差异。为了解决这个问题，本文提出了一种简洁而创新的方法，该方法利用结合了物体的材料特性和变形规律的物理模拟器。我们利用由单目相机图像的轮廓构建的视锥体空间来有效地限制模板基于物理的自由运动。此外，我们采用网格去噪技术来确保变形后表面的平滑度。为了评估我们的形状推断结果，我们利用从多视点图像生成的地面实况 3D 点云。结果表明，与其他方法相比，我们的方法在准确推断变形方面具有优越的性能，特别是在特征点不可观察的情况下。这种方法在虚拟现实、数字建模和医疗手术培训等不同领域具有重要的实际意义。