The three-dimensional reconstruction of vocal folds in medicine usually involves endoscopy and an approach to extract depth information like structured light or stereo matching of images. The resulting mesh can accurately represent the superior area of the vocal folds, while new approaches also try to reconstruct the inferior area. We propose a novel approach to extract the time-dependent 3D geometry of the vocal fold from optical measurements on both the superior and inferior side, requiring optical measurements only from the superior side. First, a time-dependent, tri-variate surface velocity vector field is reconstructed using a high-speed camera and a laser Doppler vibrometer in an experimental environment. This vector field serves as target in an inverse finite-element simulation that optimizes the forces applied to a deformable vocal fold model such that the resulting movement after FEM simulation matches the velocity observations on the superior side. The required forces for the finite element method simulation are treated as unknowns and are assembled using multiple scalar fields. We use tensor products in B\'ezier Bernstein basis for our scalar fields to reduce the degrees of freedom for our optimization. We use gradient descent to optimize the control points of the force field polynomials. Our utilized error metric for gradient descent consists of two terms. The first term is used to match the simulated velocities to the observed measurements, while the second term measures the silhouette difference between observation and simulation.

翻译：医学中的声带三维重建通常涉及内窥镜技术以及深度信息提取方法，如结构光或图像立体匹配。生成的网格可精确表征声带上表面区域，而新兴方法则尝试重建下表面区域。我们提出一种创新方法，通过仅从声带上表面进行光学测量，即可提取其随时间变化的三维几何形态，该方法同时需要上下表面的光学测量数据。首先，在实验环境下利用高速相机和激光多普勒测振仪重建随时间变化的三变量表面速度矢量场。该矢量场作为逆向有限元仿真的目标，通过优化作用于可变形声带模型的力场，使有限元模拟生成的运动与上表面的速度观测值相匹配。有限元仿真所需的力场作为未知量，由多个标量场组合构成。我们采用Bézier-Bernstein基函数的张量积表达这些标量场，从而降低优化问题的自由度。通过梯度下降法优化力场多项式的控制点，所使用的误差度量包含两项：第一项使仿真速度与观测数据吻合，第二项衡量观测与仿真图像之间轮廓的差异。