目的 为提高曲线3维重建的精度，提出一种基于曲率无穷范数约束根据2幅图像重建3维非参数空间曲线的方法。方法 分析以重建曲线的反投影误差、曲率的加权和作为目标函数的缺点。为了避免引入不确定的权系数，同时使求解结果更好地逼近全局最优解，把原目标函数中的曲率项转化为曲率无穷范数的不等式约束，即限制了曲线上所有点的曲率值都必须小于某个较小阈值，从而保证了重建曲线的连续性。结果 模拟曲线实验验证了方法的可行性、鲁棒性和优越性；圆柱相贯线的重建结果显示重建曲线在特定方向上的相对误差为2.98%；最后把方法应用于果树枝干骨架的3维重建，重建的果树枝干骨架符合肉眼观察的视觉效果。结论 本文方法适用于不同场合下的曲线3维重建，且重建精度较高。

Objective 3D curve reconstruction is indispensable in computer vision. The traditional 3D reconstruction considerably relies on point-based correspondences. However, point-based reconstruction ignores the structural information between sample points and may reduce reconstruction accuracy. To avoid this problem, high-level geometric primitives are needed to reconstruct 3D scenes, typically as a 3D curve. Method This study proposes a vision-based method under the L-infinity norm of curvatures for the 3D reconstruction of nonparametric space curves from a pair of images. An initial cost function for minimization was defined as a weighted sum of reprojection errors and curvatures of the reconstructed curve. Reaching the global minimum is difficult, specifically if the initial cost function is not significantly close to the actual result, because of nonconvexity. In addition, the weight coefficients that control the relative significance between the reprojection errors and curvature were not readily. To address this issue, L-infinity norm replaced with L₂ norm of the curvatures was used as an inequality constraint. The curvatures of all discrete points along the curve should be less than the maximal curvature κ_max, which can be estimated from the projection curves of the two images. The reconstructed curve, given a small κ_max, was smooth under the inequality constraint. A method utilizing a generalized Lagrange multiplier was used to solve this nonlinear optimization problem with inequality constraint. Result An experiment using synthetic data showed that the reconstructed curve was significantly similar to the real results and that its reconstruction error was less than 1/7 from the point-based method. These findings illustrate that the proposed method is evidently superior to the point-based method. The proposed method also has higher accuracy than a previously reported method [12]. The influences of the 3D reconstruction errors with respect to κ_max in a certain range were not large, thereby validating the robustness of the proposed method. In the noise tests, reconstruction errors linearly increased with the noise. Strong noise probably caused a large stereo ambiguity along the curve and increased uncertainty of the space curve. The intersection line of two crossed cylinders was reconstructed using the proposed method. The reconstructed curve was projected in the XY plane, wherein the projection of the actual intersection line was a circle. The radius of one cylinder can be estimated after fitting the projection curve of the reconstructed curve as a circle. The relative deviation between the estimated and real radii was 2.98%. This value indicates that the proposed method has high accuracy for general industrial applications. The proposed method was used to reconstruct 3D skeletons of a fruit tree trunk; the resultant 3D skeletons were visually acceptable. Conclusion The proposed method can be used to reconstruct 3D space curves for various applications. However, the stereo ambiguity and uncertainty of camera parameters may reduce the accuracy of the method because only two images were used. The number of projection curves may be increased to solve this problem.