We present an efficient method to propagate sparse user edits indicated by strokes on 360${}^{\circ }$ panoramas. Our algorithm first projects each equirectangular pixel to its corresponding position on a 3D unit sphere, so each pixel can be characterized by a feature vector consisting of its 3D coordinates and RGB color values. We formulate edit propagation as an optimization problem that aims to satisfy the user edit constraints while preserving the manifold structure of the image at the same time. To solve the problem using a linear system efficiently, we first construct the K-D tree structure in the feature space to cluster pixels. Then we optimize the manifold structure where both the number of nearest neighbors and their corresponding weights are determined by the feature distributions. We further apply a multiresolution strategy to speedup the edit propagation. Our method is the first to perform interactive edit propagation on 360${}^{\circ }$ panoramas. Experiments show that our method is able to generate seam-free and visually pleasing results, and users can receive instant feedback during interactive editing.

我们提出了一种有效的方法来传播由360上的笔画指示的稀疏用户编辑${}^{\circ }$全景图。我们的算法首先将每个等矩形像素投影到3D单位球面上的相应位置，因此每个像素都可以通过包含其3D坐标和RGB颜色值的特征向量来表征。我们将编辑传播公式化为一个优化问题，旨在满足用户编辑约束，同时保留图像的流形结构。为了有效地使用线性系统解决问题，我们首先在特征空间中构造KD树结构以对像素进行聚类。然后，我们优化流形结构，其中最近邻的数目及其对应的权重均由特征分布确定。我们进一步应用多分辨率策略来加快编辑传播。我们的方法是第一个在360度上执行交互式编辑传播的方法${}^{\circ }$全景图。实验表明，我们的方法能够生成无接缝且视觉上令人愉悦的结果，并且用户可以在交互式编辑期间收到即时反馈。