Reconstructing a 3D shape based on a single sketch image is challenging due to the large domain gap between a sparse, irregular sketch and a regular, dense 3D shape. Existing works try to employ the global feature extracted from sketch to directly predict the 3D coordinates, but they usually suffer from losing fine details that are not faithful to the input sketch. Through analyzing the 3D-to-2D projection process, we notice that the density map that characterizes the distribution of 2D point clouds (i.e., the probability of points projected at each location of the projection plane) can be used as a proxy to facilitate the reconstruction process. To this end, we first translate a sketch via an image translation network to a more informative 2D representation that can be used to generate a density map. Next, a 3D point cloud is reconstructed via a two-stage probabilistic sampling process: first recovering the 2D points (i.e., the x and y coordinates) by sampling the density map; and then predicting the depth (i.e., the z coordinate) by sampling the depth values at the ray determined by each 2D point. Extensive experiments are conducted, and both quantitative and qualitative results show that our proposed approach significantly outperforms other baseline methods.

翻译：以单一草图图像为基础重建一个 3D 形状具有挑战性, 原因是一个稀疏、 不规则的草图和一个常规、 密集的 3D 形状之间存在巨大的域差。 现有的工程试图利用从草图中提取的全球特征直接预测 3D 坐标, 但他们通常会失去与输入草图不相符的精细细节。 通过分析 3D 到 2D 的投影过程, 我们注意到, 2D 点云分布特征的密度图( 即投影飞机每个地点预测点的概率) 可以用作便利重建进程的代名词。 为此, 我们首先通过图像翻译网络将草图转化为一个更丰富的 2D 表示, 用于生成密度图。 接下来, 3D 点云会通过一个两阶段的概率性取样过程重建 : 首先通过对密度图进行取样来恢复 2D 点( x 和 y 坐标 ) ; 然后通过对每2D 点确定的一个射线的深度值进行取样( ) ( z 坐标) 来预测深度 。 为此, 我们首先通过一个图像翻译网络将一个更清楚的2D 的2D 方法, 并展示其他 进行定量和 的实验 。