  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.
