3D shape reconstruction from images in the frequency domain

Reconstructing the high-resolution volumetric 3D shape from images is challenging due to the cubic growth of computational cost. In this paper, we propose a Fourier-based method that reconstructs a 3D shape from images in a 2D space by predicting slices in the frequency domain. According to the Fourier slice projection theorem, we introduce a thickness map to bridge the domain gap between images in the spatial domain and slices in the frequency domain. The thickness map is the 2D spatial projection of the 3D shape, which is easily predicted from the input image by a general convolutional neural network. Each slice in the frequency domain is the Fourier transform of the corresponding thickness map. All slices constitute a 3D descriptor and the 3D shape is the inverse Fourier transform of the descriptor. Using slices in the frequency domain, our method can transfer the 3D shape reconstruction from the 3D space into the 2D space, which significantly reduces the computational cost. The experiment results on the ShapeNet dataset demonstrate that our method achieves competitive reconstruction accuracy and computational efficiency compared with the state-of-the-art reconstruction methods.