  3D image processing is an important problem in computer vision and pattern
recognition fields. Compared with 2D image processing, its computation
difficulty and cost are much higher due to the extra dimension. To
fundamentally address this problem, we propose to embed the essential
information in a 3D object into 2D space via spectral layout. Specifically, we
construct a 3D adjacency graph to capture spatial structure of the 3D voxel
grid. Then we calculate the eigenvectors corresponding to the second and third
smallest eigenvalues of its graph Laplacian and perform spectral layout to map
each voxel into a pixel in 2D Cartesian coordinate plane. The proposed method
can achieve high quality 2D representations for 3D objects, which enables to
use 2D-based methods to process 3D objects. The experimental results
demonstrate the effectiveness and efficiency of our method.

Computer Vision and Pattern Recognition