3D shape completion and generation using multilayer spherical depth parameters with deep learning methods

3D geometry generation with artificial neural networks has been a topic worked on for a long time. Because the artificial neural networks accept their inputs in specific formats, 3D geometry information has to be in the related formats before passing them as a parameter to the artificial neural networks. A two dimensional convolutional neural network does not accept input in one or three dimensions, which is an example to that case. However, because the 3D geometry information is stored in point clouds and polygon meshes most of the time which are stored in one dimension in an irregular way, the data has to be converted to a format which is meaningful to a neural network. This conversion must preserve most or all of the information the 3D geometry contains and it has to be optimal in terms of memory/time complexity because 3D geometry information contains a lot of features. Decrease in the polynomial degree decreases both the learning time and the testing time of the neural network drastically. \\ In the first two chapters of this work, completion of missing parts of the 3D shape is done using Multilayer Spherical Depth Parameters with convolutional neural networks, and the resulting images is converted to the 3D space. Processing time complecity of the multilayer spherical depth parameters is O(n^2), which is a lot efficient and having better performance than the traditional O(n^3) time complexity approaches like 3D occupancy maps. Here the n term implies the number of possible samples in each of the axes. In an nxnxn voxel map there are n^3 possible samples while in a 2D nxn image, there are n^2 possible samples. Number of samples can be different than the number of possible samples. Some of the pixels and voxels may not store information. Our method is also comparable to the O(n^2) state of the art approaches. Because the inpainting will take place in 2D image space, the methods going to be used will be 2D image processing and computer vision techniques. Multilayer spherical depth parameters were inpainted with a U-Net based regression network. The results of that approach were also analyzed and compared to a state of the art 3D shape inpainting approach. In the second chapter, multilayer spherical depth parameters were divided into an octree and the convolution operations were applied on that octree representation to reduce the number of operations by eliminating unnecessary details. This way, the inpainting operation has been optimized. In the third and the last chapter, spherical depth parameters were generated by a conditional generative adversarial network and this way, authentic samples of the learned classes has been generated.