Date of Award

December 2019

Degree Type


Degree Name

Master of Science


Computer Science

First Advisor

Zeyun Yu

Committee Members

Tian Zhao, Yi Hu


3D Segmentation, Fully Convolutional Network, Graph Convolution, Mesh Segmentation, Segmentation, Surface Mesh


This thesis presents an implementation of a 3-Dimensional triangular surface mesh segmentation architecture named Shape Fully Convolutional Network, which is proposed by Pengyu Wang and Yuan Gan in 2018. They designed a deep neural network that has a similar architecture as the Fully Convolutional Network, which provides a good segmentation result for 2D images, on 3D triangular surface meshes. In their implementation, 3D surface meshes are represented as graph structures to feed the network. There are three main barriers when applying the Fully Convolutional Network to graph-based data structures.

• First, the pooling operation is much harder to apply to general graphs.

• Second, the convolution order on a graph structure is unstable.

• Third, the raw data of surface meshes cannot be directly applied to the network.

To solve these problems, first, all the nodes inside the graph are re-ordered into a 1-dimensional list based on a multi-level graph coarsening algorithm, which allows the pooling operation to be applied as easily as a 1D pooling. Second, a self-defined generating layer is added before each convolution layer in the network to generate the neighbors of each node on the graph, and at the same time, sort all neighbors based on the L2 similarity to keep the convolution operation in a stable manner. Finally, three translation and rotation free low-level geometric features are pre-processed and used as input to train the network. This Shape Fully Convolution Network can effectively learn and predict triangular face-wise labels. In the end, to achieve a better result, the final labeling is optimized by the multi-label graph cut algorithm, which gives punishment to the predicted result based on the smoothness of the surface. The experiments show that the model can effectively learn and predict triangle-wise labels on surface meshes and yields good segmentation results.