PolyNet: Polynomial Neural Network for 3D Shape Recognition with PolyShape Representation

TL;DR

PolyNet introduces a novel polynomial neural network architecture with a specialized polygon mesh representation, PolyShape, to improve 3D shape recognition by effectively handling mesh variations and aggregating features.

Contribution

The paper proposes PolyNet with polynomial convolution and polygonal pooling, addressing mesh variation challenges and enhancing 3D shape recognition accuracy.

Findings

Outperforms existing polygon mesh-based methods in classification tasks

Demonstrates robustness to vertex permutations and degree variations

Effective in 3D shape retrieval and graph-based image classification

Abstract

3D shape representation and its processing have substantial effects on 3D shape recognition. The polygon mesh as a 3D shape representation has many advantages in computer graphics and geometry processing. However, there are still some challenges for the existing deep neural network (DNN)-based methods on polygon mesh representation, such as handling the variations in the degree and permutations of the vertices and their pairwise distances. To overcome these challenges, we propose a DNN-based method (PolyNet) and a specific polygon mesh representation (PolyShape) with a multi-resolution structure. PolyNet contains two operations; (1) a polynomial convolution (PolyConv) operation with learnable coefficients, which learns continuous distributions as the convolutional filters to share the weights across different vertices, and (2) a polygonal pooling (PolyPool) procedure by utilizing the multi-resolution structure of PolyShape to aggregate the features in a much lower dimension. Our experiments demonstrate the strength and the advantages of PolyNet on both 3D shape classification and retrieval tasks compared to existing polygon mesh-based methods and its superiority in classifying graph representations of images. The code is publicly available from https://myavartanoo.github.io/polynet/.