1. Summary

Published in TVCG 2021 Periodical
One sentence introduction ： Generate a point cloud Turn into To solve the problem of topology expression learning .

2. motivation

Feature capture ： Use a hierarchical hybrid model = Self-attention + Tree Structure
generator ： Unsupervised approach

3. Method

3.1 The overall framework ：

The generation model consists of two modules ：OGC + SAG

OGC：2 individual BAN Module to sample the generated $Z$ + $\varphi$ Function to adjust the information inherited from child nodes . Just a few basic diagram structures .

SAG： Self attention mechanism module based on graph network

Benefit from the structure diagram in essence + Self monitoring mode

3.2 OGC In the block BAN modular ：

BAN： branching and adjustment Network.

Graph initialization

BAN Definition ： The following figure on the left

Preliminary figure initialization BAN Defined as formula （1）

${\varphi }_{\alpha }$ ${\varphi }_{\beta }$ It is used to adjust the weight of information inheritance , ${\mathbf{W}}_b$ Is a learnable matrix .
be-all $\varphi$ Function is used to MPL Realization .
${\mathbf{X}}^{(0)}$: Namely latent code $Z$
${\mathbf{X}}^{(l)}$: At the level $l$ Characteristics of

Graph convolution

It's basically the Laplace convolution of a graph , That is, the Fourier transform of a graph . Normalized Laplace form, such as formula （2）

Define spectrum and convolution kernel ：
In the formula $U$ And triangle symbols fenbieshi $L$ Characteristic matrix and diagonal value of . $f_{\theta }surfaceinsuperginsengCountOfvolumeproduct$

adopt Chebyshev Polynomials can be rewritten as formulas （4）：
${\lambda }_{max}$: $\mathbf{L}$ The eigenvalues of the
${\mathbf{P}}_k$: $K$ rank Chebyshev The second of polynomials $k$ term

In order to smooth the convolution , here Think $\frac{2}{{\lambda }_{max}}\mathbf{L}$ near $\mathbf{I}_N $. according to [13], ${\lambda }_{max}=2$.
Therefore, the formula can be simplified （4） It's a formula （5）：

therefore , This gives a generalized version of the spectral convolution , Defined as the following formula ：

${\mathbf{A}}_g=\mathbf{A}+{\mathbf{I}}_N$
${\mathbf{D}}_g$: ${\mathbf{A}}_g$ The degree matrix of
$\mathbf{X}\in R^{N\times C}$: Picture signal , there C Is the number of input channels .

3.3 SAGN：

attention modular ：

In fact, it is to enhance the weight of graph features .

self-attention The score is defined as The formula 7：

among $\sigma$ yes tanh Activation function ,$Z_G$ Spectral convolution , Definition such as formula 6：

The degree matrix ：${\mathbf{A}}_g=\mathbf{A}+{\mathbf{I}}_N$, ${\mathbf{D}}_g$
Picture signal ：$\mathbf{X}\in {\mathbb{R}}^{N\times C}$, among $C$ Is the number of input channels

Dynamic graph learning ：

according to self-attention ${\mathbf{S}}_G$ To enhance the initialization weight , As formula 8

SGAN Module left branch , The following figure left ：

SGAN Module right branch branch, The following figure to the right ：

SGAN Output module ：

there ${\varphi }_3$ and ${\varphi }_4$ use MLP.

3.4 Training

Basically is WGAN Training mode , In this paper, penalty term and normalization term are introduced .

4. experiment

See the effect of generating tasks ：

Visualization ：

Difficult sample analysis ：

Ablation Experiment ： It shows that the punishment gradient can promote the collapse of the potential model of network customer service .

5. Discuss

It can be understood as the design and processing of an extended framework from image to point cloud .