The evolution of mesh denoising techniques: from simple filters to 3D deep learning

In this overview article, you will learn what mesh denoising is, what methods have been used and are being used to eliminate noise on polygonal meshes (from classic filters to advanced graph neural networks), and get a general idea of the development of the direction.

Why do you need mesh denoising?

3D- . , ? Twin3d ( ) 3D-, . , , //. , .

3D- . reverse engineering CAD- , . CAD-, — , , , . , .

3D-, , mesh denoising. smoothing, «». 3D- , , . 3D-? , .

- … , (Laplacian smoothing, Taubin smoothing).

Laplacian smoothing

2003 Bilateral mesh denoising – ( 2D ) . – , : , . 7 , (Bilateral normal filtering for mesh denoising), .

Bilateral Normal Filtering :

$n_i ^ k = \ Lambda (\ sum_ {f_j \ in N_i} A_jW_s (|| c_i-c_j ||) W_r (|| n_i-n_j ||) n_j),$

N_i — f_i , n_j — f_j , A_j — f_j , c_j — f_j ( ), $W (x) = exp (-x ^ 2 / (2 \ sigma ^ 2))$ — , $\ Lambda$ — .

, . W_s (x) — f_i f_j — , . W_r (x) , , . A_j

2015 Guided Mesh Normal Filtering, .

? , , . 3D- , .

mesh denoising, . , , Mesh Denoising via L0 minimization , . , – CAD- .

mesh denoising

2016 Mesh Denoising via Cascaded Normal Regression, . , noisy ground truth (GT) 3D- ( ).

(Synthetic) (Kinect v1, Kinect v2, Kinect Fusion). Synthetic noisy ( ). , . GT Artec Spider c , Microsoft Kinect.

Examples from the dataset

– noisy ground truth GT . – . , . , . , .

Cascaded Normal Regression Pipeline

? -, . -, . , . , mesh denoising.

NormalNet: Learning based Guided Normal Filtering for Mesh Denoising. – , Guided Mesh Normal Filtering. (voxel – ), CNN. .

NormalNet pipeline

NormalNet. CNN 4- , , . () — . ResNet, , . . , .

CNN architecture in NormalNet — CNN NormalNet

, CNN , Guided Normal Filtering, . , Guided Normal Filtering.

, DNF-Net: a Deep Normal Filtering Network for Mesh Denoising . , end-to-end . ResNet , .

DNF-Net architecture — DNF-Net

DNF-Net : . multi-scale feature embedding unit . . (. ) , ( ). F .

Multi-scale Feature Embedding Unit

residual learning unit . KNN (K-Nearest Neighbors) k . k . “” .

Residual learning unit

, , “” . , , .

, — , .. , “” .

Deep learning

, , . , - . 3D DL : .

, Mesh Denoising with Facet Graph Convolutions end-to-end pipeline , (, ) – , . — .

Facet Graph Convolution pipeline

U-Net, , .

Graph Convolution Network Architecture — Graph Convolution Network

Convolution graph

U-Net ( ), .

, 3D . - , -: , .

mesh denoising, , , , , ( ), .

Twin3d , mesh denoising . , ;)

All Articles