기존 방법 : predefined geometric features사용 Many previous methods on 3D mesh labeling achieve impressive performances by using predefined geometric features.

문제점 : generalization능력이 약함 However, the generalization abilities of such low-level features, which are heuristically designed to process specific meshes, are often insufficient to handle all types of meshes.

제안 방식 : learn a robust mesh representation that can adapt to various 3D meshes by using CNNs.

절차

• In our approach, CNNs are first trained in a supervised manner by using a large pool of classical geometric features.
• In the training process, these low-level features are nonlinearly combined and hierarchically compressed to generate a compact and effective representation for each triangle on the mesh.
• Based on the trained CNNs and the mesh representations, a label vector is initialized for each triangle to indicate its probabilities of belonging to various object parts.
• Eventually, a graph-based mesh-labeling algorithm is adopted to optimize the labels of triangles by considering the label consistencies.

1. Introducion

3. MESH LABELING VIA CNNS

CNN을 이용하여 효율적인 mesh representations생성 방법 기술 we will present how to learn compact and effective mesh representations by using deep CNNs.

1. First, we extract a large pool of geometric features to form a 2D feature matrix so as to characterize each triangle on the mesh.
2. Second, we present the architecture of the deep CNNs that are used to learn mesh representations from massive feature matrices.
3. Third, we show the details of training the CNNs.
4. Finally, we make a brief description of the mesh label optimizing process.

3.1 Geometric Feature Extraction

In our approach, we aim to learn a compact and effective mesh representation from low-level features.

A. 잘 알려진 7가지 Feature추출

Thus, we first extract seven types of geometric features that are widely used in existing studies,including:

1. curvature (CUR) [Gal and Cohen-Or 2006],
2. PCAfeature (PCA) [Kalogerakis et al. 2010],
3. shape diameter function(SDF) [Shapira et al. 2010],
4. distance from medial surface (DIS) [Liuet al. 2009],
5. average geodesic distance (AGD) [Hilaga et al. 2001],
6. shape context (SC) [Belongie et al. 2002],
7. spin image (SI)[Johnson and Hebert 1999].

While the features are calculated with face areas and different scales in consideration.

These features can well describe the characteristics of each triangle on a mesh from multiple perspectives.

B. Feature 합치기

Given these features, an intuitive solution is to concatenate them into a high-dimensional feature vector (i.e., 600 components in total).

• 단순한 합치기는 오버피팅 문제 유발 However, as suggested inHu et al. [2012]andWang et al.[2012], such simple concatenation will degrade the performance of clustering and may lead to over-fitting due to the high-dimensional descriptor space.
• 오버피팅 문제 해결법 : CNN에 입력으로 사용
  • To address this problem and to fully utilize the convolutional property of CNNs, we reorganize these 600 components to form a 30 × 20 feature matrix (as shown in Figure 1).
  • In this manner, low-level geometric features can be nonlinearly combined and hierarchically compressed through various convolutional operations in CNNs.

In experiments, we will demonstrate that the ordering of features as well as the size of feature matrix only slightly change the accuracy of mesh labeling.