# A 2D-View Depth Image- and CNN-Based 3D Model Identification Method
## 1 Introduction
### View-Based 3D Model Similarity Measurement  
Basically, view-based methods for measuring the similarity of 3D models follow the idea that \"if two 3D models are similar, they also look similar from all viewing angles.\" View-based methods convert the three-dimensional task into a two-dimensional task so that it can employ and benefit from the research that has been performed previously for 2D images, like image local features [20; 21; 22] and image processing [23]. In terms of the initial stage of the view-based methods, the most famous is the light field descriptor (LFD) [6]. The LFD method first takes multiple silhouette images from evenly distributed vertices of a dodecahedron over a hemisphere, and the silhouettes are encoded by its Zernike moments and Fourier coefficients. Then, the dissimilarity between the two 3D models is obtained by exhaustively searching the minimum distance of features that are extracted from all possible situations (60 different camera settings). In more recent research based on the LFD framework, many researchers have studied a variety of pose normalization approaches, strategies taking 2D images, and descriptors to improve performance. Pose normalization: Generally, a 3D model has arbitrary position, scale, and orientation. Thus, most view-based methods require a proper pose normalization approach such as preprocessing before taking depth images. Scale and position are usually normalized by transferring the center of mass (average of point coordinates) of 3D models to the origin and scaling the maximum polar distance of the points to a certain value. For orientation, there is principle component analysis (PCA)-based [7; 8; 9] alignment, symmetry-based alignment [10], projection area-based alignment [11], and so on. Among these approaches, the PCA-based alignment approach is most widely used. These approaches could reduce possible alignments of 3D models to decrease the computation cost of view matching. For instance, [PERSON] et al. [9] employed a PCA-based and rectilinearity-based method to align 3D models into 24 possible pose permutations so that they only need compare 24 matching pairs for two models. Strategies using 2D images: There is much research [8; 9; 12; 13; 14; 15] utilizing depth images as views for 3D models instead of simple silhouettes. This is because the silhouette is not suitable for discriminating concave geometries, whereas the depth image is capable of carrying useful 3D geometric information. [PERSON] and [PERSON] [14] utilized both silhouette and depth images to represent a 3D model. With respect to camera settings, the LFD utilized a dodecahedron to set the position of virtual camera, while other authors [8; 9] have tried some different platonic solids (octahedron, icosahedron) and their subdivision to take various numbers of images. [PERSON] et al. [15] represented 3D models as a set of panoramic views by projecting the 3D model to the lateral surface of a cylinder. Descriptors: The elevation descriptor [12] extracts six views that contain the altitude information of the 3D model from six directions. The depth line descriptor [13] extracts depth lines from captured depth images and transforms them into sequences. The difference between depth line descriptors is measured by the dynamic programming method. The compact multi-view descriptor [14] describes each captured view by employing 2D polar Fourier transform, 2D Zernike moments, and 2D Krawtchouk moments. With the great success of the 2D local features in the computer vision field, [PERSON] et al. [8] proposed a view-based method called BF-SIFT, which employs the scale-invariant feature transform (SIFT) [20] with the bag-of-features (BoF) technique [24]. This method first constructs a visual word dictionary (codebook) off-line by k-means clustering of SIFT features extracted from the depth images of 3D models in the training database. Given a 3D model, after taking depth images and extracting SIFT features, the 3D model can be represented by a word histogram that integrates the SIFT features via a codebook.