# 3D Model Identification Using Weighted Implicit Shape Representation and Panoramic View
## 2 Related Work  
Several researches have been conducted to group 3D models into corresponding categories by matching the features and comparing the similarities of the models [5; 6; 7; 8; 9; 10; 11; 14; 19; 20; 21; 22]. The matching and comparison are implemented on a huge dataset containing various models of different poses and shapes. The models are mainly classified into two types: rigid models and non-rigid (deformable) models. Early works are rigid model-based approaches. In this paper, we focus on the identification of non-rigid models. 3D model identification methods are classified into two categories: view-based and model-based methods [6; 7]. Model based methods include geometric moment [19], volumetric descriptor [20], surface distribution [21], surface geometry [22]. However, the geometry and topology based methods are generally computationally cost and are fragile to 3D model removal. View-based methods have a high discriminative property for 3D model representation [5; 6; 7; 8; 9; 10; 11]. A 2D view image is a range image obtained from a viewpoint located on a 3D model's bounding sphere. After the range image is obtained, image processing technologies are applied to the range image for extracting features. To be invariant against geometrical transformation, researchers proposed shape normalization methods to preprocess the 3D models before extracting the features. Several view-based methods have been proposed. In Ref. [9], authors proposed a view based 3D model retrieval method using the SIFT and a bag-of-features approach. The bag-of-features was inspired by the bag-of-words in the text retrieval approach, which classifies documents by histograms of words in the text. The method extracted SIFT features from the range images of the model viewed from dozens of viewpoints located uniformly around the model. The bag-of-features was composed of the SIFT features. The well-known k-means clustering algorithm was applied to the bag-of-features to classify the features and generate visual words. The visual words are integrated in to a histogram and become a feature vector of the model. However, the large number of the range images leads to large capacity of features and slow matching speed. In [10; 11], authors proposed 3D model descriptors using the panoramic views which can describe the orientation and position of the model's surface. In [10], the panoramic views were obtained by projecting the model to surfaces of cylinders parallel to three principal axes. The principal axes were obtained by using continuous PCA and normal PCA. For each cylinder, the coefficients of 2D discrete Fourier transform and 2D discrete wavelet transform were extracted to generate the 3D shape descriptors. However, these descriptors are not suitable for distinguishing the 3D models well. In [11], the axes were perpendicular to the surfaces of a dodecahedron generated around the model. Three panoramic views were obtained from each axis. The other two panoramic views were obtained from additional two axes which are orthogonal to each other and to the principal axis. Then, the SIFTfeatures were extracted to generate the 3D model descriptors. However, because of using dozens of panoramic views, the method leads to large capacity of features and slow matching speed. In [8], authors normalized the model with the PCA and extracted 18 views from the vertices of a bounding 32-hedron of the model. The 3D model descriptors were composed of 2D Zernike moments, 2D Krawtchouk moments and coefficients of Fourier transform. However, the PCA is fragile to partial removed and deformed models, which means the PCA can't extract the same axes from the deformed and removed models as those of original models. Hence, the different axes lead to different views and descriptors. Eventually, the method can't identify the deformed and partial removed versions of the original models. In [13], authors proposed a shape normalization method for 3D volumetric models using ISR.