# 3D Model Identification Using Weighted Implicit Shape Representation and Panoramic View
## 1 Introduction  
Development of 3 dimensional (3D) printing technology has led to the explosive growth of 3D models recently. Hence the 3D printing services are increasing rapidly [1; 2]. However, copyright infringement of 3D models has become an issue for 3D printing ecosystem of product distribution websites, 3D scanning and design-sharing [3; 4]. To prevent the copyrighted 3D models from distributing and using illegally, the identification of 3D models remains.  
2 dimensional (2D) view-based 3D model identification has a high discriminative property for 3D model representation [5; 6; 7; 8; 9; 10; 11]. Generally, a 2D view image is a range image obtained from a viewpoint located on a 3D model's bounding sphere. The identification is implemented by matching the features extracted from the range images. However, the existent approaches suffer from big size of features and slow matching speed. To overcome these problems, we propose an approach using only one range image, which means a panoramic view is used for identification. The panoramic view bridges the gaps between the range images rendered from multiple views. It is obtained by projecting a 3D model onto the surface of a cylinder, which is parallel to a principal axis determined by 3D shape normalization. The purpose of the 3D shape normalization is to normalize 3D models into a canonical coordinate frame to guarantee a unique representation [12; 13; 14]. Nevertheless, how to determine the principal axes is the keypoint. The most common method is principal component analysis (PCA). However, it is not preferable when 3D models have unobvious orientations or undergo large deformations. If the shape normalization cannot determine the principal axes of a query model as similar as those of original model in database, the identification needs many more range images to match them. Implicit shaperepresentation (ISR) was described in [13] for normalizing 3D articulated models. However, it has some limitations when some parts of a 3D model are removed or when a 3D model undergoes a large deformation. In this paper, the 3D shape normalization uses a weighted ISR (WISR) to reduce the influence caused by shape deformation and partial removal. It estimates the number of clusters based on rate distortion theory [15]. It also shows the most representative part for one viewpoint of the six degree of freedom.  
After the shape normalization, the model is wrapped by the cylinder to generate a range image. The range image is used for providing features of the model. The feature used in our approach is the scale invariant feature transform (SIFT) descriptor [16]. The SIFT is generally used to extract geometric transformation invariant local features from images [17; 18]. It detects interest points called keypoints and assigns orientation information to each keypoint based on local gradient directions. With the SIFT descriptor, object recognition approaches can achieve high performance in feature matching. In this paper, the 3D models are identified by matching the SIFT descriptors of the query model with those in database. In the section of experimental results, we show the comparisons between the precision of identification of the proposed method and those of other methods.