# Cube of Space Sampling for 3D Model Retrieval
## 2 Literature Review
### Model-Matching Methods  
Previous research in model-matching methods can be classified broadly into: feature-based; graph-based; and other methods [1].  
* Feature-based: previous feature-based research can be divided into: global features; global feature distribution; spatial maps; and local features. Feature-based model matching represents features of a model using a single descriptor consisting of a d-dimensional vector of values, where the dimension (\(d\)) is fixed for each model. 1. Global features: [PERSON] and [PERSON] [8] extracted global features such as volume, area, statistical moments, and Fourier transform coefficients efficiently. [PERSON] et al. [9] applied bounding boxes, cord-based, moment-based and wavelet-based descriptors for 3D shape matching. [PERSON] et al. [10] described a reflective symmetry descriptor as a 2D function associating a measure of reflective symmetry to every plane (specified by two parameters) through the model's centroid. Since these methods only used global features to characterize the overall shape of the objects, they could not describe objects in detail, but their implementation was straightforward [1].
2. Global feature distribution: [PERSON] et al. [11] introduced and compared shape distributions, which measured properties based on distance, angle, area and volume measurements between random surface points. [PERSON] et al. [12] investigated shape histograms that were discretely parameterized along the principal axes of the inertia of the model. [PERSON] et al. [13] investigated the application of shape distributions in the context of CAD and solid modeling. However, they often performed poorly when they needed to distinguish between shapes having similar gross shape properties but significantly different detailed shape properties [1].
3. Local features: [PERSON] and [PERSON] [14] described the 3D Shape Spectrum Descriptor, which was defined as the histogram of shape index values, and calculated over an entire mesh. The shape index, first introduced by [PERSON] [15], was defined as a function of the two principal curvatures on continuous surfaces.
4. Graph-based: graph-based methods can be roughly divided into three categories according to the type of graph used, which are: model graphs; Reeb graphs; and skeletons [1, 16].  
In skeletons, the focus is on skeletal graph matching with node-to-node correspondence based upon the topology and radial distance about the edge [14].  
For Reeb graphs, mathematically, they are defined as the quotient space of a shape (S) and a quotient function (\(f\)). [PERSON] et al. [17] compared Reeb graphs obtained by using different quotient functions and highlighted how the choice of f determines the final matching result.  
The advantages of graph-based methods include the fact that that they are good at capturing shape features, which are relatively high-level and natural, meaning graph-based methods can support local and multi-resolution retrieval. In addition, they are robust when the model has a detailed level of structure. However, the drawbacks include the fact that they are computationally expensive, sensitive to noise and difficult to index and match [16].
* Other methods: other methods, such as view-based similarity, assumes that two 3D models are similar. In particular, the level of similarity between 3D models is judged by different viewing results [17; 18]. For example, LightField Descriptor is one of many outstanding 3D model feature descriptors. On the other hand, [PERSON] and [PERSON] [19] introduce a geometry similarity approach to 3D shape matching, which is based on calculating the volumetric error between one object and a sequence of offset hulls of the other objects. Another approach is weighted-point set-based similarity, where shape descriptors consist of weighted 3D points [20].