## Hussein Kanaan* and Alireza Behrad*## |

Class name | Correct classification rate (%) |
---|---|

Airplanes | 70.0 |

Ants | 100 |

Birds | 62.5 |

Crabs | 80.0 |

Chairs | 100 |

Cups | 100 |

Dinosaurs | 87.5 |

Dolphins | 100 |

Fishes | 80.0 |

Four-limbs | 83.3 |

Hands | 50.0 |

Humans | 75.0 |

Octopus | 70.0 |

Pliers | 100 |

Snakes | 100 |

Spectacles | 84.6 |

Spiders | 76.1 |

Tables | 71.4 |

Teddy-bears | 100 |

All classes | 83.7 |

Table 2.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1. Airplane | 0.70 | - | 0.20 | - | - | - | 0.10 | - | - | - | - | - | - | - | - | - | - | - | - |

2. Ants | - | 1 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

3. Birds | - | - | 0.63 | - | - | - | - | - | - | - | 0.13 | - | 0.13 | - | 0.13 | - | - | - | - |

4. Crabs | - | - | - | 0.80 | 0.05 | - | - | - | - | - | 0.05 | - | - | - | 0.10 | - | - | - | - |

5. Chairs | - | - | - | - | 1 | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

6. Cups | - | - | - | - | - | 1 | - | - | - | - | - | - | - | - | - | - | - | - | - |

7. Dinosaurs | - | - | - | - | - | - | 0.88 | - | - | 0.13 | - | - | - | - | - | - | - | - | - |

8. Dolphins | - | - | - | - | - | - | - | 1 | - | - | - | - | - | - | - | - | - | - | - |

9. Fishes | - | - | - | - | - | - | 0.20 | - | 0.80 | - | - | - | - | - | - | - | - | - | - |

10. Four-limbs | 0.08 | - | - | - | - | - | 0.09 | - | - | 0.83 | - | - | - | - | - | - | - | - | - |

11. Hands | - | - | - | - | - | - | - | - | - | - | 0.50 | 0.20 | 0.10 | 0.10 | 0.10 | - | - | - | - |

12. Humans | - | - | - | 0.08 | - | - | 0.08 | - | - | - | 0.08 | 0.75 | - | - | - | - | - | - | - |

13. Octopus | - | 0.10 | - | - | - | - | - | - | - | - | 0.20 | - | 0.70 | - | - | - | - | - | - |

14. Pliers | - | - | - | - | - | - | - | - | - | - | - | - | - | 1 | - | - | - | - | - |

15. Snakes | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 1 | - | - | - | - |

16. Spectacles | - | - | - | - | - | 0.08 | - | - | - | - | - | - | - | 0.08 | - | 0.85 | - | - | - |

17. Spiders | - | - | - | 0.05 | - | - | - | - | - | - | - | - | 0.19 | - | - | - | 0.76 | - | - |

18. Tables | 0.14 | - | - | - | 0.14 | - | - | - | - | - | - | - | - | - | - | - | - | 0.71 | - |

19. Teddy-bears | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 1 |

Table 3.

With the sparse representation | Without the sparse representation | |
---|---|---|

Percentage orrect classification | 83.7 | 77.3 |

To show the effectiveness of the proposed algorithm, we also compared the results of the proposed algorithm on the MSB database with those of method of Atmosukarto et al. [16]. This method uses the histogram of low-level features like Besl–Jain and Gaussian curvatures for salient point extraction. Salient points are then transformed into a 2D longitude-latitude spatial map as a descriptor to classify 3D models. Fig. 7 illustrates the correct classification rate of method of Atmosukarto et al. [16] on the MSB database using K nearest neighbors (KNN) classifier with various K values. The results of Fig. 7 show the maximum correct classification ratio of 65.47% for K=1. Table 4 illustrates the confusion matrix for the classification of 3D objects in the MSB database using Atmosukarto et al. method. A comparison between the results of Tables 2 and 4 shows the effectiveness of the proposed algorithm.

Table 4.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1. Airplane | 0.80 | - | - | - | - | - | - | - | 0.10 | - | - | - | - | - | - | - | - | 0.10 | - |

2. Ants | - | 0.64 | - | 0.07 | - | - | - | - | - | - | - | 0.28 | - | - | - | - | - | - | - |

3. Birds | 0.22 | - | 0.44 | - | - | - | - | - | - | 0.11 | - | - | - | - | - | 0.11 | - | 0.11 | - |

4. Crabs | - | - | - | 0.84 | - | - | 0.08 | - | - | 0.08 | - | - | - | - | - | - | - | - | - |

5. Chairs | - | - | 0.10 | - | 0.40 | - | - | - | 0.10 | - | - | - | - | - | - | 0.10 | - | 0.30 | - |

6. Cups | - | - | - | - | - | 0.83 | - | - | - | 0.08 | - | - | - | - | - | - | - | - | 0.08 |

7. Dinosaurs | - | - | - | - | - | - | 0.76 | - | 0.07 | 0.16 | - | - | - | - | - | - | - | - | - |

8. Dolphins | 0.20 | - | - | - | - | - | - | 0.30 | 0.05 | - | - | - | - | - | - | - | - | - | - |

9. Fishes | - | - | - | - | - | - | - | - | 1 | - | - | - | - | - | - | - | - | - | - |

10. Four-limbs | - | - | - | - | - | - | - | - | - | 1 | - | - | - | - | - | - | - | - | - |

11. Hands | - | 0.20 | - | - | - | - | - | - | - | - | 0.30 | 0.10 | - | - | - | - | 0.40 | - | - |

12. Humans | - | - | - | - | - | - | - | - | - | - | - | 0.81 | - | 0.09 | - | - | 0.09 | - | - |

13. Octopus | - | - | - | - | - | 0.08 | - | 0.08 | - | 0.16 | - | 0.08 | 0.33 | 0.16 | - | - | 0.08 | - | - |

14. Pliers | - | - | - | - | - | - | - | - | - | - | - | - | - | 0.80 | - | 0.20 | - | - | - |

15. Snakes | 0.16 | 0.16 | - | - | - | - | - | - | 0.16 | - | - | - | - | - | 0.33 | - | - | 0.16 | - |

16. Spectacles | 0.08 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 0.91 | - | - | - |

17. Spiders | - | - | - | - | - | 0.07 | 0.07 | 0.07 | - | 0.35 | - | 0.07 | - | - | - | - | 0.35 | - | - |

18. Tables | - | - | - | - | - | - | - | - | 0.40 | - | - | - | - | - | - | - | - | 0.60 | - |

19. Teddy-bears | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 1 |

Fig. 8 shows the correct classification rate of the proposed algorithm on the PSB database. SVM classifiers with linear kernel function are experimentally used in this experiment as well. Fig. 8 illustrates the percentage of correct classification for the various dimensions of the sparse representation, i.e., k values. In this experiment, 907 objects are used to train the classifiers as well as obtaining the dictionary for sparse representation. The 907 remaining objects are also utilized to test the proposed algorithm. The results of Fig. 8 demonstrate that the maximum allowable dimension of sparse representation, i.e., k=907, results in the maximum percentage of correct classification.

Table 5 shows the correct classification rate of the proposed algorithm on the PSB database with and without applying the sparse representation stage on intermediate features. The results of Table 5 show that the sparse representation of intermediate features increases the correct classification rate of the proposed algorithm up to 16.99%.

Table 5.

With the sparse representation | Without the sparse representation | |
---|---|---|

Percentage orrect classification | 85.9 | 68.91 |

We also compared the results of applying the proposed algorithm on the PSB database with the methods of Bu et al. [18] and Hamid and Nakajima [38]. Bu et al. [18] leveraged the geodesics-aware bag-offeatures (GA-BoF) as the initial features. Then DBNs were used for dimensionality reduction and 3D shape classification. They also reported the results of shape classification using GA-BoF features and some of other dimensionality reduction algorithms such as PCA, multidimensional scaling (MDS), linear discriminant analysis (LDA), and locally linear embedding (LLE) algorithms. Table 6 compares the results of the proposed algorithm on the PSB database with GA-BoF features with DBNs and some other dimensionality reduction algorithms as well as the method of Hamid and Nakajima [38]. The results of this table demonstrate the higher performance of the proposed algorithm.

Table 6.

Algorithm | Percentage of correct recognition |
---|---|

GA-BOF | 71.4 |

PCA | 76.5 |

MDS | 77.1 |

LDA | 72.5 |

LLE | 73.7 |

DBN | 85.1 |

Hamid and Nakajima [38] | 70.05 |

Proposed method with 9 views | 85.9 |

Proposed method with 20 views | 89.7 |

This study reports a new approach for 3D shape recognition using 3D local features of model views. In comparison with the existing view-based approaches that mostly extract the silhouette of 3D models, we consider the distances of the points from the center of mass of a 3D model as the intensities of the pixels of extracted views. Then, we use Gabor-based filters to extract proper features for shape classification. To take into account the relationships between various views, we use a new approach for 3D local feature extraction by the construction of view cubes. Additionally, we describe intermediate features in the sparse domain to enhance the accuracy of classification.

Experimental results on both the PSB and MSB databases demonstrate the effectiveness and higher performance of the proposed method on the classification of 3D objects. Additionally, the comparisons of the results generated by the proposed method with those of other state-of-the-art approaches show that more reliable results could be obtained using the proposed method.

The experimental results also show that the sparse representation of intermediate features increases the accuracy of the proposed algorithm. Our experiments using SVM classifiers with a radial basis function (RBF) as a kernel demonstrate that the correct classification rate decreases with an RBF kernel function. This effect shows that the sparse representation of intermediate features makes them linearly separable.

According to the results obtained by the proposed approach, the increase in the number of coefficients for the sparse representation enhances the performance of the proposed approach. In the proposed approach, we experimentally used the maximum number of allowable coefficients in the training phase, i.e., the number of intermediate features of shape models. This effect indicates the scalability for the proposed algorithm, because by increasing the number of classes and shape models it is possible to increase the number of coefficients for the sparse representation.

He received the B.S. degree in biomedical engineering in 2008. In 2012, he received the M.S. degree in communication engineering from Shahed University, Tehran, Iran. He has been working towards the PhD degree in electronic engineering at Machine Vision and Image Processing laboratory of Shahed University, Tehran, Iran, since 2012. His current research interests include 3D object recognition, classification and machine vision.

He received the B.S. degree in electronic engineering from Electrical Engineering Faculty, Tabriz University, Tabriz, Iran, in 1995. In 1998, he received M.S. degree in digital electronics from Electrical Engineering Faculty, Sharif University of Technology, Tehran, Iran. He received Ph.D. degree in electronic engineering from Electrical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran, in 2004. Currently, he is an associate professor of Electrical Engineering Department, Shahed University, Tehran, Iran. His research fields are image and video processing and machine vision.

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