Results and discussion

In this section, we implement the proposed HPYPGGM algorithm on the challenging Change Detection dataset [70] which consists of 31 videos categorized into 6 differ- ent categories (baseline, shadows, dynamic background, intermittent object motion, camera jitter, and thermal). To evaluate the efficiency of the proposed model, we consider six videos of the Change Detection dataset which are described as follows:

• Pedestrians: This video sequence shows pedestrians walking in a park. • Office: This video sequence shows a person walking around in an office. • Library: This thermal video sequence shows a person walking in the library. • Corridor: This thermal video sequence shows a person walking in the corridor. • Canoe: This video sequence shows a moving canoe in a dynamic background. • Badminton: This video sequence shows players playing badminton.

Sample images from the videos can be found in Fig. 11. In our experiments, we initialize threshold Υ = [0.55, 0.75] for different videos. Our results for each of the

(a) Pedestrians. (b) Office. (c) Library.

(d) Corridor. (e) Canoe. (f) Badminton.

Figure 11: Sample frames of the video sequences from Change Detection dataset.

video sequences can be observed in confusion matrix form in Fig. 12. We evaluate the classification measure by accuracy, recall and precision which are defined as accuracy = (TP + TN)/Total no of observations, recall = TP/(TP + FN) and precision = TP/(TP + FP) where TP, TN, FP, and FN represent the total number of true positives, true negatives, false positives, and false negatives respectively. The reported results of precision and recall are based on the macro averages of the overall frames.

(a) Pedestrians. (b) Office. (c) Library.

(d) Corridor. (e) Caneo. (f) Badminton.

We compare our results with four other approaches from the literature; namely, K-means, GMM, variational GMM (VGMM) and Dirichlet process GMM (DPGMM). We set the number of components to 6 for K-means, GMM, VGMM and DPGMM. The threshold Υ is set to the same value as HPYPGGM for a fair comparison between the models. A visual comparison of the results from all the video sequences can be observed in Fig. 13 and Table 4 shows the comparison of the proposed HPYPGGM against K-means, GMM, VGMM and DPGMM. We can observe in the Pedestrians video sequence, that our model performed better in classifying between the back- ground and foreground pixels while the others misclassified most of the background with foreground pixels. In the Office video sequence, K-means, GMM, VGMM and DPGMM were not able to precisely distinguish between the background and fore- ground pixels. This may be due to the close color intensity of the person’s jeans with the color intensity of the box next to him. Nonetheless, HPYPGGM was able to segment a better foreground compared with the other models. All the models performed better in the Library video sequence where the background pixels are dark with perfect illumination, thereby resulting in a high accuracy with a supporting high precision and recall for all the models. In the Canoe video sequence all the models misclassified background water with foreground. However, HPYPGMM was able to give a better classification between the background and the foreground pixels. This can be observed clearly in Fig. 13. Similar results were obtained in the Badminton video sequence. Table 4 shows that the proposed HPYPGGM model outperformed K-means, GMM, VGMM and DPGMM in most cases in terms of precision, recall and accuracy.

Table 4: The macro average results of background subtraction with the Change De- tection dataset.

Model Precision (%) Recall (%) Accuracy (%) Pedestrians K-means 67.30 73.11 96.48 GMM 60.12 73.42 94.02 VGMM 57.21 71.60 92.31 DPGMM 67.48 65.33 93.33 HPYPGGM 77.31 69.10 97.64 Office K-means 67.51 65.23 90.52 GMM 56.10 60.40 81.30 VGMM 58.92 65.11 81.51 DPGMM 89.48 87.12 87.21 HPYPGGM 93.31 65.20 94.05 Library K-means 98.97 96.02 98.04 GMM 98.56 96.01 98.06 VGMM 98.61 96.30 98.09 DPGMM 98.48 98.13 98.09 HPYPGGM 99.01 96.31 98.72 Corridor K-means 92.31 62.01 84.22 GMM 94.12 76.89 90.25 VGMM 95.23 78.12 83.50 DPGMM 94.48 93.21 93.01 HPYPGGM 96.01 83.51 93.43 Caneo K-means 80.10 78.26 93.22 GMM 76.82 77.12 92.59 VGMM 71.13 77.23 90.64 DPGMM 93.10 74.42 93.46 HPYPGGM 97.01 74.51 95.66 Badminton K-means 61.12 72.51 95.22 GMM 57.51 74.12 93.52 VGMM 57.12 74.71 93.50 DPGMM 66.48 65.47 94.73 HPYPGGM 66.01 66.52 97.40

Figure 13: The foreground mask results for each of the original images (Pedestrians, Office, Library, Corridor, Caneo and Badminton from top to bottom respectively) obtained by K-means, GMM, VGMM, DPGMM and HPYPGMM algorithms are shown in columns 1 to 5 respectively.

Chapter 5

Conclusion

Clustering algorithms have been broadly applied in many research areas such as com- puter vision, signal processing, and pattern recognition. A mixture model, one of the most predominant statistical techniques, clusters data into a collection of homoge- neous groups. Gaussian distribution has been widely used and studied with success for many applications involving computer vision, machine learning, image processing and statistical analysis. However, in many real applications, Gaussian fails to fit different shapes of data.

In this thesis, first we have presented a variational inference approach for general- ized Gaussian Distribution. The algorithm was based on treating the shape parameter as a variable. Using the single-step update of Newton’s method, the shape param- eter is updated in the VM-step. Experimental results on medical, astrological, and image segmentation applications have shown the effectiveness of the algorithm when compared with the traditional models.

Second, we extended the variational inference approach to the infinite case using Dirichlet process and applied feature selection. Also, by extending the model to infinity with simultaneous feature selection, we were able to detect the number of mixture components and relevant features without the need to specify the number of mixture components a priori thereby resulting in an overall better accuracy. The variational learning approach aided in approximating the posteriors and experimental results have shown that the proposed variational IGGM with feature selection has favorable results compared to standard models.

hierarchical Pitman-Yor process prior for our model. The proposed model tackles the estimation of parameters via variational learning. We inspected the benefits of our approach on video background subtraction using the challenging Change Detection dataset. The experimental results compared with the traditional models as well as the Dirichlet process of Gaussian distributions shows that our nonparametric Bayesian framework performed better over other models resulting in significant outcomes.

In conclusion, when compared with existing models and techniques which are mostly based on Gaussian assumption, our approach’s can model non-Gaussian data with an efficient approximation of the model parameters resulting in better accuracy. Our models were also able to automatically determine the better number of mixture components resulting in overall better performance.

Future work could be dedicated to investigating online variational techniques for our proposed approaches and also extending the proposed models with component splitting. Another potential future work related to video background subtraction can be to modify the pixel based approach into segmenting each pixel of all the frames might lead to better over all performance in terms of classifying foreground and background pixels.

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