T2-FMOG: Application to Background Modeling

Type-2 Fuzzy Mixture of Gaussians: Application to Background Modeling

Introduction

Background modeling is a key step of background subtraction methods used in the context of static camera. The goal is to obtain a clean background

and then detect moving objects by comparing it with the current frame. Mixture of Gaussians (MOG) [1] [2] is the most popular technique and presents some limitations when dynamic changes occur in the scene like camera jitter, illumination changes and movement in the background. Furthermore, the MOG is initialized using a training sequence which may be noisy and/or insufficient to model correctly the background. All these critical situations generate false classification in the foreground detection mask due to the related uncertainty.

To take into account this uncertainty, we propose to model the background by Type-2 Fuzzy Mixture of Gaussians (T2F-MOG). Results show the relevance of the proposed approach in presence of camera jitter, waving trees and water rippling.

Principle

Each pixel is characterized by its intensity in the RGB color space. So, the observation is a vector in the RGB space. Then, the MOG is composed of K mixture components of multivariate Gaussian as in [1]. Then, we generate the multivariate Gaussian with uncertain mean vector called T2-FMOG-UM and the multivariate Gaussian with uncertain variance vector T2F-MOG-UV.

Experimental Results

We have applied the T2-FMOG-UM and T2-FMOG-UV algorithms to indoor and outdoor videos where different critical situations occur like camera jitter, movement in the background, illuminations change and shadows. The experiments are conducted to compare the results of T2-FMOG with the MOG [1].

Fig. 1 shows the robustness of T2-FMOG for the waving trees (Campus sequence). Fig. 2 shows the robustness of T2-FMOG for the water rippling (Fountain sequence) and water surface (Water Surface sequence). In each case, the T2-FMOG-UM gives the best result followed by the T2-FMOG-UV and the MOG. These different experiments confirm that to take into account the uncertainty using T2-FMOG performs the MOG. Furthermore, the T2-FMOG-UM is more robust than the T2F-MOG-UV.

Fig. 1. The first row shows the original frames for Campus sequence. The second row presents the segmented images obtained by the MOG [1]. The third and the fourth rows illustrate the result obtained using the T2-FMOG-UM and the T2-FMOG-UV respectively.

Fig.2 . The first row shows the original frames for Fountain and Water Surface sequences. The second row presents the segmented images obtained by the MOG [1]. The third and the fourth rows illustrate the result obtained using the T2-MOG-UM and the T2-FMOG-UV respectively.

References

[1] C. Stauffer and W. Grimson, “Adaptive background mixture models for real-time tracking”, IEEE Conference on Computer Vision and Pattern Recognition, CVPR 1999, pp. 246-252, 1999

[2] T. Bouwmans, F. El Baf, B. Vachon, “Background Modeling using Mixture of Gaussians for Foreground Detection: A Survey”, Recent Patents on Computer Science, Volume 1, No 3, pages 219-237, November 2008.

Publication

Journal

T. Bouwmans, F. El Baf, “Modeling of Dynamic Backgrounds by Type-2 Fuzzy Gaussians Mixture Models”, MASAUM Journal of Basic and Applied Sciences, Volume 1, Issue 2, pages 265-277, September 2009.

Conferences

F. El Baf, T. Bouwmans, B. Vachon, “Fuzzy Statistical Modeling of Dynamic Backgrounds for Moving Object Detection in Infrared Videos”, OTCBVS 2009, pages 60-65, Miami, Florida, June 2009.

F. El Baf, T. Bouwmans, B. Vachon, “Type-2 Fuzzy Mixture of Gaussians Model: Application to Background Modeling”, International Symposium on Visual Computing, ISVC 2008, pages 772-781, Las Vegas, USA, December 2008.

Note: My publications are available on Academia, Research Gate, Science Stage and Publication List.

Source

The source is available on resquest at tbouwman at univ-lr.fr.