Principle of Gaussian mixture Algorithm in opencv

Note: The following content is translated by the author from the International Conference. In view of my limited level, the translation will inevitably be incorrect. Please be more inclusive.

Original:

An Improved Adaptive Background Mixture Model for real-time tracking with shadow detection; p. kaewtrakualpong, R. Bowden; In Proc. 2nd European workshop on advanced video based surveillance systems, avbs01. Sept 2001

Abstract:

Real-time moving target detection for continuous video sequences is the basis of many computer vision applications. A common method is the background subtraction method. Therefore, researchers have also proposed many background modeling methods to deal with various problems in the background subtraction method. One of the more successful methods is the multi-channel Adaptive Background Modeling method proposed by Grimson and so on for each pixel. However, this method must endure the slow background model learning process in the initial stage, which is even worse for complex backgrounds. In addition, this method cannot distinguish between motion shadows and moving targets. This paper proposes an improved method for Adaptive Background Modeling. Through a re-Study of (model) Update variance, we found that different update variance can be used at different stages. In this way, our system can learn faster and more accurately. At the same time, our system can adapt to environment changes better. In addition, this paper also proposes a method for shadow detection. It uses our background model for Color Space estimation to implement (shadow detection. In addition, this article provides a comparison and test of the two algorithms. The comparison results show that our algorithm is superior to Grimson in terms of learning speed and accuracy. If we combine the new shadow detection method in this article, our method will be far better than the Grimson algorithm.

1. Introduction:

The background subtraction method is used to construct a reference image (pure background), subtract each new video frame from the reference image, and perform binarization to obtain the moving foreground. This means that the result of the Background Subtraction Method is a highlighted representation of non-static areas. The simplest way to build a reference image is to average a series of consecutive background images over time. This method has many problems. At the same time, it also requires a sequence of images with no foreground appearance but a pure background as a training sample. After training, the background movement and the rest of the foreground in the training phase are regarded as the moving target. In addition, this method cannot cope with the gradual change of light in the scenario. Such problems indicate that any solution must take into account the continuous update (reevaluation) process of the background model. Many Adaptive Background modeling methods have been proposed for the process of changing signals. In this paper, Friedman and Russell propose to construct three Gaussian distribution adaptive hybrid parameter models for each pixel in the scenario. In addition, they provided a brief discussion about online update equations using large volumes of statistical data. Koller uses the Kalman filter to track the background illumination changes of each pixel. They adopted a selective strategy to introduce possible background pixels into the background update equation for background maintenance and updating. This method can well cope with changes in light. However, it cannot be processed when a new target enters the scene or when a new target leaves the scene. One solution is to create a multi-channel background model for each pixel. Grimson and other methods use a non-parametric adaptive Gaussian mixture model to solve this problem. Their models can also solve small and repetitive movements, such as the shaking of trees, the floating of dwarf trees, and the tiny vibrations of cameras. Elgammal uses a kernel method for each pixel to estimate and update the background. The kernel sample (kernel examplars) is obtained through a mobile window. They adopted a method called "spatial consistency" to reduce the problems brought about by tiny moves. This method is calculated by comparing the circular connected areas around the (current frame) and the background model (corresponding position. Despite the many methods proposed by the author to accelerate computing, the calculation of the algorithm itself is still very complex. Other advanced processing methods (image processing ?) The method to assist in Background Modeling was also proposed by researchers. Our method is based on the Grimson algorithm framework. The difference is that the update equation and the initialization method are different, and a shadow detection method is introduced.

A common optimization method for Gaussian mixture model is the EM (expectation maximisation, maximum expectation) algorithm. The EM algorithm is an iterative method that ensures convergence to the local maximum value in the search space. Considering the time domain and airspace requirements during background image maintenance, an online EM algorithm is required. Many online em algorithms have been studied. They can be roughly divided into two types: the first type is to use probability density functions for parameter estimation. In other words, we use new data to update previous (parameter) estimates without changing the previous model structure. This process was proposed by nowlan and explained based on the findings of Neal and Hinton. Traven proposes a process for n recent Windows versions (n most recent window version) to solve the parameter estimation problem ). McKenna and others extended the Traven method to use the running results of the L batch em to form the latest Windows version and use it for multi-channel foreground target tracking. This method cannot run effectively without good initial estimates. The second type is non-parameter methods. Priebe et al. proposed to use the random threshold value to generate a new Gaussian Kernel for the existing Gaussian mixture model to obtain an adaptive Gaussian Model. Grimson and stauffer use a fixed threshold.

In addition to Grimson and others, many other researchers have also proposed creating a hybrid model for each pixel in the scenario. Rowe and Blake proposed to Apply batch em algorithms to offline training in the virtual image space. However, their background modeling method is not updated with the passage of time. Therefore, this method will become ineffective when the light in the scene changes over time. Friedman and Russell perform Gaussian mixture modeling for each pixel in the scenario. The model for each pixel is composed of three Gaussian distributions, which are applied to roads, shadows, and vehicle distributions. Pattern classification is a heuristic Calculation Method Based on Brightness space correlation distance. With enough statistical rules, their method achieves better (prospective) segmentation. However, this still requires a preprocessing initialization process, which uses the batch EM algorithm to provide an initial background model.

In section 2.1, we will introduce the background model algorithms of Grimson and stauffer. The solution we provide is described in section 2.2. Section 2.3 describes our shadow detection algorithm. The results of each method and the comparison tests between the results will be presented in section 3rd. Section 4th provides the conclusion of this article.

2. Background Modeling

In this section, we will discuss the work of Grimson and stauffer and the shortcomings of their proposed algorithms. The authors propose to construct a background model by combining K (with a value of 3-5) Gaussian distribution for each background pixel. Different Gaussian distributions represent different color channels. The coefficients of K Gaussian distribution combinations represent the time ratio of a color distribution in the current scenario. Unlike the Friedman method, assuming that the background contains B colors that are most likely, the entire background component is determined by B colors. The most likely colors are those that last for a long time and remain static. A static monochrome target tends to form a firm clustering in color space, while a moving target has different reflectivity because different parts of the target are displayed in the image during the moving process, so that it tends to form a loose clustering in the color space. In the author's paper, there is a method called fitness to measure this feature. In order to adapt the background model to the variation of light, and to ensure the real-time operation, the author adopted a selective (background model) Update strategy. The fitness between each new pixel value and the background model is calculated once and sorted accordingly. The most matched Gaussian component will be updated. If no Gaussian component is matched, a Gaussian component will be added, and the mean value of the newly added Gaussian component will be the color, assign it a large covariance matrix and a small weight coefficient.