# Adaptive Background Mixture Models for real-time tracking

Source: Internet
Author: User
Real-time tracking of adaptive hybrid background model Chris stauffer W. e.l grimsonbob Kuo Translation: Artificial Intelligence Laboratory of the Massachusetts Institute of Technology, Zhangye City, Ma 02139
If each pixel value is under a specific illumination in a specific scenario, the single Gaussian Model of the pixel will be sufficient, but it will produce some noise. If only the light changes over time, the adaptive single Gauss of pixels is sufficient. In fact, multiple surfaces appear when the cone and light conditions of specific pixels change. Therefore, adaptive multi-Gaussian is required. We use Hybrid Adaptive Gaussian to approach this process. Each time the Gaussian parameter is updated, the Gaussian function is evaluated with a simple inspiration, assuming that it is most likely part of background processing. Gaussian distribution values that do not match any background pixel are grouped by connected components. Finally, the connection component uses a multi-hypothesis tracker to be tracked in the video. 1:
Figure 1: Program Execution. (A) Current image, (B) the most likely background model's Gaussian average value image, (c) Foreground pixel, (d) the current image with overlapping tracking information. Note: In this example, the shadow is regarded as the foreground. If the surface is overwritten by the shadow for a long time, this Gaussian function has enough reason to consider this point as the background. 2.1 online hybrid model
We regard specific pixel values that change over time as a "pixel process ". A "pixel process" is a time sequence of pixel values, such as a scalar of a gray image or a vector of a color image. T is the time, {x0, y0} is the specified pixel value, and I is the image sequence.
Some "pixel processes" are represented by (R, G) scalar points in figure 2 (a)-(c)
Figure 2: The red and green scalar values of multiple images change with time sequence. It illustrates some differences in actual scenarios. (A) Two-pixel scalar point changes within 2 minutes. (B) shows two-way model distribution of pixel values in the mirror reflection of the water meter. (C) shows another two-way model with a mirror blinking. The requirements of the adaptive system for automatic threshold are described. The highlights of Figure 2 (B) and (c) require a multi-model representation. The value of each pixel represents the measured value of the radiant light that the light emits to an object of interest and is reflected to the sensor. In a fixed scenario and in a fixed light, this value is a constant. Assume that it is independent, and Gaussian noise is generated during the sampling process. The density distribution is described by the single Gaussian distribution at the mean of a center. Unfortunately, most video sequences include light changes, scene changes, and moving objects. If light changes occur in static scenarios, it is necessary to use Gaussian Functions to track these changes. If a static object is put into the scene and is not integrated into the background, unless it is placed more time than the previous object, the corresponding pixels are considered as foreground at any time. In the prospective estimation, this may cause accumulation errors and lead to poor tracking behavior. These factors indicate that the closer the observed Gaussian parameter is, the more important the decision is. If a mobile object appears in the scene, an auxiliary transformation will occur. Even a moving object with a relatively fixed color is expected to generate a larger variance than a static object. In addition, generally, more data should support the background distribution model, because they are replaced, and different object pixel values have different colors. There are dominant factors in our selection model and update program. The historical value of each pixel, {x1,..., xt}, is modeled by a mixed K Gaussian distribution. The current value is obtained in the following way:

K is the number of distributions, WI, T is a weight value evaluated by the I-th Gaussian (how much data is occupied by this Gaussian function), UI, T is the mean value of the I-th Gaussian function at the T moment. Σ I, T is the matrix covariance of the I-th Gaussian function at the T moment. Gini is the Gaussian probability density function.

K is determined by the available memory space and computing power. Currently, 3-5 is used. In addition, due to the computing power, the covariance matrix is assumed to be in the following format:

This assumption is that the values of red, green, and blue pixels are independent and have the same variance. However, this is uncertain. This assumption can avoid an expensive matrix conversion problem at the expense of some precision.

Therefore, the distribution of each pixel value in the scenario is a Gaussian mixture feature distribution. A new pixel value is usually represented and updated by the most important component of the hybrid model.

If the pixel process is a stable process, a standard expectation maximization method is used to maximize the possible observed data. Unfortunately, each pixel process changes with the changing state of the world, so we use an approximate method to essentially treat the new observed value as a sample with a size of 1, and integrate the new data with a standard learning rule.

Since each pixel of an image has a Gaussian mixture model, it is expensive to execute a precise EM algorithm in the window of recent data. Instead, we execute an online K-means approximation algorithm. Each new pixel value xt is used to check whether the existing K-Gaussian distribution exists until a matching value is displayed. The matching is defined as a pixel value within the 2.5 Standard Deviation distribution. This threshold can be weakly disturbed in performance. Each pixel value/distribution threshold is valid. This is useful when different areas have different light (see figure 2 (a) because the noise of an object in the shadow is less than that in the light. A unified threshold often causes the object to disappear when it enters the shadow area.

If no K distribution matches the current pixel value, the minimum probability distribution will be replaced by the average value, initial variance, and low-priority weight of the current value.

The weight priority of K distribution at t time is ω K, T. The formula is as follows:

In the formula, α is the square of the learning rate. mk, T = 1 indicates matching, and MK, T = 0 indicates the residual model. After approximate calculation, the weight value is normalized again. 1/α is defined as a time constant, which determines the speed at which the distribution parameter changes. ω K, t is too tively
A causal low-pass filtered average of the (Thresholded) posterior probability that pixel values have matched model k given observations from time 1 through T. this is equivalent to an exponential window on the expected value.

The μ and α parameters are still the same for unmatched distributions. The distribution parameter matches the new observed value and is updated as follows:

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