3.2Методыудалениефона

In visual surveillance applications that work with outdoor scenes, the background of the scene contains many non-static objects such as tree branches and bushes whose movement depends on the wind. This kind of background motion causes the pixel intensity values to vary significantly with time. For example, one pixel can be image of the sky at one frame, tree leaf at another frame, tree branch on a third frame and some mixture subsequently; in each situation the pixel will have a different color.

Background subtraction is a method typically used to detect unusual motion in the scene by comparing each new frame to a model of the scene background.

There are two simplest ways to model the background. First one is to take as a reference (background) image one frame when there was no extraneous object in the scene. This method has two drawbacks. The first one is that it is often impossible to get such an “empty” frame. The second drawback is that without being updated this background image will not include any new changes in the background of the scene (including new background objects and illumination changes).

The second simple way to model the background of a scene is to take as a reference image one from a recent history. In particular it can be the i-1 frame, where i is the number of the frame to analyze. This model is more robust as it is being updated continuously, but it cannot hold any static objects that were brought into the scene and left or just stopped. The model will “forget” about these objects.

This explains why one needs a more complex background model to describe a dynamic background of an outdoor scene. Statistical approaches are proved to be adequate background modeling techniques.

The objective of a background model is to capture very recent information about the image sequence, continuously updating this information to capture fast changes in the scene background. The intensity distribution of a pixel can change quickly. So the model must estimate the density function of this distribution at any moment of time given only very recent history information. The first approach is to assume that the distribution is normal and estimate its mean value and dispersion. The mean value can be used to build the reference image, and the dispersion can be used to estimate the background/foreground threshold:

A robust method of the background model initialization can be proposed. Instead of averaging estimation of the mean value and dispersion one can use median technique. As shown in the preliminary experiments it allows building of an appropriate background model even in a case when there are moving foreground objects. An averaging model would include these objects in the background model.

An update of this model can be performed by using a moving average. Varying the updating weights one can change how fast the system will adapt to the scene changes. Also Kalman filtering for adaptation is used in [14-16].

In [13] a mixture of three Normal distributions was used to model the pixel value for traffic surveillance applications. The pixel intensity was modeled as a weighted mixture of three Normal distributions: road, shadow and vehicle distribution. An incremental EM algorithm was used to learn and update the parameters of the model. Although, in this case, the pixel intensity is modeled with three distributions, still the unimodal distribution assumption is used for the scene background, i.e. the road distribution.

In [6, 7] a generalization to the previous approach was presented. The pixel intensity is modeled by a mixture of K Gaussian distributions (K is a small number from 3 to 5) to model variations in the background like tree branch motion and similar small motion in outdoor scenes. The probability that a certain pixel has intensity xt at time t is estimated as

where wj is the weight, j is the mean andis the covariance for the jth distribution. The K distributions are ordered based onand the first B distributions are used as a model of the background of the scene where B is estimated as

The threshold T is the fraction of the total weight given to the background model. Background subtraction is performed by marking any pixel that is more that 2.5 standard deviations away from any of the B distributions as a foreground pixel. The parameters of the distributions are updated recursively using a learning rate , where 1/controls the speed at which the model adapts to change.

The third algorithm [3, 4] is based on a nonparametric technique for modeling the background of a scene. Let x1,…,xN be a recent sample of intensity values for a pixel. Using this sample, the probability density function that this pixel will have intensity value xt at time t can be non-parametrically estimated using the kernel Kh as

If one choose the kernel estimator function, Kh, to be a Gaussian kernel , Kh = N(0,S) whereSrepresents the kernel function bandwidth, and we assume diagonal correlation matrixSwith different kernel bandwidthssj for the jth color channel, then the density can be estimated as

Using this probability estimate, the pixel is considered a foreground pixel if Pr(xt) < th, where the threshold th is a global threshold over the whole image that can be adjusted to achieve a desired percentage of false positives. Practically, the probability estimation can be calculated in a very fast way using pre-calculated lookup tables for the kernel function values given the intensity value difference, (xt - xi), and the kernel function bandwidth. Moreover, a partial evaluation of the summation is usually sufficient to surpass the threshold at most image pixels, since most of the image is typically sampled from the background. This allows a very fast implementation of the probability estimation.

In addition to the statistical approaches described above other techniques can be used. Leaves moving and waves appear as a high-frequency noise that can be partially removed by using a low-pass Fourier or averaging filter.

One more technique can be applied on a higher level of motion analysis. It can be seen that a waving tree moves around its centroid that is not moving itself. So, any moving trees that were detected as foreground can be classified as a tree in the trajectory estimation module.