DIFFUSION BACKGROUND MODEL FOR MOVING OBJECTS DETECTION

In this paper, we propose a new approach for moving objects detection in video surveillance systems. It is based on construction of the regression diffusion maps for the image sequence. This approach is completely different from the state of the art approaches. We show that the motion analysis method, based on diffusion maps, allows objects that move with different speed or even stop for a short while to be uniformly detected. We show that proposed model is comparable to the most popular modern background models. We also show several ways of speeding up diffusion maps algorithm itself.


INTRODUCTION
Recently a lot of background models intended for moving object detection and foreground segmentation were introduced.Moreover, changedetection.netbenchmark was created (Goyette, 2012, Y. Wang, 2014) for testing and ranking existing and new algorithms for change and motion detection.In the paper (Vishnyakov, 2012) we introduced the regression pseudospectrum background model, that was based on the fast way of accumulating the layers of the spectrum using the regression model.However, despite the very high computation speed, that approach lacked quality in complex conditions (swaying branches, changeable lighting conditions, slow objects).The idea of our new approach is as follows: we improve regression background model using diffusion maps and diffusion regressive filtering.Below in this paper we describe our approach and provide evaluation results on the changedetection.netdatabase for the most suitable categories: «baseline», «thermal», «bad weather», «low framerate».

Diffusion map
Let () be the input image on the frame .Let us assume that () is a grayscale image (or it has been converted to grayscale), (, ) is the brightness value of the image  in pixel .The basis of our approach is the diffusion morphology (Vizilter, 2013) which allows comparing images by shape matching using the projection of image one on image two.In this morphology the projection is evaluated using diffusion maps, that were introduced in (Lafon, 2004, Coifman, 2006a, Coifman, 2006b): where ,  -points, -a diffusion operator (diffusion map), () -a feature vector, calculated in the point  of the image  with the square kernel, ‖⋅‖ -a distance between two feature vectors.

Complex LBP Descriptor
In the papers (Gorbatsevich, 2014, Vishnyakov, 2014) the complex LBP descriptor was introduced as a feature vector v(⋅) along with the hamming distance ‖⋅‖ as a distance between feature vectors for the diffusion maps.This allows very fast computation of the diffusion map.
Our implementation provides a possibility for real time image processing.The computation of diffusion filtering with heat kernel in its original form is an extremely time-consuming procedure even for reasonable neighbourhood of .We propose to substitute such computationally unpleasant descriptors by the combination of intensity () and threshold LBP (Ahonen, 2004) for ().In our experiments, the mean value of intensity in the p neighbour was used.Mean value is computed by a fast algorithm with sliding sum recalculation (but this is not presented in code below).The local binary pattern (LBP) is calculated as a 64-bit vector for each pixel  based on a comparison of its value and values of its neighbours in sliding window.If the value of neighbour pixel is less than the value of central pixel and the difference between them is greater than threshold, then the corresponding bit is set to 1, otherwise -to 0. We substitute the original neighbourhood matching metrics by LBP matching metric -Hamming distance, the mean values of intensities are compared by threshold.As local binary patterns are stored as bit fields, the computation of Hamming distance is performed via bitwise XOR operation.The exponent is calculated using table values.Due to this, the usage of our complex LBP descriptor allows both increasing the computational speed and obtaining heat kernels very similar to original.

Background model
The idea of the paper is as follows: the approach for the image comparison in the diffusion morphology can be also used for the moving object detection.For robustness of the approach we propose regression accumulators (Vishnyakov, 2012)   () and   * () for both the original image and the filtered image respectively: where  * () =    () () () is a diffusion filter of the (), which is the projection of () on the memory   (), n is a parameter, related to the memory length,  = ().
After computing   () and   * (), we compare the difference to the threshold in each pixel and get the binary moving object mask ():

Illustrations
On figure 1 we show smoothed accumulator (memory)   * () using regression model for the projection image  * () -a diffusion filter of the ().As you can see, no moving object is present on this accumulator.In addition, the accumulator is smoothed because of smoothing properties of the diffusion map.On figure 2 we show the projection image  * () itself.One moving object is present on this image.The projection image is also smoothed.On figure 3 we show the difference () between projection image  * () and smoothed accumulator   * ().On figure 4 we show image () -binarized using threshold difference image ().

Table 1 .
approach was compared to 37 other existed methods results available from change detection 2012 benchmark.For «Bad Weather», «Low Frame-Rate» categories the results of proposed approach was compared to 22 other existed methods results available from change detection 2014 benchmark.Baseline category.Results for each video in this category.

Table 6 .
Thermal category.Rank each metric for proposed method presented.Results for «Bad Weather» category is shown inTable 7, 8, 9.

Table 7 .
Bad Weather category.Results for each video in this category.

Table 8 .
Bad Weather category.

Table 9 .
Bad Weather category.Rank for each metric for proposed method presented.

Table 10 .
Low Frame-Rate category.Results for each video in this category.

Table 12 .
Low Frame-Rate category.Rank for each metric for proposed method presented.