# Background Subtraction for Dynamic Scenes Using Gabor Filter Bank and Statistical Moments
## 1 Introduction  
The study of background subtraction for moving object detection is an active research area divided into two main paradigms: modeling the scene with stationary and non-stationary objects. Traditionally, methods found in the literature try to create groupings of space-time regions that present coherence in the movement to discern between the model representing the scene and non-stationary objects. There are several challenges in posing the detection problem as a motion segmentation problem. The most straightforward approach is based on translational motion, in which two frames are compared [1, 2, 3]. This method is highly adaptable to dynamic changes in the scene but generally leads to poor results due to incorrect motion detection and not detecting uniform regions of the objects, which contain relevant information for segmentation. Moreover, probabilistic models set the object as the detection of outliers in motion [4, 5, 6]. These methods use pixel statistics to update and maintain background model information and compare it with the statistical data of moving objects. Probabilistic models are increasingly used for their reliability in scenarios where shadows, noise, and lighting changes are present. Even so, they assume that the movement changes are relatively small compared to the scene. So, if the statistical information does not come from the background, the problem becomes more challenging. These models are capable of modeling variability in video sequences, which is why they have been widely used primarily in applications of video surveillance [7; 8; 9], moving object detection [10; 11], human detection [12; 13; 14], and vehicle detection for traffic [15; 16], among others. The ability of the method to reduce the influence of noise [17], shadows, changes in lighting [18], changes in the structure of the object [19], or textures [20] depends on the robustness of the algorithm [21]. Although there are many concepts for background modeling or foreground detection, algorithms dedicated to solving all these situations increase their complexity, so the focus of actual methods is to solve more specific problems. Some solutions to these problems are described below. \(\Sigma\Delta\) Background Estimation (\(\Sigma\Delta\)). In the method proposed by [22], a variance estimator is used to understand the variability of pixel intensity. This estimator is used as a threshold. Then, their intensity fluctuations are compared to update the background to a temporal dispersion. Some limitations are the inefficiency of detecting moving objects in complex or very dense backgrounds and temporarily settled objects; these objects are quickly incorporated into the background model. Markov Random Field-Based Motion Detection (MRFMD). This method, introduced by [23], divides the image into several regions to segment it spatially. In the Markov model, the color distribution, temporal color coherence, and edge map in the time frame are used to determine a moving object's spatial direction, color characteristics, and temporal direction. The advantage of this model is to preserve edges to improve object detection with fewer contour effects. Difference-Based Spatio-Temporal Entropy Image (DSTEI). As described in [24; 25; 26], changes in pixel intensities are considered as energy. Moving objects produce more energy, so a normalized histogram is calculated for the area in the image to obtain the frequency of intensity changes. Finally, color information is quantified with the scalar product between the logarithm of the frequency vector and the frequency vector. The advantage of this method is its robustness to gradients, but it is susceptible to false detections, such as sudden changes in shadows or lighting. Eigen-Background Subtraction. This technique is used by many authors, such as [27; 28; 29]. Here, the background is represented by a reconstructed image from a set of dominant eigenvectors. Then, only the difference between the current image and the reconstructed image is calculated to find the foreground object.