# Background Subtraction for Dynamic Scenes Using Gabor Filter Bank and Statistical Moments
## 1 Introduction
Consequently, researchers have transitioned from conventional to deep learning models for background subtraction. Convolutional neural networks (CNNs) were introduced for background subtraction in 2016 [33]. Trained in a supervised way, the CNNs used in background subtraction are categorized into basic CNN, multi-scale and cascaded CNNs, fully CNNs, deep CNNs, 3D-CNNs, and structured CNNs [21]. Deep learning-based methods such as FgSegNet [53; 54] and its variants represent the field's current state; however, their supervised nature relies on the availability of large amounts of data for training. This paper proposes a background subtraction method based on local texture analysis. We assume that the discrete topological surface of the scene satisfies a specific frequency and direction of the Gabor filter bank. The Gabor filter is a linear filter mainly used for texture analysis and discrimination. In its two-dimensional representation, it is a Gaussian kernel function modulated by a sine wave, characterized by the parameters \(\lambda,\sigma_{x},\sigma_{y},\theta\) and \(\phi\). In this work, we use it as a texture descriptor. We propose to use the magnitude and phase of the filter to characterize the information that is not sensitive to light changes and build a background model. Based on the results, our method maintains the invariance of subtle changes in light. We assess computational efficiency by processing image series of varying sizes and resolutions. Our test is run on Intel(R) Core i7-7500U CPU with 32.0 GB RAM, achieving a processing rate of 10 frames per second. Upon repeating the experiments, variability in the execution times for each series is observed, which is why it is decided to carry out 30 repetitions, analyzing a total of 181,470 images. The purpose of this is to calculate descriptive statistics, thus obtaining the following results showed in Table 1.  
While the proposed method may not achieve the same level of performance as deep learning approaches, it offers several advantages that make it a valuable alternative in certain scenarios. For example, the method is particularly useful when the traditional method cannot handle situations where an object's color intensity and texture are similar to its surroundings. The proposed method is also invariant to light changes, a common challenge in video surveillance systems. Moreover, the proposed method is computationallyefficient and can process video data in real time, making it a faster alternative to deep learning approaches that require large amounts of computational resources and training data. These advantages suggest that the proposed method may be more suitable for real-time object detection and tracking applications, such as video surveillance systems. The main contributions of this work are (i) the spatio-temporal algorithm that incorporates statistical moments into the Gabor filter bank, (ii) overcoming the shadow detection problem, and (iii) the segmentation of objects with uniform texture around the environment. The rest of this document is organized as follows. Section 2 describes the theoretical aspects, and Section 3 describes the experimental model, in which texture analysis and motion detection are performed. Section 4 presents the experiments and results. Section 5 discusses the results, and Section 6 presents the conclusion and limitations of the approach.