# Efficient Crowd Anomaly Detection Using Sparse Feature Tracking and Neural Network
## 3 Materials and Methods
### Crowd Representation and Behaviour Descriptors
#### 3.1.1 Local Feature Extraction  
This section outlines the local features incorporated into our methodology. Specifically, we utilise Features from the Accelerated Segment Test (FAST), Scale-Invariant Feature Transform (SIFT), and Accelerated-KAZE (AKAZE), each of which will be detailed in the following sub-sections. 1. Features from Accelerated Segment Test (FAST) The FAST algorithm was initially proposed by [PERSON] and [PERSON] [32] and has been used to identify interest points in an image. Interest points are pixels with well-defined positions that can be reliably detected. These points contain significant local information and should be consistently detected across different images. It scans the image using a circular neighbourhood around each pixel and identifies potential key points based on intensity differences. The algorithm employs acceleration techniques, such as a corner criterion using predetermined sample points, to reduce the computational overhead. Non-maximum suppression is applied to select the most salient key points, discarding redundant ones. Interest point detection finds application in image matching, object recognition, and tracking and can also be utilised for crowd anomaly detection. While there are established algorithms for corner detection, such as Harris and SUSAN, the FAST algorithm was developed to address the need for a  
Figure 1: A schematic representation of the proposed approach. computationally efficient interest point detector suitable for real-time applications with limited computational resources, like SLAM on a mobile robot [33]. 2. Scale Invariant Feature Transform (SIFT) The SIFT algorithm, which was first introduced in [34], is one of the most widely known feature detection-description algorithms. It approximates the Laplacian-of-Gaussian (LoG) by utilising the Difference-of-Gaussians (DoG) operator. The DoG operator is employed to search for local maxima in images at various zoom levels, enabling the identification of feature points. To extract a robust descriptor, SIFT computes 128 bin values by considering a 16 \(\times\) 16 neighbourhood around each detected feature and segmenting it into sub-blocks. Although SIFT exhibits robust invariance to image rotations, scales, and limited affine variations, its major drawback is its high computational cost. In Equation (1), the Difference-of-Gaussians (DoG) response at a given scale in the Scale Invariant Feature Transform (SIFT) algorithm is obtained by convolving the image _I(x, y)_ with the difference of two Gaussian filters calculated at different scales. The result of this convolution represents the DoG response, which is used to detect feature points in the image. \[D(x,y,\sigma)=(G(x,y,k\sigma)-G(x,y,\sigma))*I(x,y)\] (1)
3. Accelerated-KAZE (AKAZE) The Accelerated-KAZE (AKAZE) algorithm, introduced in [11], is an extension of the KAZE algorithm that utilises a computationally efficient framework called Fast Explicit Diffusion (FED) to construct its non-linear scale spaces. AKAZE is based on non-linear diffusion filtering and employs the determinant of the Hessian matrix for feature detection. To enhance the rotation invariance, AKAZE utilises Scharr filters. The maximum responses obtained from the detectors indicate specific feature point locations. These feature points serve as the foundation for AKAZE's robust and distinctive feature detection. The AKAZE descriptor relies on the Modified Local Difference Binary (MLDB) algorithm, which is both powerful and efficient. AKAZE's scale spaces have a non-linear nature, resulting in invariance to scale, rotation, and limited affine transformations. Moreover, AKAZE's features become increasingly distinctive as they are scaled up or down. In our approach, SIFT, AKAZE, and FAST were individually evaluated, emphasising their distinct feature extraction capabilities for anomaly detection within sparse feature tracking. SIFT is renowned for its robustness to changes in scale, rotation, and illumination; it excels in extracting distinctive key points from crowd images.