## 1 Introduction
Moreover, deep learning techniques have been integrated with threshold segmentation algorithms to enhance the training efficiency of deep learning models and improve segmentation accuracy. To reduce the loss of semantic information and increase prediction accuracy, [PERSON] et al. [36] developed a fire detection model based on deep learning by integrating dynamic threshold grayscale segmentation with residual network transfer learning. [PERSON] et al. [37] combined convolutional neural networks with threshold segmentation, effectively addressing the limitations of fixed thresholds and improving algorithm accuracy. [PERSON] et al. [38] incorporated fuzzy computing into the standard U-Net architecture, creating a prediction matrix and then applying thresholding to obtain visual results, achieving more precise detection and segmentation of cell nuclei. In grayscale medical image segmentation, [PERSON] et al. [39] presented a novel method combining thresholding techniques with 2D and 3D object detection technologies to address issues such as segmentation errors and noise regions caused by varying intensity distribution characteristics in grayscale images, leading to higher scores and improved performance. [PERSON] et al. [40] developed a multi-level closing pre-processing framework to remove hair from dermatoscopic images, achieving an average accuracy of 95.87%. [PERSON] et al. [41] proposed a deep learning model termed 'Deep Threshold Prediction Network (DTP-Net),' where grayscale versions of macro-images are used as input to train the model, and the corresponding gray-level threshold values that maximize the Dice similarity index (DSI) between the segmented and ground-truth images are defined as the targets. [PERSON] et al. [42] introduced a hybrid method that combines OTSU thresholding with fully convolutional networks (FCN), where the OTSU thresholding algorithm automatically labels the images and deep learning estimates the coverage, resulting in better performance than either method alone. [PERSON] et al. [43] employed a variation of the convolutional neural network model LeNet-5 for classification and used the OTSU multi-thresholding method with an optimization algorithm for image segmentation, thereby enhancing the computational power of deep learning techniques. In summary, the random search capability of meta-heuristic algorithms (MAS) enables segmentation algorithms to identify optimal solutions within a broad solution space, even in the presence of uncertainty, without the need to traverse the entire space. This capability significantly reduces search time and computational costs. The integration of deep learning techniques with threshold segmentation algorithms typically involves applying threshold algorithms either before or after deep learning models to enhance training efficiency or improve segmentation accuracy. However, both types of algorithms process all the pixels in an image. As the number of pixels increases, classification accuracy and segmentation precision improve. Nonetheless, this also leads to longer processing times and reduced efficiency, making these approaches less suitable for large-scale or real-time image processing scenarios. In light of these considerations, in 2022, the author of the blog \"Magefreehome\" [44] proposed an innovative image segmentation method, referred to here as the Magefreehome algorithm. The algorithm begins by converting the image to grayscale, calculating the center point's position based on the image size, and extracting pixel grayscale values from the row and column where the center point is located. Through vectorized operations using the NumPy library [45], the algorithm compares the specified threshold with the grayscale values of each coordinate point in the row and column of the center point. It retains only those coordinate points with grayscale values greater than the specified threshold for subsequent operations.