## 2 Materials and Methods
### ROI Image Extraction
#### 2.2.1 Edge Detection  
In the process of object detection, it is critical to prevent the omission of objects. To this end, filters that effectively detect object boundaries are employed, with representative methods, including the Sobel filter, Canny edge filter, and Laplacian filter [19; 20; 21]. The Sobel filter detects edges through first-order derivative operations and is simple and efficient. However, its edge detection accuracy tends to be lower than that of second-order derivative-based methods such as the Laplacian filter. The Canny edge filter, a robust edge detection technique, suppresses noise and selectively detects significant edges but has limitations due to potential information loss depending on the threshold settings. In contrast, the Laplacian filter, based on second-order derivatives, does not rely on specific thresholds and emphasizes edge information while retaining maximum boundary details.  
Figure 3: ROI image extraction process using Laplacian filter.  
Figure 2: Partitioning results of image containing drone: (**a**) original image; (**b**) partitioned image.  
RGB images consist of three channels, namely, red, green, and blue, each with independent intensity values. The Laplacian filter operates as a single-channel operator and requires independent filtering for each channel when applied to RGB images. However, boundaries calculated separately for each channel may overlap and mix, leading to ambiguous boundaries. To address this, grayscale conversion is used to focus on luminance information, thereby allowing the Laplacian filter to detect more distinct boundaries. Grayscale conversion is achieved through a weighted combination as follows:  
\[\mathrm{I}_{(i,j)}^{\mathrm{gry}}=0.299\bullet\mathrm{I}_{(i,j)}^{\mathrm{ grad}}[\mathrm{R}]+0.587\bullet\mathrm{I}_{(i,j)}^{\mathrm{grad}}[\mathrm{G}]+0.114 \bullet\mathrm{I}_{(i,j)}^{\mathrm{grad}}[\mathrm{B}]. \tag{2}\]  
Here, \(\mathrm{I}_{(i,j)}^{\mathrm{gry}}\) denotes the pixel value of the image converted to grayscale, and \(\mathrm{I}_{(i,j)}^{\mathrm{grad}}[\mathrm{R}]\), \(\mathrm{I}_{(i,j)}^{\mathrm{grad}}[\mathrm{G}]\), and \(\mathrm{I}_{(i,j)}^{\mathrm{grad}}[\mathrm{B}]\) denote the pixel values of the R, G, and B channels, respectively.  
The Laplacian filter, based on second-order derivatives, calculates the rate of change in image brightness and effectively emphasizes abrupt intensity variations near edges. The Laplacian filter is defined as follows:  
\[\mathrm{I}_{(i,j)}^{\mathrm{lap}}=\frac{\partial^{2}\mathrm{I}_{(i,j)}^{ \mathrm{gry}}}{\partial^{2}\mathrm{x}^{2}}+\frac{\partial^{2}\mathrm{I}_{(i,j) }^{\mathrm{gry}}}{\partial^{2}\mathrm{y}^{2}}. \tag{3}\]  
Here, \(\frac{\partial^{2}\mathrm{I}_{(i,j)}^{\mathrm{gry}}}{\partial\mathrm{x}^{2}}\) and \(\frac{\partial^{2}\mathrm{I}_{(i,j)}^{\mathrm{gry}}}{\partial\mathrm{y}^{2}}\) denote the second-order derivatives along the x-axis and y-axis, respectively, which calculate the curvature of the pixel values. This curvature calculation results in higher values at the boundaries where there is a sharp change in image brightness, thereby enabling a clearer emphasis on the object edges.