Source Code Program for Extracting Dot Center Coordinates from Images Using Gray-Level Centroid Method

This program implements the gray-level centroid method to extract center coordinates of circular dots from images. The gray-level centroid method is a widely-used image processing technique that determines the center position of a region by calculating the weighted average of gray values. In our implementation, the program first converts the input image to grayscale format. The algorithm then computes the center coordinates by calculating two key sums: the sum of products between each pixel's gray value and its coordinate position, and the sum of all gray values within the target region. The center coordinates (x_c, y_c) are derived using the formula: x_c = Σ(x_i * I_i) / ΣI_i and y_c = Σ(y_i * I_i) / ΣI_i, where (x_i, y_i) represents pixel coordinates and I_i denotes the gray value. This method provides high precision in locating dot centers, enabling accurate subsequent image analysis and processing operations. The code includes optimized functions for image preprocessing, coordinate calculation, and result validation to ensure robust performance across various image conditions.