Calculating Spot Center Using Center of Gravity Method

In the field of image processing, calculating the center position of a light spot is a common task, particularly in applications such as optical measurement and laser positioning. The center of gravity method is a simple yet effective approach that determines the center coordinates by analyzing the gray-scale distribution within the spot region of an image.

Principle of Center of Gravity Method The core concept treats the light spot as a two-dimensional mass distribution, where each pixel's gray value represents its "mass." Similar to calculating the center of gravity in physics, the spot's center coordinates are obtained through weighted averaging of all pixels' gray values. The X and Y coordinates are calculated by summing the products of pixel positions and their gray values in respective directions, then dividing by the total gray value sum.

Implementation Approach Image Preprocessing: First convert the image to grayscale format to directly access pixel intensity values using functions like cv2.cvtColor() in OpenCV. Threshold Processing: Apply thresholding (e.g., cv2.threshold()) to filter background noise, retaining only spot region pixels for calculation. Coordinate Traversal: Iterate through all valid pixels, accumulating the products of gray values and coordinates using nested loops or vectorized operations. Normalization Calculation: Divide the accumulated results by the total gray value sum using simple arithmetic operations to obtain final X and Y center coordinates.

Considerations Avoid overexposed or underexposed images as they affect gray distribution accuracy. For spots with trailing or distortion, supplemental algorithms like ellipse fitting may be required. In multi-spot scenarios, first perform connected component analysis (using cv2.connectedComponents()) to segment individual spots before calculation.

The center of gravity method remains a classic approach for spot localization due to its computational efficiency and ease of implementation, making it suitable for real-time applications requiring high performance.