Error analysis in determining the centroids of circular objects in images

Detecting the size and/or location of circular object(s) in an image(s) has application in many areas, like, flow diagnostics, biomedical engineering, computer vision, etc. The detection accuracy of circular object(s) largely depends on the accuracy of centroiding algorithm and image preprocessing technique. In the present work, an error analysis is performed in determining the centroids of circular objects using synthetic images with eight different signal-to-noise ratios ranging from 2.7 to 17.8. In the first stage, four different centroiding algorithms, namely, Center of Mass, Weighted Center of Mass, Späth algorithm, and Hough transform, are studied and compared. The error analysis shows that Späth algorithm performs better than other algorithms. In the second stage, various image preprocessing techniques, consisting of two filters, namely, Median and Wiener, and five image segmentation methods, namely, Sobel, Prewitt, Laplacian of Gaussian (LoG) edge detector, basic global thresholding, and Otsu’s global thresholding, are compared to determine the centroids of circular objects using Späth algorithm. It is found that Wiener filter plus LoG edge detector performs better than other preprocessing techniques. Real images of a calibration target (typical in flow diagnostics) and the secondary atomization of water droplets are then considered for centroids detection. These two images are preprocessed using Wiener filter plus LoG edge detector and then processed using Späth algorithm to detect the centroids of circular objects. It is observed that the results of real image of the calibration target and synthetic images are comparable. Also, based on visual inspection, the centroids detected in the real image of water droplets are found to be reasonably accurate.