###### Abstract
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Strengths** & **Weaknesses** \\ \hline \hline ✓ & Not limited to specific shapes & \(\boxtimes\) & With more parameters the dimension of the accumulator space increases \\ ✓ & Any parametric curve can be used & \(\boxtimes\) & The calculation demand grows exponentially with the number of parameters \\ \hline ✓ & Easy to parallelize (the transformation & \(\boxtimes\) & Can be computationally expensive \\  & itself is independently executed for each & - & for high-resolution images \\  & edge point) & - & for complex shapes \\ \hline ✓ & Can identify partial and & \(\boxtimes\) & Shorter curve segments with fewer points \\  & obstructed curves & \(\boxtimes\) & result in weaker peaks in the \\  & & & accumulator space \\ \cline{3-3}  & & \(\boxtimes\) & Sensitive to noise. Noise may lead to \\  & & & additional peaks in the \\  & & & accumulator space \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The practical strengths and weaknesses of Hough transform. As a first step we introduced fuzzy Hough transform, as it provides more tolerance to the deviations from the ideal curve's points, and colorectal polyps in real colonoscopy images are not precisely circular [40]. As a second step, we targeted the large computational demand of the Hough transform, as the low computational load is one of the most essential requirements for algorithms used in computer-aided diagnosis (CAD) systems. Hough transform starts with an edge detection (mostly Canny edge detection), and all the edge pixels have to be transformed. However, the edge pixels can be decimated, as the Canny edge detection tends to have a dense edge map because of the necessarily high connectivity of the edge points. Colonoscopy images contain edges other than colorectal polyps' borderlines, however, these edges often either have smaller or larger intensity steps compared to the edges of colorectal polyp contours. Based on these considerations, the possibility of removing Canny edge detected points with too small or too high gradient magnitude values was investigated in [41]. The research was performed on all the images of three colonoscopy image datasets CVC-Clinic [9], CVC-Colon [42], and ETIS-Larib [34]. The study's goal was to eliminate edge points that do not belong to polyp contours, and at the same time, to keep as many polyp contour edge points, as it is necessary for the colorectal polyp contour to be detectable. Setting a global gradient magnitude threshold domain that could achieve both a low total number of Canny edge pixels and at the same time a sufficiently accurate matching with the colorectal polyp contour was not possible. However, if the continuity of the Canny edges is given up, other edge detecting methods could provide a better basis for Hough transform, as there the continuity of the lines is not needed, only that the edge points are on the contours of the polyp. This is one of the ideas that were studied in this paper. The main contributions of this article are as follows. First, the performance of four edge detection algorithms (Canny, Prewitt, Roberts, and Sobel) was compared, and the most ideal one that gave the most polyp-contour-related and least unnecessary edge points was selected. Two metrics, based on the normalized gradients of contour and non-contour edges were used to determine which algorithm is the most appropriate. Second, to further reduce the number of edges that do not belong to the polyp contours, a gradient magnitude thresholding process was applied for the results of the selected edge detection method. Finally, to make the circle detection more tolerant to shape uncertainty, the fuzzy version of the Hough transform was also tested together with the classical one using a gradient-weighted voting approach. To evaluate the results, the radial displacement and the average radius were introduced to characterize the roundness of the objects to be detected.