###### Abstract  
Classical circular Hough transform was proven to be effective for some types of colorectal polyps. However, the polyps are very rarely perfectly circular, so some tolerance is needed, that can be ensured by applying fuzzy Hough transform instead of the classical one. In addition, the edge detection method, which is used as a preprocessing step of the Hough transforms, was changed from the generally used Canny method to Prewitt that detects fewer edge points outside of the polyp contours and also a smaller number of points to be transformed based on statistical data from three colonoscopy databases. According to the statistical study we performed, in the colonoscopy images the polyp contours usually belong to gradient domain of neither too large, nor too small gradients, though they can also have stronger or weaker segments. In order to prioritize the gradient domain typical for the polyps, a relative gradient-based thresholding as well as a gradient-weighted voting was introduced in this paper. For evaluating the improvement of the shape deviation tolerance of the classical and fuzzy Hough transforms, the maximum radial displacement and the average radius were used to characterize the roundness of the objects to be detected. The gradient thresholding proved to decrease the calculation time to less than 50% of the full Hough transforms, and the number of the resulting circles outside the polyp's environment also decreased, especially for low resolution images. colorectal polyp; image analysis; Hough transform; fuzzy point; edge detection; gradient filter; fuzzy Hough transform; roundness; radial displacement +
Footnote †: journal: Medical Image Analysis—Case Study: Colonoscopy. Footnote †: journal: Medical Image Analysis: Medical Image Analysis: Colonoscopy. Footnote †: journal: Medical Image Analysis: Medical Image Analysis. healthcare professionals would be able to prioritize urgent cases, promptly select appropriate treatments, and efficiently analyze clinical results. Therefore, developing reliable computer-aided diagnosis techniques that can automatically and precisely localize polyps in colonoscopy images is currently one of the most demanding needs in the healthcare sector [1; 2; 3]. To aid the gastroenterologists, various machine learning and deep learning architectures have been currently developed as prominent solutions to automatize polyp detection and localization tasks and enhance the accuracy of their consequences [4; 5; 6]. A method for real-time detection, classification, and localization of gastrointestinal tract disorders from colonoscopy images was presented in [7]. Both online available (hyper-Kvasir dataset) and private locally collected samples were utilized. The method was developed using the pre-trained transfer learning SSD, YOLOv4, and YOLOv5 object detection models, with minimal fine-tuning of the hyperparameters, and their final performance was compared, whereas the utilization of the YOLOv5 object detection algorithm and the artificial bee colony (ABC) optimization algorithm was proposed in [8]. The YOLOv5 algorithm was employed for polyp detection, while the ABC algorithm was used to enhance the performance of the model by finding the optimal activation functions and hyperparameters for the YOLOv5 algorithm. The proposed method was executed on the SUN and PICCOLO datasets and achieved good performance in real-time polyp detection. Not only the deep learning approaches but also the polyp characterization computational methods are widespread in the literature. These methods mainly compute some shape [9; 10] and texture-based [11; 12] feature descriptors over the full image or a segment of it to be able to detect and localize and the polyp's area precisely. In pattern recognition literature, Hough transform is considered as a great mathematical tool for object detection since the first appearance of its classical version for machine analysis of bubble chamber pictures by [PERSON] in 1959 [13].