###### Abstract  
The number of infectious spots or pathological structures recorded on dermatological images is a tool to aid in the diagnosis and monitoring of disease progression. Dermatological images for the detection and monitoring of the evolution of acne infections are evaluated globally, comparing whether the increase or decrease in infectious lesions appearing on an image is significant. This evaluation method is only indicative since its accuracy is low. The accuracy problem could be improved by an exact count of the number of structures and spots appearing on the image. The mathematical function circular Hough transform (CHT) function implemented in MATLAB is here applied to develop a procedure for counting these structures. CHT has been used in the recognition of benign and distorted red blood cells, in the detection of pellet sizes in industrial processes and in the automated detection and morphological characterization of breast tumor masses from infrared images, as well as for the detection of brain aneurysms and use in magnetic resonance imaging. The sensitivity factor is one of the many parameters required to feed the CHT algorithm. Its choice is unclear as there is no proper methodology to select an optimum value suitable for each image. In this work, a procedure for determining the optimal value of the sensitivity factor is proposed. The approach is validated by comparison with the results of the manual counting of the points (ground truth). circular Hough transform function; image processing; statistics; sensitivity; MATLAB; dermatological images +
Footnote †: journal: Medical Imaging  
**Citation:** [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON] Hough Transform Sensitivity Factor Calculation Model Applied to the Analysis of Acne  
When monitoring the course of a pathological processes in dermatology, such as acne infections [1], it is common to record images of the control [2]. The structures of interest that are analyzed in the dermatological images studied in this article have circular or quasi-circular shapes. It is therefore interesting to study the application of CHT in the processing of monochromatic dermatological images. The CHT function is implemented in the MATLAB software, within the Image Processing Toolbox. This function has different input arguments such as radius or maximum and minimum diameter of the structures to be detected, background shape (brightness-blackness), etc. Of all the input arguments, and as described below, one of the most difficult parameters to choose for the application of this function is the sensitivity factor S. This factor has values in the range (0-1). The closer we get to the value 1, the more faint and partially obscured circles the algorithm can detect, but at the same time the risk of false detection increases. With the same sensitivity factor value, we do not obtain the same results in two different images and, therefore, the choice of an optimal value for each image to be processed is important. Thus far, this value has been chosen empirically [3], through trial and error stack overflow. As this way of choosing has proved to be inefficient and imprecise, and as the need to determine the optimum value for processing each image is evident, a methodology is proposed that allows a standardized and automated way of finding an optimum value for each image to be processed and analyzed. The possibility of quickly and automatically quantifying the number of structures that appear in medical images has been studied in works such as [4], where different segmentation algorithms are proposed. In [5], an algorithm for the recognition and quantification of cells present in different histological slices is proposed. In [6] it is used circle Hough transform to analyze immune responses by quantifying the amount of cytokine secreted by cells. ELISPot and FluoroSpot images were analyzed. [2] used the circle Hough transform for cell detection in blood samples. Ref. [7] used CHT for femoral head detection in perfhes MR slices. Ref.