## 1 Introduction  
Cervical cancer is the fourth most common type of cancer among women worldwide, with an approximate incidence of 660,000 new cases and 350,000 deaths in 2022 [1]. The highest incidence and mortality rates for cervical cancer are recorded in low- and middle-income countries. This situation reflects significant inequalities stemming from the lack of access to national HPV (human papillomavirus) vaccination services, as well as cervical cancer screening and treatment, and is influenced by social and economic determinants [1]. Rates have decreased in most regions of the world over the past decades due to rising socioeconomic levels, reduced risk of persistent HPV infection, and ongoing early detection activities. In Mexico, as of 2020, cervical cancer is the second most diagnosed and the second leading cause of death among women, with an estimated 9439 new cases and 4335 deaths. The incidence rate is 12.6 and the mortality rate is 5.7 per 100,000, although a significant decrease in incidence has been observed compared with that 2012 [2]. In 2021, the Mexican Institute of Social Security (IMSS) detected 1155 new cases and 1059 deaths, with an incidence rate of 2.26 per 100,000 and a mortality rate of 5.23 per 100,000 [2]. Therefore, this study focuses on the detection of cervical cancer through cytological screening methods, specifically Conventional Cytology (Pap smear). This method has inherent limitations in its process, making effective implementation and maintenance challenging. It is essential to have systems in place that ensure timely feedback and efficient communication of test results, as well as appropriate follow-up for women with positive screening results. Additionally, the transportation of samples to the laboratory and the subsequent delivery of results to the clinic add a layer of logistical complexity. Cytology programs require rigorous quality control, both clinically and in the laboratory, to ensure the reliability of results. The interpretation of samples is subjective, which can affect diagnostic accuracy, as vaginal smear slides are examined microscopically at various magnifications. Cytologists must examine thousands of fields of view (FOVs) per slide, limiting the number of samples they can review per day. Despite the apparent simplicity in detecting abnormal cervical cells, experienced physicians are required for accurate diagnosis, and many developing countries lack these healthcare resources. Furthermore, even with experienced pathologists, examining Pap smear slides through a microscope is a tedious task. The detection of cervical cancer cells can be missed due to the small size of cervical intraepithelial neoplasia, overlapping cell clusters, or masking by mucus, blood, and artifacts. Considering the limitations of the current method, various technologies have been proposed to improve the efficiency and accuracy in detecting cervical cancer while reducing the subjectivity of the process [3; 4; 5; 6; 7]. Generally, the algorithms used in cervical cancer detection are divided into two steps: segmentation of the cytoplasm and nucleus, and their detection and classification. For instance, [PERSON], [PERSON] et al. focus on the segmentation of adherent cervical cells, addressing the low segmentation accuracy of existing methods [8]. This article proposes a new convolutional neural network based on star convex polygons with an encoder-decoder structure, called SPCNet. Similarly, [PERSON], [PERSON] et al. use an iterative shape-based method to detect cell nuclei and employ a marker-controlled watershed approach to separate overlapping cytoplasm, combining image segmentation, feature extraction, and selection techniques [9]. Additionally, [PERSON] et al. apply and compare different detection methods on Pap smear images, focusing on image segmentation and nucleus detection, and perform an image quality evaluation to determine the best method [10]. [PERSON] et al.