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Evidence from recent research shows that automatic visual evaluation (AVE) of photographic images of the uterine cervix using deep learning-based algorithms presents a viable solution for improving cervical cancer screening by visual inspection with acetic acid (VIA). However, a significant performance determinant in AVE is the photographic image quality. While this includes image sharpness and focus, an important criterion is the localization of the cervix region. Deep learning networks have been successfully applied for object localization and segmentation in images, providing impetus for studying their use for fine contour segmentation of the cervix. In this paper, we present an evaluation of two state-of-the-art deep learning-based object localization and segmentation methods, viz., Mask R-convolutional neural network (CNN) and Mask^X R-CNN, for automatic cervix segmentation using three datasets. We carried out extensive experimental tests and algorithm comparisons on each individual dataset and across datasets, and achieved performance either notably higher than, or comparable to, that reported in the literature. The highest Dice and intersection-over-union (IoU) scores that we obtained using Mask R-CNN were 0.947 and 0.901, respectively.