Automatic segmentation of nuclei on breast cancer histology images is a basic and important step for diagnosis in a computer-aided diagnostic approach and helps pathologists discover cancer early. Nuclei segmentation remains a challenging problem due to cancer biology and the variability of tissue characteristics; thus, their detection in an image is a very tedious and time-consuming task. In this context, overlapping nuclei objects present difficulties in separating them by conventional segmentation methods; thus, active contours can be employed in image segmentation. A major limitation of the active contours method is its inability to resolve image boundaries/edges of intersecting objects and segment multiple overlapping objects as a single object. Therefore, we present a hybrid active contour (connected component + active contours) method to segment cancerous lesions in unsupervised human breast histology images. Initially, this approach prepares and pre-processes data through various augmentation methods to increase the dataset size. Then, a stain normalization technique is applied to these augmented images to isolate nuclei features from tissue structures. Secondly, morphology operation techniques, namely erosion, dilation, opening, and distance transform, are used to highlight foreground and background pixels while removing overlapping regions from the highlighted nuclei objects on the image. Consequently, the connected components method groups these highlighted pixel components with similar intensity values and assigns them to their relevant labeled component to form a binary mask. Once all binary-masked groups have been determined, a deep-learning recurrent neural network (RNN) model from the Keras architecture uses this information to automatically segment nuclei objects having cancerous lesions on the image via the active contours method. This approach, therefore, uses the capabilities of connected components analysis to solve the limitations of the active contour method. This segmentation method is evaluated on an unsupervised, augmented human breast cancer histology dataset of 15,179 images. This proposed method produced a significant evaluation result of 98.71% accuracy score.