Automated image analysis of slides of thin blood smears can assist with early diagnosis of many diseases. Automated detection and segmentation of red blood cells (RBCs) are prerequisites for any subsequent quantitative highthroughput screening analysis since the manual characterization of the cells is a time-consuming and error-prone task. Overlapping cell regions introduce considerable challenges to detection and segmentation techniques. We propose a novel algorithm that can successfully detect and segment overlapping cells in microscopic images of stained thin blood smears. The algorithm consists of three steps. In the first step, the input image is binarized to obtain the binary mask of the image. The second step accomplishes a reliable cell center localization that utilizes adaptive meanshift clustering. We employ a novel technique to choose an appropriate bandwidth for the meanshift algorithm. In the third step, the cell segmentation purpose is fulfilled by estimating the boundary of each cell through employing a Gradient Vector Flow (GVF) driven snake algorithm. We compare the experimental results of our methodology with the state-of-the-art and evaluate the performance of the cell segmentation results with those produced manually. The method is systematically tested on a dataset acquired at the Chittagong Medical College Hospital in Bangladesh. The overall evaluation of the proposed cell segmentation method based on a one-to-one cell matching on the aforementioned dataset resulted in 98% precision, 93% recall, and 95% F1-score index.