The hemocompatibility of blood-contacting medical devices remains one of the major challenges in biomedical engineering and makes research in the field of new and improved materials inevitable. However, current in-vitro test and analysis methods are still lacking standardization and comparability, which impedes advances in material design. For example, the optical platelet analysis of material in-vitro hemocompatibility tests is carried out manually or semi-manually by each research group individually. As a step towards standardization, this paper proposes an automation approach for the optical platelet count and analysis. To this end, fluorescence images are segmented using Zach's convexification of the multiphase-phase piecewise constant Mumford--Shah model. The resulting connected components of the non-background segments then need to be classified as platelet or no platelet. Therefore, a supervised random forest is applied to feature vectors derived from the components using features like area, perimeter and circularity. With an overall high accuracy and low error rates, the random forest achieves reliable results. This is supported by high areas under the receiver-operator and the prediction-recall curve, respectively. We developed a new method for a fast, user-independent and reproducible analysis of material hemocompatibility tests, which is therefore a unique and powerful tool for advances in biomaterial research.