The manual evaluation, classification and counting of biological objects demands for an enormous expenditure of time and subjective human input may be a source of error. Investigating the shape of red blood cells (RBCs) in microcapillary Poiseuille flow, we overcome this drawback by introducing a convolutional neural regression network for an automatic, outlier tolerant shape classification. From our experiments we expect two stable geometries: the so-called slipper and croissant shapes depending on the prevailing flow conditions and the cell-intrinsic parameters. Whereas croissants mostly occur at low shear rates, slippers evolve at higher flow velocities. With our method, we are able to find the transition point between both phases of stable shapes which is of high interest to ensuing theoretical studies and numerical simulations. Using statistically based thresholds, from our data, we obtain so-called phase diagrams which are compared to manual evaluations. Prospectively, our concept allows us to perform objective analyses of measurements for a variety of flow conditions and to receive comparable results. Moreover, the proposed procedure enables unbiased studies on the influence of drugs on flow properties of single RBCs and the resulting macroscopic change of the flow behavior of whole blood.