Many physiological processes and pathological phenomena in the liver tissue are spatially heterogeneous. At a local scale, biomarkers can be quantified along the axis of the blood flow, from portal fields (PFs) to central veins (CVs), i.e., in zonated form. This requires detecting PFs and CVs. However, manually annotating these structures in multiple whole-slide images is a tedious task. We describe and evaluate a fully automated method, based on a convolutional neural network, for simultaneously detecting PFs and CVs in a single stained section. Trained on scans of hematoxylin and eosin-stained liver tissue, the detector performed well with an F1 score of 0.81 compared to annotation by a human expert. It does, however, not generalize well to previously unseen scans of steatotic liver tissue with an F1 score of 0.59. Automated PF and CV detection eliminates the bottleneck of manual annotation for subsequent automated analyses, as illustrated by two proof-of-concept applications: We computed lobulus sizes based on the detected PF and CV positions, where results agreed with published lobulus sizes. Moreover, we demonstrate the feasibility of zonated quantification of biomarkers detected in different stainings based on lobuli and zones obtained from the detected PF and CV positions. A negative control (hematoxylin and eosin) showed the expected homogeneity, a positive control (glutamine synthetase) was quantified to be strictly pericentral, and a plausible zonation for a heterogeneous F4/80 staining was obtained. Automated detection of PFs and CVs is one building block for automatically quantifying physiologically relevant heterogeneity of liver tissue biomarkers. Perspectively, a more robust and automated assessment of zonation from whole-slide images will be valuable for parameterizing spatially resolved models of liver metabolism and to provide diagnostic information.