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When the cornea becomes hydrated above its physiologic level it begins to significantly scatter light, loosing transparency and thus impairing eyesight. This condition, known as corneal edema, can be associated with different causes, such as corneal scarring, corneal infection, corneal inflammation, and others, making it difficult to diagnose and quantify. Previous works have shown that Second Harmonic Generation Microscopy (SHG) represents a valuable non-linear optical imaging tool to non-invasively identify and monitor changes in the collagen architecture of the cornea, potentially playing a pivotal role in future in-vivo cornea diagnostic methods. However, the interpretation of SHG data can pose significant problems when transferring such approaches to clinical settings, given the low availability of public data sets, and training resources. In this work we explore the use of three Deep Learning models, the highly popular InceptionV3 and ResNet50, alongside FLIMBA, a custom developed architecture, requiring no pre-training, to automatically detect corneal edema in SHG images of porcine cornea. We discuss and evaluate data augmentation strategies tuned to the specifics of the herein addressed application and observe that Deep Learning models building on different architectures provide complementary results. Importantly, we observe that the combined use of such complementary models boosts the overall classification performance in the case of differentiating edematous and healthy corneal tissues, up to an AU-ROC=0.98. These results have potential to be extrapolated to other diagnostics scenarios, such as differentiation of corneal edema in different stages, automated extraction of hydration level of cornea, or automated identification of corneal edema causes, and thus pave the way for novel methods for cornea diagnostics with Deep-Learning assisted non-linear optical imaging.