While deep learning models can learn human-like features at earlier levels, which suggests their utility in modeling human vision, few attempts exist to incorporate these features by design. Current approaches mostly optimize all parameters blindly, only constraining minor architectural aspects. This paper demonstrates how parametrizing neural network layers enables more biologically-plausible operations while reducing trainable parameters and improving interpretability. We constrain operations to functional forms present in human vision, optimizing only these functions' parameters rather than all convolutional tensor elements independently. We present two parametric model versions: one with hand-chosen biologically plausible parameters, and another fitted to human perception experimental data. We compare these with a non-parametric version. All models achieve comparable state-of-the-art results, with parametric versions showing orders of magnitude parameter reduction for minimal performance loss. The parametric models demonstrate improved interpretability and training behavior. Notably, the model fitted to human perception, despite biological initialization, converges to biologically incorrect results. This raises scientific questions and highlights the need for diverse evaluation methods to measure models' humanness, rather than assuming task performance correlates with human-like behavior.