The functionality of human intelligence relies on the interaction and health of neurons, hence, quantifying neuronal morphologies can be crucial for investigating the functionality of the human brain. This paper proposes a deep learning (DL) based method for segmenting and quantifying neuronal structures in fluorescence microscopy images of developing neuronal cells cultured in vitro. Compared to the majority of supervised DL-based segmentation methods that heavily rely on creating exact corresponding masks of neuronal structures for the preparation of training samples, the proposed approach allows for imperfect annotation of neurons, as it only requires tracing the centrelines of the neurites. This ability accelerates the preparation of training data by several folds. Our proposed framework is built on a modified version of PSPNet with an EfficientNet backbone pre-trained on the CityScapes dataset. To handle the imperfectness of training samples, we incorporated a weighted combination of two loss functions, namely the Dice loss and Lovász loss functions, into our network. We evaluated the proposed framework and several other state-of-the-art methods on a published dataset of approximately 900 manually quantified cultured mouse neurons. Our results indicate a close correlation between the proposed method and manual quantification in terms of neuron length and the number of branches while demonstrating improved analysis speed. Furthermore, the proposed method achieved high accuracy in neuron segmentation, as evidenced by the evaluation of the neurons’ length and number of branches.