Advanced Driver Assistance Systems (ADAS) are designed with the main purpose of increasing the safety and comfort of vehicle occupants. Most of current computer vision-based ADAS perform detection and tracking tasks quite successfully under regular conditions, but are not completely reliable, particularly under adverse weather and changing lighting conditions, neither in complex situations with many overlapping objects. In this work we explore the use of hyperspectral imaging (HSI) in ADAS on the assumption that the distinct near infrared (NIR) spectral reflectances of different materials can help to better separate the objects in a driving scene. In particular, this paper describes some experimental results of the application of fully convolutional networks (FCN) to the image segmentation of HSI for ADAS applications. More specifically, our aim is to investigate to what extent the spatial features codified by convolutional filters can be helpful to improve the performance of HSI segmentation systems. With that aim, we use the HSI-Drive v1.1 dataset, which provides a set of labelled images recorded in real driving conditions with a small-size snapshot NIR-HSI camera. Finally, we analyze the implementability of such a HSI segmentation system by prototyping the developed FCN model together with the necessary hyperspectral cube preprocessing stage and characterizing its performance on an MPSoC.