This paper presents a vision-based people detection system for improving safety in heavy machines. We propose a perception system composed of a monocular fisheye camera and a LiDAR. Fisheye cameras have the advantage of a wide field-of-view, but the strong distortions that they create must be handled at the detection stage. Since people detection in fisheye images has not been well studied, we focus on investigating and quantifying the impact that strong radial distortions have on the appearance of people, and we propose approaches for handling this specificity, adapted from state-of-the-art people detection approaches. These adaptive approaches nevertheless have the drawback of high computational cost and complexity. Consequently, we also present a framework for harnessing the LiDAR modality in order to enhance the detection algorithm for different camera positions. A sequential LiDAR-based fusion architecture is used, which addresses directly the problem of reducing false detections and computational cost in an exclusively vision-based system. A heavy machine dataset was built, and different experiments were carried out to evaluate the performance of the system. The results are promising, in terms of both processing speed and performance.