This paper is concerned with polarimetric dense map reconstruction based on a polarization camera with the help of relative depth information as a prior. In general, polarization imaging is able to reveal information about surface normal such as azimuth and zenith angles, which can support the development of solutions to the problem of dense reconstruction, especially in texture-poor regions. However, polarimetric shape cues are ambiguous due to two types of polarized reflection (specular/diffuse). Although methods have been proposed to address this issue, they either are offline and therefore not practical in robotics applications, or use incomplete polarimetric cues, leading to sub-optimal performance. In this paper, we propose an online reconstruction method that uses full polarimetric cues available from the polarization camera. With our online method, we can propagate sparse depth values both along and perpendicular to iso-depth contours. Through comprehensive experiments on challenging image sequences, we demonstrate that our method is able to significantly improve the accuracy of the depthmap as well as increase its density, specially in regions of poor texture.