Owing to poor descriptiveness, weak robustness, and high computation complexity of local shape descriptors (<small>LSDs</small>), point-cloud registration in the case of partial overlap and object recognition in a cluttered environment are still challeng- ing tasks. For
this purpose, an <small>LSD</small> is developed in this article by proposing a new local reference frame (<small>LRF</small>) method and designing a novel feature representation. In the <small>LRF</small> method, two weighting methods are applied to obtain
robustness to noise, point-density variation, and incomplete shape. Additionally, a vector representation is calculated to disambiguate the sign of the x-axis. The feature representation encodes the local information by generating the local coordinate images from five views. Thus, more geometric
and spatial information is included in the descriptor. Finally, the performance of the <small>LRF</small> method and the <small>LSD</small> is evaluated on several popular data sets. The experimental results demonstrate well that the <small>LRF</small> is
robust to noise, point-density variation, and incomplete shape, and the <small>LSD</small> holds strong robustness, superior descriptiveness, and high computational efficiency.