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Ubiquitous availability of inexpensive three dimensional (3D) sensors has led to an abundance of keypoint detection and feature description techniques for point-clouds. While some recent methods utilize color along with geometric information, most only implicitly discuss-if not completely disregard-the information provided by scale. Scale is an inherent characteristic of any keypoint or feature that describes its physical size or region of support. Exploiting information provided by scale facilitates the processes of keypoint detection and feature description. A 3D scale-space, extended from robust and popular 2D methods, is constructed to diffuse a signal on triangulated meshes. Methods of scale-parameter estimation and a novel neighborhood definition are presented that improve the methods' robustness to noise and arbitrary mesh connectivity. Keypoint repeatability experiments show that a novel definition of the Laplace-Beltrami operator (LBO) leads to the most accurate scale-space. A point-cloud feature descriptor, popular in the robotics community and recently proposed for spacecraft relative navigation (RelNav), is modified to explicitly utilize scale in the description and matching processes. The Scaled Oriented Unique Clustered Viewpoint Feature Histogram (SOUR-CVFH) uses a cluster's scale to expedite the histogram matching procedure and increase pose estimation accuracy. SOUR-CVFH is demonstrated in experiments of (1) object recognition in both isolated and cluttered scenes and (2) simulated RelNav of a spacecraft to a asteroid.