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With the rapid development of 3D laser scanners, point-based discrete shape modeling is being widely used in many engineering applications, e.g. quality control, reverse engineering, computer graphics and machine vision. Point cloud discrete curvature estimation is considered a basic operation in point cloud operations and is used in many applications related to cloud points. This paper presents a novel method for point clouds surface curvature estimation. One of the key components of point clouds surface curvature calculation is neighbor coordinates of query point. For selecting neighbors, homogeneous neighborhood method is used. This method of choosing neighbors, in addition to the distance, takes into consideration the directional balance by improving the k nearest neighbors. Surface normal vector is estimated by neighbors coordinates. In this paper surface curvature is calculated based on normal vector and homogeneous neighbors coordinates. Surface curvature calculated using the novel method is called umbrella curvature. To evaluate how this method performs, umbrella curvature values are calculated for a number of cloud points and the results are used in some different applications. The results show that the proposed method performs well in point clouds curvature estimation. [ABSTRACT FROM AUTHOR]