Three-Dimensional Gradient-Based Laplacian Spatial Filter of a Field of Vectors for Geometrical Edges Magnitude Detection in Point Cloud Surfaces

Also known as the second derivative, the Gradient-Based Laplacian, that is used for geometrical edge magnitude detection in point clouds, is still an important problem that can form a basis for a wide range of applications such as object recognition and detection. Typically, the Laplacian, of a field of scalars are used as gray-scale edge detectors and classifiers. The problem statement is defining the Gradient-Based Laplacian of a field of vectors (used for detecting 3-D surface geometrical edges) that is analogous to the Gradient-Based Laplacian of a field of scalars (used for detecting intensity edges) in the sense that it complies with the typical rules for the Laplacian operator. The contributions is we propose a novel definition of the Gradient-Based Laplacian of the field of vectors (used for detecting 3-D surface geometrical edges) using the absolute difference of the Gradient values, we do behavioral analyses on the Step edge, Plane, and Ramp areas for two cases when the absolute difference and when the signed difference are used, we do performance analyses on TUM data set, and comparison study with the state of the art edge detectors on NYUD data set which shows that our Gradient-Based Laplacian is efficient.