Extended Gaussian images

By Berthold K. P. Horn. 1984

This is a primer on extended Gaussian images. Extended Gaussian images are useful for representing the shapes of surfaces. They can be computed easily from: 1. needle maps obtained using photometric stereo; or 2. depth maps generated by ranging devices or binocular stereo. Importantly, they can also be determined simply from geometric models of the objects. Extended Gaussian images can be of use in at least two of the tasks facing a machine vision system: 1. recognition, and 2. determining the attitude in space of an object. Here, the extended Gaussian image is defined and some of its properties discussed. An elaboration for nonconvex objects is presented and several examples are shown.

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Citations in the corpus

Volumetric and Multi-view CNNs for Object Classification on 3D Data (2016, background): “For instance, shapes can be represented as histograms or bag-of-feature models which are constructed from surface normals and curvatures [13].”
Multi-view Convolutional Neural Networks for 3D Shape Recognition (2015, background): “For example, shapes can be represented with histograms or bag-of-features models constructed out of surface normals and curvatures [15], distances, angles, triangle areas or tetrahedra volumes gathered at sampled surface points [25], properties of spherical functions defined in volumetric grids [16]”
Orientation-boosted Voxel Nets for 3D Object Recognition (2016, background): “Descrip-tors based on surface normals have been very popular, too [14, 23].”
FusionNet: 3D Object Classification Using Multiple Data Representations (2016, methodology): “In the past, shapes have been represented as histograms or bag of features models which were constructed using surface normals and surface curvatures [8].”
Fully Automatic Registration of 3D Point Clouds (2006, methodology): “Our rotation estimate is obtained by exhaustively traversing the space of rotations to ﬁnd the one which maximizes the correlation between EGIs.”
A search engine for 3D models (2003, methodology): “Other shape representations, such as Extended Gaussian Images [38], Spherical Attribute Images [27, 28], moments [68, 84], and wavelets [34], require a priori registration into a canonical coordinate system, which is difficult to achieve robustly.”
Point Signatures: A New Representation for 3D Object Recognition (1997, background): “Some of the notable contributions to the recognition of complex objects are as follows: The Extended Gaussian Image (EGI), which contains a 2D distribution of surface normals of the object, was proposed and developed by Horn (1984) , Brou (1984) and Ikeuchi (1981).”
On Bending Invariant Signatures for Surfaces (2003, background): “Thacker et al. [1], [5], [3], [4], and Horn [22] presented shapes in images by histograms of either differential measures, like normals or curvatures, or semilocal structures , like angles and distances between pairs of line segments.”
Context-driven automated target detection in 3D data (2004, methodology): “This algorithm uses an MST segmentation [3,4] performed at full resolution and recombines the information in a way that is constrained by the original segmentation and some simple consistency rules.”
Aligning point cloud views using persistent feature histograms (2008, methodology): “of surfaces and can be approximated using the spherical histogram of surface orientations [23].”
Feature-based similarity search in 3D object databases (2005, methodology): “One way to represent this distribution is using the Extended Gaussian Image (EGI) [Horn 1984; Ip and Wong 2002].”
Pairwise Decomposition of Image Sequences for Active Multi-view Recognition (2016, background): “Shape descriptors include distributions of local surface properties [14, 32], spherical harmonic functions over voxel grids [24], and 3D local invariant features [25].”
Fast 3D recognition and pose using the Viewpoint Feature Histogram (2010, methodology): “EGIs describe objects based on the unit normal sphere, but have problems handling arbitrarily curved objects.”
A Reflective Symmetry Descriptor (2002, methodology): “In contrast, shape descriptors that involve computation of model derivatives, either as normals or gradients [25,10], have the property of amplifying the contribution of high-frequency components, making them unstable in the presence of high-frequency noise.”