Abstract

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 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. (MIT AI Memo 740)

Citations

303	Photometric method for determining surface orientation from multiple images - Woodham - 1980
221	Regular polytopes - Coxeter - 1973
178	Elementary Differential Geometry - O’Neill - 1997
177	do Carmo, Differential Geometry of Curves and Surfaces - P - 1976
135	Geometry and the Imagination - Hilbert, Cohn-Vossen - 1952
97	Determining surface orientation of specular surfaces by using the photometric stereo method - Ikeuchi - 1981
77	Obtaining 3-dimensional shape of textured and specular surfaces using four-source photometry - Coleman, Jain - 1982
72	The curve of least energy - Horn - 1983
57	Photometric stereo: A reflectance map technique for determining surface orientation from image intensity - WOODHAM - 1978
45	Determining Shape and Reflectance Using Multiple Images - Silver - 1980
31	Polyhedron Models - Wenninger - 1971
16	Determining shape and reflectance using multiple images - Horn, Woodham, et al. - 1978
16	Allgemeine Lehrsätze über die Konvexen Polyeder - Minkowski
15	An iterative method for reconstructing convex polyhedra from extended gaussian images - Little - 1983
13	The mechanical manipulation of randomly oriented parts - Horn, Ikeuchi - 1984
13	Convex figures and polyhedra - Lyusternik - 1963
12	Determining Attitude of Object from Needle map using Extended Gaussian Image - Ikeuchi - 1983
10	Polyhedra: A visual approach - Pugh - 1976
7	Analytical Geometry - Pogorelov - 1984
5	Three-dimensional segmentation using the Gaussian image and spatial information - Dane, Bajcsy - 1981
5	SEQUINS and QUILLS: representation for surface topography - Horn - 1979
4	Existence and uniqueness of a convex surface with a given integral curvature - Alexandroff - 1942
4	Three-dimensional Scene Analysis - Bajcsy - 1980
3	Using enhanced spherical images - Smith - 1979
3	Cooperative interactions of hemoglobin. Annu Rev Biochem 44:209—232 Faber DS, Young WS, Legendre P, Korn H - Horn - 1979
2	Finding objects in depth maps - Brou - 1983
2	Representing the orientation of dendritic fields with geodesic tessellations - Brown - 1977
2	From Images to Surfaces - Crimson - 1981
1	Detecting Object Orientation from Surface Normals - Ballard, Sabbah - 1981
1	Obtaining 3-Dimensional Sh,pe of Textured and Specular Surfaces using Four-Source Photometry - Coleman, Jain - 1982
1	Recognition of Objects Using the Extended Gaussian Image - Ikeuchi - 1981
1	Picking an Object from a Pile of Objects," M.I.T.A.I. Laboratory Memo Number 726 - Ikeuchi, Horn, et al. - 1983
1	Geodesic Math--and how to use it - Kenner - 1976
1	Mathematical Handbook--for scientists and engineers - Korn, Korn - 1968
1	Allgemeine Lehrsitze fiber die konvexen Polyeder," Nachrichten yon der KSniglichen Gesellschaft der Wissenschaft, en, mathematischphysikalische Klasse, GSttingen - Minkowski - 1897
1	Determining Shape and tefiectance Using Multiple Images, S - Silver - 1980
1	Picking an object from a pile of objects - Ikeuchi, Horn, et al. - 1983
1	Differential Geometry. Noordhoff-Groningen: The - Pogorelov - 1956