COMPUTATION OF NORMAL VECTORS OF DISCRETE 3D OBJECTS: APPLICATION TO NATURAL SNOW IMAGES FROM X-RAY TOMOGRAPHY

Estimating the normal vector field on the boundary of discrete 3D objects is essential for rendering and image measurement problems. Most of the existing algorithms do not provide an accurate determination of the normal vector field for shapes that present edges. We propose here a new and simple computational method to obtain accurate results on all types of shapes whatever their degree of local convexity. The presented method is based on the analysis of the gradient vector field of the distance map of the object. Some results on simulated data and snow images from X-ray tomography are presented and discussed.

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Submanifolds with commuting normal vector field

Journal of Soviet Mathematics ◽

10.1007/bf02105211 ◽

1985 ◽

Vol 28 (2) ◽

pp. 192-207 ◽

Cited By ~ 5

Author(s):

V. A. Mirzoyan

Keyword(s):

Vector Field ◽

Normal Vector ◽

Normal Vector Field

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Constant angle spacelike surface in de Sitter space S₁³

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v35i3.24398 ◽

2017 ◽

Vol 35 (3) ◽

pp. 79-93

Author(s):

Tugba Mert ◽

Baki Karlıga

Keyword(s):

Vector Field ◽

De Sitter Space ◽

Normal Vector ◽

Spacelike Surface ◽

De Sitter ◽

Unit Normal Vector ◽

Normal Vector Field ◽

Constant Angle ◽

Unit Normal Vector Field ◽

Unit Normal

In this paper; using the angle between unit normal vector field of surfaces and a fixed spacelike axis in R₁⁴, we develop two class of spacelike surface which are called constant timelike angle surfaces with timelike and spacelike axis in de Sitter space S₁³.

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Extension of the unit normal vector field from a hypersurface

Georgian Mathematical Journal ◽

10.1515/gmj-2015-0036 ◽

2015 ◽

Vol 22 (3) ◽

Author(s):

Roland Duduchava ◽

Eugene Shargorodsky ◽

George Tephnadze

Keyword(s):

Vector Field ◽

Existence And Uniqueness ◽

Elementary Proof ◽

Gradient Field ◽

Normal Vector ◽

Unit Normal Vector ◽

Normal Vector Field ◽

Unit Normal Vector Field ◽

Outer Unit ◽

Unit Normal

AbstractIn many applications it is important to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of this paper is to provide an elementary proof of the existence and uniqueness of such an extension.

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An integral formula for compact hypersurfaces in a Euclidean space and its applications

Glasgow Mathematical Journal ◽

10.1017/s0017089500008867 ◽

1992 ◽

Vol 34 (3) ◽

pp. 309-311 ◽

Cited By ~ 5

Author(s):

Sharief Deshmukh

Keyword(s):

Vector Field ◽

Euclidean Space ◽

Smooth Function ◽

Support Function ◽

Integral Formula ◽

Position Vector ◽

Normal Vector ◽

Unit Normal Vector ◽

Normal Vector Field ◽

Unit Normal Vector Field

Let M be a compact hypersurface in a Euclidena space ℝn+1. The support function p of M is the component of the position vector field of Min ℝn+1 along the unit normal vector field to M, which is a smooth function defined on M. Let S be the scalar curvature of M. The object of the present paper is to prove the following theorems.

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On compact minimal hypersurfaces in a sphere with constant scalar curvature

Nagoya Mathematical Journal ◽

10.1017/s0027763000018869 ◽

1980 ◽

Vol 78 ◽

pp. 177-188 ◽

Cited By ~ 4

Author(s):

Naoya Doi

Keyword(s):

Vector Field ◽

Constant Scalar Curvature ◽

Arbitrary Point ◽

Second Fundamental Form ◽

Normal Vector ◽

Unit Normal Vector ◽

Covariant Differentiation ◽

Normal Vector Field ◽

Unit Normal Vector Field ◽

Unit Normal

Let M be an n-dimensional hypersurface immersed in the (n + 1)-dimensional unit sphere Sn+1 with the standard metric by an immersion f. We denote by A the second fundamental form of the immersion / which is considered as a symmetric linear transformation of each tangent space TXM, i.e. for an arbitrary point x of M and the unit normal vector field ξ defined in a neighborhood of x, A is given by where is the covariant differentiation in Sn+i and Thus, A depends on the orientation of the unit normal vector field ξ and, in general, it is locally defined on M.

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