DIPlib Documentation - ©1995-2008 Quantitative Imaging Group, Delft University of Technology.

StructureTensor2D

Two dimensional Structure Tensor

SYNOPSIS

#include "dip_structure.h"

dip_Error dip_StructureTensor2D( in, mask, orientation, energy, l1, l2, anisotropy1, anisotropy2, boundary, gradSpec, gradSigmas, tensorSpec, tensorSigmas )

DATA TYPES

integer,float

FUNCTION

This function computes the Structure Tensor (ST) at each point in the image. For a description of this technique see the references. There are two stages in the computation. The first stage computes the gradient vector at each point, using Derivative with parameters gradSpec and gradSigmas. The second stage, the tensor smoothing, is also performed using Derivative (with order = 0). The parameters used are tensorSpec and tensorSigmas.

If a mask image is given, a technique called normalised convolution (see references) is used to "fill in" the missing data.

The routine has a number of output images. Each of these can be set to zero. If set to zero, the corresponding result will not be computed. The following quantities are computed by this routine:

orientationOrientation. Lies in the interval (-pi/2,pi/2).
energySum of the two eigenvalues l1 and l2.
l1The largest eigenvalue.
l2The smallest eigenvalue.
anisotropy1Measure for local anisotropy: ( l1 - l2 ) / ( l1 + l2 ).
anisotropy2Measure for local anisotropy: 1 - l2 / l1.

ARGUMENTS

Data typeNameDescription
dip_ImageinInput
dip_ImagemaskMask image (0=missing data)
dip_ImageorientationOrientation
dip_ImageenergyEnergy (l1+l2)
dip_Imagel1Largest eigenvalue
dip_Imagel2Smallest eigenvalue
dip_Imageanisotropy1Local anisotropy: (l1-l2)/(l1+l2)
dip_Imageanisotropy2Local anisotropy: 1-l2/l1
dip_BoundaryArrayboundaryBoundary conditions
dip_DerivativeSpecgradSpecParameters for derivative to compute gradient (see DerivativeSpec data structure)
dip_FloatArraygradSigmasSigmas of derivative to compute gradient
Sigma of derivative to compute gradient
dip_DerivativeSpectensorSpecParameters for Gaussian for tensor smoothing (see DerivativeSpec data structure)
dip_FloatArraytensorSigmasSigmas of Gaussian for tensor smoothing
Sigma of Gaussian for tensor smoothing

LITERATURE

Bernd Jahne, Practical Handbook on Image Processing for Scientific Applications, chapter 13, CRC Press, 1997

L.J. van Vliet and P.W. Verbeek, Estimators for Orientation and Anisotropy in Digitized Images, in: J. van Katwijk, J.J. Gerbrands, M.R. van Steen, J.F.M. Tonino (eds.), ASCI'95, Proc. First Annual Conference of the Advanced School for Computing and Imaging (Heijen, NL, May 16-18), ASCI, Delft, 1995, pp. 442-450.

C.F. Westin, A Tensor Framework for Multidimensional Signal Processing, PhD thesis, Linkoping University, Sweden, 1994

SEE ALSO

Derivative

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