[Insight-users] RV: about HessianRecursiveGaussianImageFilter

Wed Jun 30 04:50:41 EDT 2010

If you simply have a Hessian matrix (SymmetricSecondRankTensor) you can get
the same result by calculating the eigenvalues using the method
ComputeEigenValues(). This is useful for example if you calculate the
Hessian matrix in only a few points and want to calculate corresponding
eigenvalues.

I don’t know what you understand by “intensity values”. In general, what
we call a discrete image is an scalar, vectorial or tensor field that is
sampled in the form a discrete structured grid equispaced along each
direction (that is for every point of the space you get an scalar, vector or
tensor depending on the nature of the field). The values at each grid point
can be scalar (what we usually call intensity) or vectorial (this can be
several values representing for example RGB values, velocity or other
magnitudes) or tensorial (i.e. the Hessian matrix). The scalar need not to
be an integer, it can be for example floating point value and it usually
represents the output of the sensor, a calculated magnitude etc. When you
calculate an image of eigenvalues in fact you get a vector at each point
that stores those values (vector image). You can simply access the value at
each point as usual, and since here you have a vector you may use the array
[] operator after accessing the pixel vector value using iterators (best) or
GetPixel() (random access)

The EigenValueAccesor in the attached example simply accesses each component
to create three scalar images from the vector image.

I hope this answers your questions.

Best regards 

Iván

De: 苏苒 [mailto:suran.tju at gmail.com] 
Enviado el: martes, 29 de junio de 2010 3:28
Para: Ivan Macia
Asunto: Re: [Insight-users] about HessianRecursiveGaussianImageFilter

Dear Ivan:

Thank you for your answer. 

I began to use ITK library very recently. I want to compute the Hessian
matrix values and Hessian matrix eigenvalues for linear feature extraction. 

It seems from your answer that the Hessian matrix eigenvalues after using
your code(attachement) are not stored as intensity values, then, how can I
access these values? 

Thanks very much, 

Ran 

2010/6/29 Ivan Macia <imacia at vicomtech.org>

Hi,

The Hessian matrix, of type itk::SymmetricSecondRankTensor, is defined in
the filter as a matrix of real values, hence you can store positive and
negative floating point values. This is what you mean?

Iván

2010/6/28 savagegarden <suran.tju at gmail.com>

Hi Iván,
Thank you for your codes.
However, I wonder how you store the Hessian matrix values? If you store as
an image intensity, how you deal with the negative matrix value？
Ran

Iván Macía wrote:
>
> Dear Liu,
>
> I made this code based on the Curves3DExtractor application (in
> InsightApplications). It performs eigenanalysis of the Hessian matrix and
> writes 3 images that correspond to the 3 eigenvalues (if nothing is
> wrong).
>
> Hope that helps
>
> Iván
>
>    _____
>
> De: insight-users-bounces+imacia=vicomtech.es <http://vicomtech.es/> @itk.
org <http://itk.org/> 
> [mailto:insight-users-bounces+imacia
<mailto:insight-users-bounces%2Bimacia> =vicomtech.es <http://vicomtech.es/>
@itk.org <http://itk.org/> ] En nombre de
> SCHMID, Jerome
> Enviado el: jueves, 26 de enero de 2006 2:35
> Para: liu jianfei; ITK
> Asunto: RE: [Insight-users] about HessianRecursiveGaussianImageFilter
>
>
>
> Dear Liu Jianfei,
>
> Have a look in the last itk code ( cvs or release ) for the filter
> "itk::Hessian3DToVesselnessMeasureImageFilter" in files
> itkHessian3DToVesselnessMeasureImageFilter.h and
> itkHessian3DToVesselnessMeasureImageFilter.txx. It shows you how to
> perform
> most of the job: compute hessian then eigenvalues and finally compute some
> vesselness measure based on eigenvalues.
>
> Best Regards,
>
> Jerome Schmid
>
> ---------------------------------------------
> Jerome SCHMID
> Project Manager / Engineer
> Augmented and Virtual Reality
> Minimally Invasive Surgical Skills Center (MIS)
> HYPERLINK "http://www.hkmisc.org.hk/"http://www.hkmisc.org.hk/
> Prince of Wales Hospital
> Chinese University Of Hong-Kong
> ----------------------------------------------
>
>
>
> -----Original Message-----
> From: insight-users-bounces+jeromeschmid=surgery.cuhk.edu.hk
<http://surgery.cuhk.edu.hk/> @itk.org <http://itk.org/>  on
> behalf of liu jianfei
> Sent: Thu 1/26/2006 6:34 AM
> To: ITK
> Subject: [Insight-users] about HessianRecursiveGaussianImageFilter
>
>
> Hi, everyone
>
>     I've pasted a message on this class. Just now, I checked that the
> number
> of output is 6 values. They should be the component of the hessian matrix.
> Can someone tell me the order of these values.
>     Ixx  Ixy  Ixz
>            Iyy  Iyz
>                  Izz
>     Is the order of these value Ixx  Ixy  Ixz Iyy  Iyz Izz? Thanks
>
>
>      Have a nice day!
> --
> Sincerly
> Jianfei Liu
>
>
> _______________________________________________
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> Insight-users at itk.org
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