[Insight-users] Measuring tumor diameter

[Andriy Fedorov]

On Thu, Dec 11, 2008 at 1:48 PM, Neuner Markus <neuner.markus at gmx.net> wrote:
> My idea would be:
> - compute the direction of highest variability (1st eigenvector of PCA)
> - Now you can resample the volume so that this direction is orented in the
> direction of the z-axis

Well, this idea still rests on the assumption that the max diameter is
aligned with the 1st eigenvector. I believe, this will not generally
be true. I agree, it will probably be close in most cases, but you
must agree, it's not a general solution.

> Another approach would be to:
> - Extract the surface voxels (outlining) or transform it into a surface
> representation (triangulation) to obtain points on the surface
> - Compute a distance matrix (distance between each point)

This is basically the approach I outlined in my original email. I
simplified it to look only at the contour points at the largest area
slice. The problem is that it is quadratic to the number of contour
points, that's why I was looking for cheaper solutions.

I suspect, there may be no simple general solutions.

Fedorov



> - Start with the Points that have the highest distance and check if they can
> be connected by a straight line.
>  This can be done with a loop, a direction vector (with a defined length or
> stepsize). You check if a point is inside the tumor at samplingpoints.
>  The point is moved through the directionvector and a check is performed if
> it is inside the tumor.
>  If the two points with the highest distance can be connected with a
> straight line you have found the biggest diameter, otherwise go on and check
> the next ones.
>
> A nice addon would be to constrain the angle of the line with the help of a
> surface normal.
>
>
> Greets, Markus
>
>
>
>
>
> Andriy Fedorov wrote:
>>
>> Marcus,
>>
>> I have been thinking along these lines too.
>>
>> The problem I can see is that the bounding sphere diameter will not be
>> the same as the maximum shape diameter. I can understand why the
>> method you suggest works in collision detection, but in tumor
>> measurement we need precision.
>>
>> Going back to my counter-examples, if you think of a T-shaped contour
>> in 2D, the max diameter will be the length of the longer segment in T.
>> If you imagine a sphere with all points inside, its radius will exceed
>> the max diameter.... The method you suggest will give some estimate,
>> but not *the* maximum diameter.
>>
>> Fedorov
>>
>>
>>
>> On Thu, Dec 11, 2008 at 12:10 PM, Neuner Markus <neuner.markus at gmx.net>
>> wrote:
>>
>>>
>>> Hi,
>>>
>>> I would sggest an approch that is called:  "Bounding Sphere"
>>> and is commonly used in graphics to calculate bounding spheres that are
>>> independent of object rotations.
>>>
>>> Several methods exist to compute a bounding spere and some good examples
>>> of
>>> how to compute and implement this is outlined in the book "Real-Time
>>> Collision Detection" from Christer Ericson.
>>>
>>> One good method is to use the direction of maximum spread from a PCA
>>> (primary component analysis) of all "contour points".
>>> Then you pick points farhest away along this direction (1st eigenvector).
>>> This is done by projection (Dot-Product) of the points onto the direction
>>> vector and you increase the diameter of a shpere until all points are
>>> inside.
>>>
>>> I dont know if PCA is implemented in ITK to compute the covariancematrix,
>>> eigenvectors and eigenvalues of a point set.
>>>
>>>
>>> Regards, Markus
>>>
>>>
>>> Andriy Fedorov wrote:
>>>
>>>>
>>>> On Thu, Dec 11, 2008 at 10:17 AM, Somer, Edward <edward.somer at kcl.ac.uk>
>>>> wrote:
>>>>
>>>>
>>>>>
>>>>> Having segmented the tumour I'd try a 3D-distance transform to find the
>>>>> interior pixel furthest from any edge of the mask. Isn't the maximum
>>>>> diameter then twice the value of the distance transform at this point?
>>>>>
>>>>>
>>>>>
>>>>
>>>> This will not work, unfortunately. Here's a counterexample.
>>>>
>>>> Imagine I-like shape of some thickness in 2d. Then the maximum
>>>> distance from distance transform will be half the thickness of the
>>>> shape. However, the diameter will be equal to the *length* of this
>>>> shape. So in this case you are getting non-maximum diameter with the
>>>> approach you suggest.
>>>>
>>>>
>>>>
>>>>
>>>>>
>>>>> Perhaps I'm missing something,
>>>>>
>>>>> Ed
>>>>>
>>>>> Andriy Fedorov wrote:
>>>>>
>>>>>
>>>>>>
>>>>>> Luis,
>>>>>>
>>>>>> I am actually looking for an automatic tool.
>>>>>>
>>>>>> The approach I am currently considering is this:
>>>>>>
>>>>>> 1) go through the axial slices, find the one with the largest area
>>>>>> 2) extract that slice contour
>>>>>> 3) go through all possible combinations of the contour points, find
>>>>>> the pair of most distant points, and take this as a diameter
>>>>>> 4) follow the line between the points in the previous step, and
>>>>>> subtract the parts of the line that are outside the contour (this is
>>>>>> how the tumor measurements are actually taken). This may change the
>>>>>> measured diameter.
>>>>>> 5) repeat steps 3 and 4 until the maximum is found after taking into
>>>>>> account diameter parts outside the countour
>>>>>>
>>>>>> The problem of course is that this procedure will be quadratic to the
>>>>>> number of contour points, and I am looking for ways to speed this up,
>>>>>> or find an existing implementation, or find a better way to find the
>>>>>> farthest point. I thought about kd-tree to optimize point location,
>>>>>> but I am not sure how to use it for farthest point.
>>>>>>
>>>>>> Any comments are welcome
>>>>>>
>>>>>> Andriy Fedorov
>>>>>>
>>>>>>
>>>>>> On Thu, Dec 11, 2008 at 9:47 AM, Luis Ibanez <luis.ibanez at kitware.com>
>>>>>> wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>>>
>>>>>>> Hi Andi,
>>>>>>>
>>>>>>>
>>>>>>> Are you looking for an automatic tool ?
>>>>>>> or for an interactive method ?
>>>>>>>
>>>>>>> In VTK you will find 3D Widgets designed
>>>>>>> for taking measurements in-plane.
>>>>>>>
>>>>>>>
>>>>>>>  Regards,
>>>>>>>
>>>>>>>
>>>>>>>  Luis
>>>>>>>
>>>>>>>
>>>>>>> ------------------------
>>>>>>> Andriy Fedorov wrote:
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>>> Hi,
>>>>>>>>
>>>>>>>> I need to measure the longest diameter of a 3D tumor segmentation. I
>>>>>>>> was wondering, if anybody is aware of any existing tools for this
>>>>>>>> purpose? If not, are there tools to quickly measure the diameter of
>>>>>>>> a
>>>>>>>> 2D projection of the segmentation?
>>>>>>>>
>>>>>>>> I just wanted to have the community opinion before starting to
>>>>>>>> implement something myself.
>>>>>>>>
>>>>>>>> Andriy Fedorov
>>>>>>>> _______________________________________________
>>>>>>>> Insight-users mailing list
>>>>>>>> Insight-users at itk.org
>>>>>>>> http://www.itk.org/mailman/listinfo/insight-users
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>
>>>>>> _______________________________________________
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>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>> --
>>>>> Edward Somer, PhD.
>>>>> Senior PET Methodologist
>>>>> The PET Imaging Centre St Thomas' Hospital
>>>>> London, UK
>>>>> SE1 7EH
>>>>>
>>>>> work tel: +44 (0) 20 7188 1497
>>>>> work fax: +44 (0) 20 7620 0790
>>>>> e-mail: Edward.Somer at kcl.ac.uk / Edward.Somer at googlemail.com
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>
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>>>>
>>>>
>>
>>
>