[Insight-users] Measuring tumor diameter

[Andriy Fedorov]

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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>>>> Insight-users at itk.org
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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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>