Understanding the inner workings of the radon function (from skimage)

[Kaloyan Marinov]

Dear Juan,

Thank you for the reference.

I am afraid I have not had exposure to Cython, so I was wondering if I may 
ask the following basic questions:

   - the comments below the definition of a_matrix_transform seem to 
   suggest that H is supposed to be a 2D array of shape (3,3); however, the 
   code for a_matrix_transform seems to refer to H as a 1D array of length 9. 
   Does that mean the comment is inaccurate?
   - the third input in the call of a_matrix_transform (within the nested 
   for loops) is &M[0,0], which is neither a 2D array of shape (3,3), nor a 1D 
   array of length 9; this seems to a bit contradictory to me. Do you happen 
   to know how the third input in the call of a_matrix_transform is to be 
   interpreted?
   - I am interested in the case when order = 1 so, for me, interp_func = 
   bilinear_interpolation; where could I find the sourcecode (or clear 
   description) for bilinear_interpolation?
   - last but not least, the type of img is defined to cnp.ndarray, and 
   then one converts it to a contiguous array; what is the purpose/advantage 
   of doing this conversion?
   - I do have a _warps_cy.so on my harddrive, but I don't know what 
   application it can be opened it; could you let me know about that?
   
I would be very thankful for any feedback you may offer.

Best,
Kaloyan


On Friday, April 11, 2014 3:11:46 AM UTC+3, Juan Nunez-Iglesias wrote:
>
> Hi Kaloyan,
>
> I'm not familiar with the radon transform but the _warps_cy source file is 
> a Cython file (.pyx extension), _warps_cy.pyx here:
>
> https://github.com/scikit-image/scikit-image/tree/master/skimage/transform
>
> Others might weigh in on the actual maths of the discrete radon transform. 
> =)
>
> Juan.
>
>
> On Thu, Apr 10, 2014 at 9:25 PM, Kaloyan Marinov <kaloya... at gmail.com<javascript:>
> > wrote:
>
>> I am familiar with the mathematical theory of the continuous Radon 
>> transform, but am having trouble understanding its discrete implementation 
>> from skimage. Below I list my two questions on the topic.
>>
>> *Question 1*
>>
>> Let us define a matrix A as follows:
>>
>> A = np.zeros( (4,4) )
>> A[1:3,1:3] = 1
>>
>> Compute its Radon transform as follows:
>>
>> radTranfOfA = skimage.transform.radon(A,[45])
>>
>> This computed radTranfOfA to be the following array of shape (6,1):
>>
>> array([[ 0.        ],
>>        [ 0.        ],
>>        [ 0.87867966],
>>        [ 2.42893219],
>>        [ 0.87867966],
>>        [ 0.        ]])
>>
>> Could someone explain to me (preferably in a mathematically precise way) 
>> exactly how Python computed this?
>>
>> *Question 2*
>>
>> I have attempted to study the radon_transform.py source-code file from 
>> the skimage package, but the definition of the radon function there depends 
>> on a function called _warp_fast which is imported from _warps_cy. However, 
>> I cannot see the sourcecode for _warps_cy; could anyone suggest a way 
>> around this (or a precise mathematical explanation of what _warps_cy does 
>> and how its output is stored)?
>>  
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