Integration using 2 images of Slopes

Hi everybody!

I don't know if my topics is really clear...
In fact, lets say that 'I' is an image.
I have the image of 'dI/dX' and 'dI/dY'.
Is it possible to get the image 'I' from those slopes (using MATLAB)?

I didn't find any topics related to this, hope I didn't miss it.

Thomas Telandro wrote:
> Hi everybody!
>
> I don't know if my topics is really clear...
> In fact, lets say that 'I' is an image.
> I have the image of 'dI/dX' and 'dI/dY'.
> Is it possible to get the image 'I' from those slopes (using MATLAB)?
>
> I didn't find any topics related to this, hope I didn't miss it.

Hello Thomas,

I don't use Matlab, so I can't speak for that program, but basically it
sounds like you have the 1st deravitive info for the image along two
orthgonal axes.So my best guess is start in a corner and pick an
initial value for the pixel and then use numerical integration in a
step by step way to build the image. Could these be simple deltas
instead of derivatives?  If your image gets too bright or the pixel
levels go negative, you adjust your intial value. Or just just do the
DC offset correction on the final image. This seems like an odd way to
get picture info. Is somebody trying to do some sort of compression by
storing just deltas instead of actual pixel values?

IHTH,

Clay S. Turner

>
>Thomas Telandro wrote:
>> Hi everybody!
>>
>> I don't know if my topics is really clear...
>> In fact, lets say that 'I' is an image.
>> I have the image of 'dI/dX' and 'dI/dY'.
>> Is it possible to get the image 'I' from those slopes (using MATLAB)?
>>
>> I didn't find any topics related to this, hope I didn't miss it.
>
>Hello Thomas,
>
>I don't use Matlab, so I can't speak for that program, but basically it
>sounds like you have the 1st deravitive info for the image along two
>orthgonal axes.So my best guess is start in a corner and pick an
>initial value for the pixel and then use numerical integration in a
>step by step way to build the image. Could these be simple deltas
>instead of derivatives?  If your image gets too bright or the pixel
>levels go negative, you adjust your intial value. Or just just do the
>DC offset correction on the final image. This seems like an odd way to
>get picture info. Is somebody trying to do some sort of compression by
>storing just deltas instead of actual pixel values?
>
>IHTH,
>
>Clay S. Turner
>
>

Sorry for taking so much time to answer.
Thanks for you answer!

In fact, I am trying to reconstruct a Wavefront from his slopes.
Usually from the slopes, using Zernike polynomials you can approximate the
integrated image using least square fit approx.  At the time of my first
post I had not done yet this approximation. 
Now it has been done and giving quite good results but recently I have
found an interesting thing.
Finding integral of image using Fourier Transformation and direct
integration :
http://www.freshpatents.com/Wavefront-reconstruction-using-fourier-transformation-and-direct-integration-dt20041223ptan20040257530.php

At the moment it is not completly clear to me.
If someone has some more detailed explications on this method or other
similar ideas, he is welcome (^-^)

Thomas Telandro