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Topic: Sub pixel measurements?

Hi everybody!
I was thinking about the "sub-pixel displacement measurements". I am a bit confused about the term "sub-pixel" . Becasue in remote sensing of landcover this term is usually used to discribed about how much fraction of different landcovers is present in a pixel. This means that we have lets say 20% grass and 50% snow and 30%bare soil in a pixel or spatial resolution of satellite data.

Well I think this term (sub-pixel) is used in different context in the paper "Automatic and precise orthorectification, coregistration, and subpixel correlation of satellite images, Application to ground deformation measurements - IEEE vol 45, No., 6, June 2007."  The precise interpretation (to my understanding) of the results is that "It can measure displacement that is smaller than the scale of measurements but it cannot give distribution of displacement for every pixel within the window used to get power spectrum of the spatial signal". Well, but on the other hand if we use window step size of ONE then the algorithm can calculate displacement in every pixel of the images.

I will be very grateful if some one help in the interpretation of the scale of resulting displacment field.

Kind regards
MJM

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Re: Sub pixel measurements?

Hello,

Sorry for my late answer, this week has been quite busy preparing for different conferences. The term "sub-pixel displacement  measurement" means that we can resolve a geometrical motion in the image with accuracy better than the pixel size. For instance, we can generally provide estimation of ground motion with a standard deviation around 1m, although images may have a 10m ground resolution.

In vegetation studies, this term refers to a radiometric quantity rather than a geometric one. For vegetation, it relates to mixing issues, which we don't care here.

We are able to retrieve relative image displacement between pairs of images (sometimes also called disparity) for each correlation window. Hence, the measurement we obtain is an average displacement over all the pixels contained in the window. To be more precise, it is a weighted average with maximum weight given at the center of the window and weights decrease to zero at the window edges. When we claim sub-pixel accuracy, we mean that the uncertainty on this average displacement is less than the pixel size.

You have to differentiate between the window size and the sampling of its result. The correlation step refers to the sampling of the results. Because the correlation windows are weighted with maximum weight at the windows' center, the pixels in the center window will contribute more to the average displacement measured. If your step is less than the size of the window, neighboring measurements will not be independent. In other words, the displacement is filtered (smoothed) over the correlation window. Hence although you can output a displacement for every pixel, it will be a smoothed version. It's like the displacement information was diffused over the window size. The smaller the window size, the more spatial resolution you get. Unfortunately, starting at and below a size of 16x16 pixels, the Fourier transform cannot be robustly estimated, hence subpixel estimation starts to fail.
Thus, because we always observe a smooth version of the displacement, we don't need a sampling at every pixel. Typically, a sampling comprised between 1/8 - 1/4 of the window size will provide you with the maximum information you can extract from the images.

Hope this help,

Regards,
Sebastien

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Re: Sub pixel measurements?

Dear Sebastien, Best of luck for your furture conferences and work!

Thanks a lot for the reply! I was keenly waiting for your reply.

Kind Regards
MJM