next up previous contents
Next: Numerical experiments Up: Description of the algorithm Previous: Muti-grid approach and optimization   Contents

Quality estimate

An estimation of the quality of our results is highly motivated by the application that we presented in the introduction, namely data assimilation. A well known issue and a crucial point in data assimilation is the knowledge of the statistics of observation errors. Hence, we propose here an estimation of the quality of the pseudo-observations identified by our algorithm.

We propose a normalized quality estimate, where the quality of the motion depends on the ratio between the grey-level differences before and after registration:

$\displaystyle e(I_0,I_1;u,v)(x,y)=1-\frac{\vert I_1(x+u(x,y);y+v(x,y))-I_0(x,y)\vert}{\vert I_1(x,y)-I_0(x,y)\vert}$ (4.17)

if the denominator is non-zero, otherwise we define $ e(I_0,I_1;u,v)=0$ .

We can clearly see that if the two images were quite different on a pixel $ (x,y)$ before the process, and much less different after, then the estimate $ e$ is nearly equal to 1. We will further see that in some regions of the images, there is almost no signal, and then the two images are equal, both before and after the identification process. This leads to an estimate $ e$ equal to 0, not because the identified velocity is wrong, but because we cannot quantify whether it is good or not. This estimator is provided by our algorithm, so that it can be used along with the identified velocity fields in data assimilation experiments.

next up previous contents
Next: Numerical experiments Up: Description of the algorithm Previous: Muti-grid approach and optimization   Contents
Back to home page