deletions | additions       diff --git a/DeclareMathOperator_argmin_arg_min_DeclareMathOperator__1.tex b/DeclareMathOperator_argmin_arg_min_DeclareMathOperator__1.tex  index 2ed35e4..c7dea90 100644  --- a/DeclareMathOperator_argmin_arg_min_DeclareMathOperator__1.tex  +++ b/DeclareMathOperator_argmin_arg_min_DeclareMathOperator__1.tex 
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matrix. The pixel position of the center in the reference image can be  used to determine the real world position by transforming the pixel  coordinates to real-world coordinates, based on the scale factors  $C_x$ and $C_y$, with $C_x = width(R) / width(I)$ \frac{width(R)}{width(I)}$  and $C_y = height(R) / height(I)$, \frac{height(R)}{height(I)}$,  where $W$ is the real-world representation and $I$ the digital pixel image. This yields a dataset  of images, labeled with $x, y$ coordinates and the number of  matches. This process already introduces noise into the dataset, since