Two Ways to Miss

A detector for a supermarket shelf camera is early in training. For one cereal box, the true box is $G$ . Two of the detector's guesses, $A$ and $B$ , are the right size but in the wrong place. Boxes are given as $(x_{\min}, y_{\min}, x_{\max}, y_{\max})$ in pixels, with $y$ growing downwards.

box	$x_{\min}$	$y_{\min}$	$x_{\max}$	$y_{\max}$
$G$ (true)	10	10	50	50
$A$	60	60	100	100
$B$	90	10	130	50

Neither guess overlaps $G$ at all. A training signal built on plain IoU therefore has nothing to say about which miss is the better one. Generalized IoU (GIoU) adds a second term for exactly this case.

Let $C$ be the smallest rectangle, with sides parallel to the image edges, that contains both boxes. Then

\text{GIoU} = \text{IoU} - \frac{\text{area}(C) - \text{area}(\text{union})}{\text{area}(C)}

where the union is the total area the two boxes cover between them. As with IoU, a higher GIoU means a better guess.

Compare each guess with $G$ . Which statement is correct?

Two Ways to Miss

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