I'm reading the frequently-cited paper Bags of Binary words for Fast Place Recognition in Image Sequences and have found something strange in the paper. The similarity measure is presented as:

$s(v_1, v_2) = 1 - \frac{1}{2}|\frac{v_1}{|v_1|}-\frac{v_2}{|v_2|}|$

where $v_1$ and $v_2$ are bag-of-word vectors. Now, suppose $image_1$ contains 100 occurrences of a certain word and $image_2$ contains just one occurrence. Because $\frac{v_1}{|v_1|} = 1$ and $\frac{v_2}{|v_2|} = 1$, wouldn't $s(v_1,v_2) = 1$ even when the two images are very different? That's a rather counter-intuitive result.


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