# Bags of visual words - counter intuitive result

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.