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I understand how an object detection algorithm (in particular neural nets) can localize one object. The question is how they can associate a particular object with a particular label when there are multiple objects in an image?

Some related publications:

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The object detection algorithms usually see an image as a set of smaller windows/bags (the regions may or may not overlap). They try to determine if these sub-image regions contain any object or not (accordingly, they are refereed as positive or negative bags).

It is common to assume each region (not an image) only contains one object or instance of an object. Therefore, localizing such instance/object within a region (as opposed to the whole image) is a very simple task.

A few papers about multiple instance learning tasks are cited in the papers you provided as example. Please take a look at them as they try to solve a similar (although not exactly the same) problem.

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