# How to convert classification maps to bounding box

I have a fully convolutional network that has been trained to classify cats and non-cats in small images (48x48). Because it is fully convolutional, I would expect that if I run it in bigger images, the result will be a classification map with overlapping 48x48 patches where I can predict bounding boxes. However, I am not sure how to convert this map (and the bounding boxes) to the original input dimensions.

I have tried something along the lines of: $$x_i = (\left \lfloor{x_{c,1} * R}\right \rfloor, \left \lceil{x_{c,2} * R}\right \rceil)$$ where $$x_{c}$$ represents the x-coordinates of the bounding box in the classification map and $$x_i$$, in the input image space. $$R$$ is the ratio between the sizes of the classification map and input image. This doesn't work.

Can someone please explain how to do it? Thanks!