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I am using a pre-trained image classification network. How is the object detection performace by passing the parts of the image individually to detect various objects. is there any other way to convert an image classification network into object detection?

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What you propose is one possible, very trivial way to perform object detection. However, there are far more advanced methods based on convolutional networks for image classification.

I recommend having look at these (some of which have nice open-source implementations for many deep learning frameworks):

All of them are based on some convolutional network for image classification, usually adding a few special layers to perform the object detection. For some explanation on how SSD works, have also look at this answer

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