creating fully convolution network

Question

I was reading this research paper fully convolutional network for semantic segmentation and following is quote from this paper

The fully connected layers of these nets have fixed dimensions and throw away spatial coordinates. However, these fully connected layers can also be viewed as convolutions with kernels that cover their entire input regions.

I didn't understand bold part, but after some researching on internet I have come to conclusion that if I remove last layer(that is fully connected layer) and then convolve last layer(which was second last before removing fully connected layer) with three 1x1 kernels, I will be doing the same thing as the bold part says. Am I correct here?

Why three 1x1 kernels?

Because in paper they are creating a heatmap in rgb from original input and rgb means three channels, but result of convolution network(without fully connected layer) is having many channels(high dimensional) and therefore convolution with three 1x1 kernels to make it an rbg image. Image from paper

Answer 1

Suppose you have a 200X200 matrix in the second last layer. Then if you are going to fully connected layer you will be converting the 200X200 matrix into a single one dimensional array. That means an array of size 40000. That is what is meant by throwing away spatial coordinates. If you are applying a 1x1 kernel the same thing will be happening. You will get a similar one with no change in the values of pixel.