In the context of a gaussian pyramid, why is the image downsampled separately although the numbers of pixels are decreased through smoothing already? In my understanding, the number of pixels will decrease due to the smoothing process already, if a gaussian filter is used. An image with 8 x 5 pixels smoothed with a gaussian filter of 3 x 2 pixels will create a 6 x 4 pixel image if the filter can only be slided within the boundaries of the original image without crossing the edges.

So if the constraint of not crossing the edges of the image is applied, why would one use additional downsampling?

In the context of a gaussian pyramid, why is the image downsampled separately although the numbers of pixels are decreased through smoothing already? In my understanding, the number of pixels will decrease due to the smoothing process already, if a gaussian filter is used within the image boundaries. An image with 8 x 5 pixels smoothed with a gaussian filter of 3 x 2 pixels will create a 6 x 4 pixel image if the filter can only be slided within the boundaries of the original image without crossing the edges.

So if the constraint of not crossing the edges of the image is applied, why would one use additional downsampling?