Gaussian pyramid why needs the image to be downsampled

1. Why the image needs to be downsampled if the number of pixels are already reducing through smoothing?
2. What is Gaussian pyramid in image processing?
3. How much space does a Gaussian pyramid take compared to the original image?

Why the image needs to be downsampled if the number of pixels are already reducing through smoothing?

In the context of a gaussian pyramid, why is the image downsampled separately although the numbers of pixels are decreased through smoothing already? The Gaussian filter adjusts the bandwidth of the content of the image. The downsampling adjusts the spatial resolution of the image.

What is Gaussian pyramid in image processing?

In a Gaussian pyramid, subsequent images are weighted down using a Gaussian average (Gaussian blur) and scaled down. Each pixel containing a local average corresponds to a neighborhood pixel on a lower level of the pyramid. This technique is used especially in texture synthesis.

How much space does a Gaussian pyramid take compared to the original image?

The whole pyramid is only 4/3 the size of the original image!