# Pyramids

## For Use in Hybrid Images

### Image Pyramids and Their Use in Hybrid Images

A image pyramid is collection of images, constructed from an original one. The two types of image pyramids we are concerned with are Gaussian and Laplacian pyramids. We can construct the Gaussian image pyramid by first first blurring the image with a Gaussian filter, then subsampling to scale the image of a factor of two. We repeat this process for each level of the pyramid, and the final collection of images from each stage is the complete pyramid. Gaussian pyramids have many applications, but for our purposes, they only serve as a means to efficiently separate high and low frequencies of an image. Each stage of the pyramid represents the orriginal image with more and more of the higher frequencies removed.A Gaussian image pyramid with all stages resized to be equivalent:

The second type of pyramid we use is the collection of high frequencies. For this, we construct a Laplacian pyramid. In fact, this second pyramid can be formed directly from the Gaussian pyramid. As we mentioned in the filtering section, the high frequencies can be extracted by first blurring an image and then subtracting the blurred image from the orriginal. To construct the Laplacian pyramid we simply subtract each level of the Gaussian pyramid from the image in the pyramid one level higher (assuming they are scaled to be the same size). A typical Laplacian pyramid might look like this:

Notice how the Gaussian pyramid captures the general essence of the picture better, while Laplacian focuses on fine details.