Is It Possible to Reconstruct the Original Image from Laplacian Pyramid?

Once we have a blurred image at any level in the Gaussian pyramid, and the corresponding Laplacian pyramid, we can reconstruct the original image by successive addition of higher frequency components at different levels.

1. Can we recover the original image by upsampling?
2. How is a Laplacian pyramid constructed?
3. Which are advantages of Laplacian pyramids over Gaussian pyramids?
4. What is pyramid blending?

Can we recover the original image by upsampling?

This depends on the order of upsampling and downsampling. If the order is correct, then you won't throw away anything and thus you should in principle be able to reconstruct the image.

How is a Laplacian pyramid constructed?

A Laplacian Pyramid is a linear invertible image representation consisting of a set of band-pass images, spaced an octave apart, plus a low-frequency residual. Formally, let. be a downsampling operation which blurs and decimates a j × j image , so that is a new image of size j / 2 × j / 2 .

Which are advantages of Laplacian pyramids over Gaussian pyramids?

The Gaussian pyramid provides a representation of the same image at multiple scales, using simple lowpass filtering and decimation techniques. The Laplacian pyramid provides a coarse representation of the image as well as a set of detail images (bandpass components) at different scales.

What is pyramid blending?

Pyramid image blending works by blending the Laplacian pyramids of two input photos: Page 2 using the Gaussian pyramid of a "mask" image as the alpha matte: The result of this blend is a new Laplacian pyramid from which we can reconstruct a full-resolution, blended version of the input photos.