Laplacian pyramid is considered as a more compact data structure than the Gaussi

Question

Laplacian pyramid is considered as a more compact data structure than the Gaussian pyramid.

The lowest level of Laplacian pyramid is the same as the Gaussian pyramid. Higher level

Laplacian pyramid is derived from Gaussian pyramid by expanding the higher level Gaussian

pyramid and use the difference between lower level Gaussian image and expanded higher

level Gaussian pyramid to generate lower level Laplacian pyramid.

Complete the following with MATLAB programming:

(a) Use the same Gaussian kernel shown in Problem (1) to generate the second level

Laplacian pyramid

(b) Compute the energy of this Laplacian pyramid and compare with that of second level

Gaussian pyramid to obtain the saving of energy in representation

(c) Complete a three level Laplacian pyramid and display all three level of Laplacian

pyramid in order

Explanation / Answer

1.
(a) Apply this 2D Gaussian kernel to "Lena" image to obtain a blurred Gaussian image
(b) Design a subsampling scheme to obtained a subsampled and blurred Gaussian image for three level of Gaussian pyramid and display them in order
(c) Compute the total energy for each level of Gaussian filtered and subsampled images and compare the loss of energy for each level of pyramid decomposition

2.
(a) Use the same Gaussian kernel shown in Problem (1) to generate the second level Laplacian pyramid
(b) Compute the energy of this Laplacian pyramid and compare with that of second level
Gaussian pyramid to obtain the saving of energy in representation
(c) Complete a three level Laplacian pyramid and display all three level of Laplacian pyramid in order

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