3.1 Image Pyramid

In last class, we learned about Image Pyramid.

 

 

 

● Image Pyramid Application

Image Pyramid Application

Image Pyramid can be used in many ways.

Image compression, Multi-scale texture mapping, Image blending, Multi-focus composites, Noise removal, Hybrid images, Multi-scale detection, Multi-scale registraion....etc

 

 

 

 

 

 

● Constructing a Gaussian Pyramid

Gaussian Pyramid

When we construct the Gaussian Pyramid, the whole pyramid is only 4/3 the size of the original image.

 

 

Gaussian Pyramid

What happens to the details of the image?

What is preserved at the higher scales?

We cannot reconstruct the original image using the upper pyramid.

 

 

As the level increases, the images become blurry, and also the information in the image is lost.

 

Residual

If we just subtract level 0 by level 1, we can see the residual, which is the lost information from the level 0 image.

This residuals can be retained with a Laplacian Pyramid.

 

 

 

 

 

 

● Laplacian Pyramid

Laplacian Pyramid

 

Laplacian Pyramid retains the residuals (details) between pyramid levels.

We can reconstruct the original image using the upper pyramid.

 

 

Let's see an example of lena.

Compared to picture of level 0, picture of level 1 has low frequency component.

So we add high frequency residual to the level 1 image to make the original level 0 image.

 

 

 

 

 

The more detailed Laplacian Pyramid is explained above.

 

 

 

To reconstruct the original image, an image needs some sequence of processes.

 

 

 

● Difference between Laplacian Pyramid and Gaussian

 

In next class, we will learn about Image Gradients and Gradient Filtering.