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About this document
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- Computer Science, Engineering, Mathematics
This document explains the lifting structure in wavelet transforms for 2D images. It provides a Matlab program and example images to illustrate the process. It is useful for understanding how 2D wavelet lifting works.
What's inside
- Introduction to 2D wavelet lifting
- Lifting structure for 2D images
- Matlab program for wavelet lifting
- Example images and results
- Comparison with linear interpolation
Who it is for: Students of computer science, engineering, and mathematics. (Postgraduate)
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Summary
Wavelet lifting in two dimensions (2D) is a method for decomposing and reconstructing images. Students learn how to apply this technique using a Matlab program and see examples of its effects on images.
The Lifting Structure
The lifting structure in 2D involves decomposing an image into two lattices. Each lattice contains half the pixels. This uses quincunx sampling and specific filterings. The process is similar to the 1D case but applied to images.
The Program
A Matlab program called imagelft.m is presented for 2D wavelet lifting. It loads an image, applies quincunx sampling, and performs lifting operations. The program displays various stages of the process, including original and sampled images.
Images
The document discusses the original Lena image and its quincunx samplings. It compares different methods of reconstruction, such as holding and linear interpolation. The effects of lifting with and without the error term d are shown.
Impulse Response Testing
A simplified program for impulse response testing is provided. It allows for the input of small, hand-constructed images and shows the outputs of the lifting operation with and without the error term d.
Key terms
- Quincunx sampling
- A method of sampling an image to create two lattices, each with half the pixels.
- Lifting operations
- Processes that predict and update image samples to achieve decomposition and reconstruction.
- Linear interpolation
- A method of reconstructing an image by estimating missing pixel values based on nearby pixels.
- Error term d
- The difference between the predicted and actual samples in the lifting process.
- Lattices
- The two sets of pixels created by quincunx sampling.
- Impulse response
- The output of the lifting operation when given a small, hand-constructed image.
Questions this document helps with
- What is quincunx sampling for 2D images?
- How do lifting operations work in 2D?
- What is the effect of the error term d in lifting?
Summary written with AI from the document's text.
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