Module5EMBEDDEDWAVELETCODINGVersion 2 ECE IIT KharagpurLesson13ZerotreeApproachVersion 2
Module
5
EMBEDDED
WAVELET
CODING
Version 2 ECE IIT, Kharagpur
Lesson
13
Zerotree
Approach.
Version 2 ECE IIT, Kharagpur
Instructional Objectives
At the end of this lesson, the students should be able to:
1. Explain the principle of embedded coding.
2. Show the parent-child relationships between subbands of same orientation. 3. Define significance and insignificance of DWT coefficients with respect to a threshold.
4. Define zerotree and zerotree root.
5. Perform
successive
approximation
quantization
(SAQ)
on
DWT
coefficients.
6. Perform dominant pass and subordinate pass for coding of DWT coefficients. 7. Implement a complete Embedded Zerotree Wavelet (EZW) encoder and study its performance on images.
13.0 Introduction
In lesson-12, we have studied Discrete Wavelet Transforms (DWT) and seen its applicability in images. We noted that DWT has excellent energy compaction capabilities and hence the coding technique must be well-designed to achieve significant image compression. In this lesson, we are going to study an embedded wavelet coding technique, known as Embedded Zerotree Wavelet
(EZW) coding that effectively exploits the self-similarity between subbands and the fact that the high-frequency subbands mostly contain insignificant coefficients. First, we define the relationship between the subbands, based on the spatial locations and then define a data structure in the form of a hierarchical tree that includes spatially related coefficients across different subbands. The tree defines a parent-child relationship of DWT coefficients across subbands.
The concept of a zerotree is introduced which identifies the parts of a tree that have all the DWT coefficients insignificant starting with a root. Since, DWT coefficients are generally insignificant at higher frequency subbands, occurrences of zerotrees are expected to be frequent and the zerotree roots can be encoded with a special symbol. The EZW algorithm is based on successive approximation quantization
5
EMBEDDED
WAVELET
CODING
Version 2 ECE IIT, Kharagpur
Lesson
13
Zerotree
Approach.
Version 2 ECE IIT, Kharagpur
Instructional Objectives
At the end of this lesson, the students should be able to:
1. Explain the principle of embedded coding.
2. Show the parent-child relationships between subbands of same orientation. 3. Define significance and insignificance of DWT coefficients with respect to a threshold.
4. Define zerotree and zerotree root.
5. Perform
successive
approximation
quantization
(SAQ)
on
DWT
coefficients.
6. Perform dominant pass and subordinate pass for coding of DWT coefficients. 7. Implement a complete Embedded Zerotree Wavelet (EZW) encoder and study its performance on images.
13.0 Introduction
In lesson-12, we have studied Discrete Wavelet Transforms (DWT) and seen its applicability in images. We noted that DWT has excellent energy compaction capabilities and hence the coding technique must be well-designed to achieve significant image compression. In this lesson, we are going to study an embedded wavelet coding technique, known as Embedded Zerotree Wavelet
(EZW) coding that effectively exploits the self-similarity between subbands and the fact that the high-frequency subbands mostly contain insignificant coefficients. First, we define the relationship between the subbands, based on the spatial locations and then define a data structure in the form of a hierarchical tree that includes spatially related coefficients across different subbands. The tree defines a parent-child relationship of DWT coefficients across subbands.
The concept of a zerotree is introduced which identifies the parts of a tree that have all the DWT coefficients insignificant starting with a root. Since, DWT coefficients are generally insignificant at higher frequency subbands, occurrences of zerotrees are expected to be frequent and the zerotree roots can be encoded with a special symbol. The EZW algorithm is based on successive approximation quantization