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Image Compression Using the Haar Wavelet Transform - PowerPoint PPT Presentation

Image Compression Using the Haar Wavelet Transform. Peggy Morton and Arne Petersen 2004. 10. 18 Yoon HeeJoo. Contents. Introduction Averaging and Differencing Image Representation Using Linear Algebra Image Compressions. 1. Introduction. Done by compressing the image

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Image Compression Using the Haar Wavelet Transform

Peggy Morton and Arne Petersen

2004. 10. 18

Yoon HeeJoo

• Introduction

• Averaging and Differencing

• Image Representation

• Using Linear Algebra

• Image Compressions

• Done by compressing the image

• Use a process called averaging and differencing to develop a new matrix representing the same image in a more concise manner.

• Eliminate some of unnecessary information, and arrive at an approximation of our original image

• 8X8 matrix, process involve three steps (2³=8)

• Step 1[3 5 4 8 13 7 5 3][4 6 10 4 -1 -2 3 1]ex. (3 + 5)/2 = 4 3 - 4 = -1

Averaging

Differencing

detail coefficient

• Step 2[4 6 10 4 -1 -2 3 1][5 7 -1 3 -1 -2 3 1]ex. (4 + 6)/2 = 5 4 - 5 = -1

Averaging

Differencing

detail coefficient

• Step 3[5 7 -1 3 -1 -2 3 1][6 -1 -1 3 -1 -2 3 1]ex. (5 + 7)/2 = 6 5 - 6 = -1

Averaging

Differencing

detail coefficient

row average

• Use the averaging and differencing process

[Figure 1]

• first row [64 2 3 61 60 6 7 57]

• Step1 [33 32 33 32 31 -29 27 -25]

• Step2 [32.5 32.5 0.5 0.531 -29 27 -25]

• Step3 [32.5 00.5 0.5 31 -29 27 -25]

• rows the results

detail coefficients

row average

columns the results

choose some number (δ) and set equal to zero

δ = 5

• apply the inverse of the averaging the differencing operations

Original Image

Decompressed Image

[Figure 2]

• Step1

Average

Difference

• Step3

• Step2

• W = A1A2A3A

• A : Original Matrix

• W : Transforming Matrix

• T : Compressed Matrix

• Figure 3a.

• Original Image

• Figure 3b.

• 65,536 entries

• 631 non-zero entries

• Compression Ratio – 103:1

• Figure 3c.

• 65,536 entries

• 1,411 non-zero entries

• Compression Ratio – 46:1

• Program

• Questions