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## Lab: Wavelet Transform

[Exercises] [Workspace]

Purpose: The purpose of this lab exercise is to perform one-level forward and inverse wavelet transforms. You will compare the reconstructed image against the original image.

Activities:

1. Read and display the image $DIP/data/gull.kdf. Use the operators User defined and Display Image.

   1. Glyphs:Input/Output:Data Files:User defined
   2. Glyphs:Visualization:Non-Interactive Display:Display Image

2. Take a one-level forward wavelet transform of the image, using the operator Wavelet Transform. Use the file $DIP/data/daub2hd.ascii as the "Highpass Filter Coefficient" file, and $DIP/data/daub2ld.ascii as the "Lowpass Filter Coefficient" file. Display the results using Display Image

   1. Glyphs:Input/Output:Data Files:User defined
   2. Glyphs:Wavelet:Linear Transforms:Wavelet Transform
   3. Glyphs:Visualization:Non-Interactive Display:Display Image

3. Take the inverse wavelet transform with one-level of decomposition using the same filter coefficient files as you used in Step 2, and display the results. Use the operators Wavelet Transform and Display Image.

   1. Glyphs:Wavelet:Linear Transforms:Wavelet Transform
   2. Glyphs:Visualization:Non-Interactive Display:Display Image

4. Calculate the absolute difference between the original image and the reconstructed image using the Absolute Diff operator and display the result. Determine the maximum and minimum of the absolute difference using the Statistics operator.

   1. Glyphs:Arithmetic:Two Operand Arithmetic:Absolute Diff
   2. Glyphs:Visualization:Non-Interactive Display:Display Image
   3. Glyphs:Data Manip:Analysis & Information:Statistics

5. Extract the low-pass image (first quadrant) from the forward wavelet transform image, zero-pad it to same size of the original image, and take the inverse wavelet transform (using the same filter coefficient files). Display the result. Use the operators Extract , Pad, and Display Image.

   1. Glyphs:Data Manip:Size & Region Operators:Extract
   2. Glyphs:Data Manip:Size & Region Operators:Pad
   3. Glyphs:Visualization:Non-Interactive Display:Display Image

6. Calculate the absolute difference between the original image and the image reconstructed with the low-pass image using the Absolute Diff operator and display the result. Determine the maximum and minimum of the absolute difference using the Statistics operator.

   1. Glyphs:Arithmetic:Two Operand Arithmetic:Absolute Diff
   2. Glyphs:Visualization:Non-Interactive Display:Display Image
   3. Glyphs:Data Manip:Analysis & Information:Statistics

Exercises

1. Perform the same experiment, but with different images.
2. Perform the same experiment, but use other quadrants of the transform to reconstruct the image.

Khoros Workspace
Execute the visual program c8s2W-compression.wk