Wavelet Toolbox

Two-Dimensional Wavelet Packet Analysis

In this section, we employ the Wavelet Packet 2-D tool to analyze and compress an image of a fingerprint. This is a real-world problem: the Federal Bureau of Investigation (FBI) maintains a large database of fingerprints -- about 30 million sets of them. The cost of storing all this data runs to hundreds of millions of dollars.

"The FBI uses eight bits per pixel to define the shade of gray and stores 500 pixels per inch, which works out to about 700 000 pixels and 0.7 megabytes per finger to store finger prints in electronic form." (Wickerhauser, see the reference [Wic94] p. 387, listed in References).

"The technique involves a two-dimensional DWT, uniform scalar quantization (a process that truncates, or quantizes, the precision of the floating-point DWT output) and Huffman entropy coding (i.e., encoding the quantized DWT output with a minimal number of bits)." (Brislawn, see the reference [Bris95] p. 1278, listed in References).

By turning to wavelets, the FBI has achieved a 15:1 compression ratio. In this application, wavelet compression is better than the more traditional JPEG compression, as it avoids small square artifacts and is particularly well suited to detect discontinuities (lines) in the fingerprint.

Note that the international standard JPEG 2000 will include the wavelets as a part of the compression and quantization process. This points out the present strength of the wavelets.

Starting the Wavelet Packet 2-D Tool.   

1. From the MATLAB prompt, type

1. wavemenu

   The Wavelet Toolbox Main Menu appears.

   

2. Click the Wavelet Packet 2-D menu item.

1. The tool appears on the desktop.

   

Loading an Image.   

From the File menu, choose the Load Image option.

3. When the Load Image dialog box appears, select the demo MAT-file detfingr.mat, which should reside in the MATLAB directory toolbox/wavelet/wavedemo. Click the OK button.

   

1. The fingerprint image is loaded into the Wavelet Packet 2-D tool.

   

Analyzing an Image.   

4. Make the appropriate settings for the analysis. Select the haar wavelet, level 3, and entropy type shannon. Click the Analyze button.

   

1. There is a pause while the wavelet packet analysis is computed.

Note    Many capabilities are available using the command area on the right of the Wavelet Packet 2-D window. Some of them are used in the sequel. For a more complete description, see Wavelet Packet Tool Features (1-D and 2-D).

5. Click the Best Tree button to compute the best tree before compressing the image.

   

De-Noising a Signal Using Wavelet Packets

Compressing an Image Using Wavelet Packets