wcompress

True compression of images using wavelets

Syntax

wcompress('c',x,cname,compmthd)

wcompress('c',fname,___)

wcompress('c',I,___)

wcompress(___,Name,Value)

[comprat,bpp] = wcompress('c',___)

xc = wcompress('u',cname)

xc = wcompress('u',cname,'plot')

xc = wcompress('u',cname,'step')

Description

The wcompress function performs either compression or uncompression of grayscale or truecolor images.

Compression

wcompress('c',x,cname,compmthd) compresses the image x using the compression method compmthd and saves the result in the file cname. The image x can be either a 2-D array containing an indexed image or a 3-D array of uint8 containing a truecolor image. Both the row and column size of the image must be powers of two.

You must have write permission in the current working directory or the function will change directory to tempdir and write the compressed image in that directory.

Note

• The Discrete Wavelet Transform uses the periodized extension mode.

• Data written to the files uses uint64 precision. In releases previous to R2016b, data was written using uint32. If your code is affected adversely by this change, use the legacy option to compress and uncompress your data using the previous behavior.

  wcompress('c',x,cname,compmthd,'legacy')

wcompress('c',fname,___) loads the image from the file fname.

wcompress('c',I,___) converts the indexed image I{1} to a truecolor image Y using the colormap I{2} and then compresses Y.

wcompress(___,Name,Value) specifies options related to display, data transform, and compression methods using one or more name-value pair arguments in addition to the input arguments in previous syntaxes. The name can be in uppercase or lowercase. For example, 'level',3,'CC','klt' sets the level of the decomposition to 3 and the Color Conversion parameter if x is a truecolor image to the Karhunen-Loève transform.

[comprat,bpp] = wcompress('c',___) returns the compression ratio comprat and the bit-per-pixel ratio bpp.

Uncompression

xc = wcompress('u',cname) uncompresses the file cname which contains the compressed image, and the returns the image xc.

xc = wcompress('u',cname,'plot') plots the uncompressed image.

xc = wcompress('u',cname,'step') shows the step-by-step uncompression (only for Progressive Coefficients Significance Methods).

Examples

Image Compression Using Basic Parameters

This example shows how to compress and uncompress the jpeg image arms.jpg.

Use the spatial orientation tree wavelet ('stw') compression method and save the compressed image to a file.

wcompress('c','arms.jpg','comp_arms.wtc','stw');

Load the stored image and display the step-by-step uncompression to produce the uncompressed image.

wcompress('u','comp_arms.wtc','step');

Compression and Uncompression of a Grayscale Image

This example shows how to compress a grayscale image using the set partitioning in hierarchical trees ('spiht') compression method. It also computes the mean square error (MSE) and the peak signal to noise ratio (PSNR) error values. You use these two measures to quantify the error between two images. The PSNR is expressed in decibels.

Load the image and store it in a file.

load mask;       
[cr,bpp] = wcompress('c',X,'mask.wtc','spiht','maxloop',12)

cr = 
2.8610

bpp = 
0.2289

Load the stored image from the file, uncompress it, and delete the file.

Xc = wcompress('u','mask.wtc');
delete('mask.wtc')

Display the original and compressed images.

colormap(pink(255))
subplot(1,2,1); image(X);  title('Original image')
axis square
subplot(1,2,2); image(Xc); title('Compressed image')
axis square

Compute the MSE and PSNR.

D = abs(X-Xc).^2;
mse  = sum(D(:))/numel(X)

mse = 
33.6564

psnr = 10*log10(255*255/mse)

psnr = 
32.8601

Image Compression and Uncompression Using Advanced Parameters.

This example show how to compress a jpeg image using the adaptively scanned wavelet difference reduction compression method ('aswdr'). The conversion color ('cc') uses the Karhunen-Loeve transform ('kit'). The maximum number of loops ('maxloop') is set to 11 and the plot type ('plotpar') is set to step through the compression. Show the compression ratio (cratio) and the bit-per-pixel ratio (bpp), which indicate the quality of the compression.

[cratio,bpp] = wcompress('c','woodstatue.jpg','woodstatue.wtc', ...
             'aswdr','cc','klt','maxloop',11,'plotpar','step');
cratio
bpp

cratio =

    3.0792


bpp =

    0.7390

Load the compressed image and step through the uncompression process.

wcompress('u','woodstatue.wtc','step');

Compression and Uncompression of a Truecolor Image

This example shows how to compress a truecolor image using the set partitioning in hierarchical trees - 3D ('spiht_3D') compression method.

Load, compress, and store the image in a file. Plot the original and compressed images. Display the compression ratio ('cratio') and the bits-per-pixel ('bpp'), which indicate the quality of the compression.

load mask;     
X = imread('wpeppers.jpg');
[cratio,bpp] = wcompress('c',X,'wpeppers.wtc','spiht','maxloop',12)

cratio = 
1.6549

bpp = 
0.3972

Xc = wcompress('u','wpeppers.wtc');
delete('wpeppers.wtc')

Display the original and compressed images.

subplot(1,2,1)
image(X)
title('Original image')
axis square
subplot(1,2,2)
image(Xc)
title('Compressed image')
axis square

Compute the mean square error (MSE) and the peak signal-to-noise ratio (PSNR) error values. You use these two measures to quantify the error between two images. The PSNR is expressed in decibels.

D = abs(double(X)-double(Xc)).^2;
mse  = sum(D(:))/numel(X)

mse = 
26.7808

psnr = 10*log10(255*255/mse)

psnr = 
33.8526

Input Arguments

x — Input image

2-D matrix | 3-D array

Input image to compress, specified as a 2-D array containing an indexed image or a 3-D array of uint8 containing a truecolor image. Both the row and column size of the image must be powers of two.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

cname — Compressed image filename

character vector | string scalar

Compression

Compressed image filename, specified as a character vector or string scalar. The wcompress function writes the compressed image to the file cname.

Uncompression

Compressed image filename, specified as a character vector or string scalar. The wcompress function reads the compressed image from the file cname for uncompression.

fname — Image filename

character vector | string scalar

Image filename, specified as a character vector or string scalar. The file is a MATLAB^® Supported Format (MSF) file: MAT-file or other image files (see imread).

compmthd — Compression method

character vector | string scalar

Compression method, specified as a character vector or string scalar. The valid compression methods are divided into two categories.

• Progressive Coefficients Significance Methods (PCSM):

  compmthd	Compression Method Name
  'ezw'	Embedded Zerotree Wavelet
  'spiht'	Set Partitioning In Hierarchical Trees
  'stw'	Spatial-orientation Tree Wavelet
  'wdr'	Wavelet Difference Reduction
  'aswdr'	Adaptively Scanned Wavelet Difference Reduction
  'spiht_3d'	Set Partitioning In Hierarchical Trees 3D for truecolor images

  For additional information of these methods, see the references and especially [3] and [6].

• Coefficients Thresholding Methods (CTM):

  compmthd	Compression Method Name
  'lvl_mmc'	Subband thresholding of coefficients and Huffman encoding
  'gbl_mmc_f'	Global thresholding of coefficients and fixed encoding
  'gbl_mmc_h'	Global thresholding of coefficients and Huffman encoding

  For additional details on the 'lvl_mmc' method, see [5]

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'IT','g' sets the Image type transform to grayscale.

Data Transform Parameters

wname — Wavelet name

'bior4.4' (default) | character vector | string scalar

Wavelet name, specified as the comma-separated pair consisting of 'wname' and a character vector or string scalar. See waveletfamilies.

level — Level of wavelet decomposition

positive integer

Level of wavelet decomposition, specified as the comma-separated pair consisting of 'level' and a positive integer. The decomposition level level must be such that 1 ≤ level ≤ levmax, where levmax is the maximum possible level (see wmaxlev).

The default level depends on the compression method compmthd.

• For PCSM methods,level is equal to levmax.

• For CTM methods, level is equal to fix(levmax/2).

Data Types: single | double

it — Image type transform

'n' (default) | 'g' | 'c'

Image type transform, specified as the comma-separated pair consisting of 'it' and one of the values listed:

• 'n' — no transformation (default), image type (truecolor or grayscale) is automatically detected

• 'g' — grayscale transformation type

• 'c' — color transformation type (RGB uint8)

cc — Color conversion parameter

'rgb' or 'none' (default) | 'yuv' | 'klt' | 'yiq' | 'xyz'

Color conversion parameter, specified as the comma-separated pair consisting of 'cc' and one of the values listed:

• 'rgb' or 'none' — no conversion (default)

• 'yuv' — YUV color space transform

• 'klt' — Karhunen-Loève transform

• 'yiq' — YIQ color space transform

• 'xyz' — CIEXYZ color space transform

Progressive Coefficients Significance Methods (PCSM)

maxloop — Maximum number of steps

10 (default) | positive integer | Inf

Maximum number of steps for the compression algorithm, specified as the comma-separated pair consisting of 'maxloop' and a positive integer or Inf.

Data Types: single | double

Coefficients Thresholding Methods (CTM)

bpp — Bit-per-pixel ratio

0.25 (default) | scalar

Bit-per-pixel ratio, specified as the comma-separated pair consisting of 'bpp' and a scalar. The ratio must be greater than 0 and less than or equal to 8 (grayscale) or 24 (truecolor).

If you specify the bit-per-pixel ratio, you cannot specify comprat.

Data Types: single | double

comprat — Compression ratio

0.25 (default) | scalar

Compression ratio, specified as the comma-separated pair consisting of 'comprat' and a scalar. The ratio must be greater than 0 and less than or equal to 100.

If you specify the compression ratio, you cannot specify bpp.

Data Types: single | double

nbclas — Number of classes for quantization

75 (default) | positive integer

Number of classes for quantization, specified as the comma-separated pair consisting of 'nbclas' and positive integer greater than or equal to 2 and less than or equal to 100.

nbclas is valid only for the global thresholding methods.

Data Types: single | double

threshold — Threshold value for compression

nonnegative integer

Threshold value for compression, specified as the comma-separated pair consisting of 'threshold' and a nonnegative number.

threshold is valid only for the global thresholding methods.

If you specify threshold, you cannot specify nbcfs, percfs, bpp, or comprat.

Data Types: single | double

nbcfs — Number of preserved coefficients

nonnegative integer

Number of preserved coefficients in the wavelet decomposition, specified as the comma-separated pair consisting of 'nbcfs' and nonnegative integer less than or equal to the total number of coefficients in the wavelet decomposition.

nbcfs is valid only for the global thresholding methods.

If you specify nbcfs, you cannot specify threshold, percfs, bpp, or comprat.

Data Types: single | double

percfs — Percentage of preserved coefficients

real number

Percentage of preserved coefficients in the wavelet decomposition, specified as the comma-separated pair consisting of 'percfs' and real number greater than or equal to 0 and less than or equal to 100.

percfs is valid only for the global thresholding methods.

If you specify percfs, you cannot specify threshold, nbcfs, bpp, or comprat.

Data Types: single | double

Display Parameter

plotpar — Plot parameter

'plot' or 0 | 'step' or 1

Plot parameter, specified as the comma-separated pair consisting of 'plotpar' and one of the values listed:

• 'plot' or 0 — plot only the compressed image

• 'step' or 1 — display each step of the encoding process (only for PCSM methods)

Output Arguments

comprat — Compression ratio

scalar

Compression ratio, returned as a scalar.

bpp — Bit-per-pixel ratio

scalar

Bit-per-pixel ratio, returned as a scalar.

xc — Uncompressed image

2-D array | 3-D array

Uncompressed image, returned as a 2-D array containing either an indexed image or a 3-D array of uint8 containing a truecolor image.

References

[1] Christophe, Emmanuel, Pierre Duhamel, and Corinne Mailhes. “Adaptation of Zerotrees Using Signed Binary Digit Representations for 3D Image Coding.” EURASIP Journal on Image and Video Processing 2007, no. 1 (2007): 054679. https://doi.org/10.1186/1687-5281-2007-054679.

[2] Misiti, Michel, Yves Misiti, Georges Oppenheim, and Jean-Michel Poggi, eds. Wavelets and Their Applications. London, UK: ISTE, 2007. https://doi.org/10.1002/9780470612491.

[3] Said, A., and W.A. Pearlman. “A New, Fast, and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees.” IEEE Transactions on Circuits and Systems for Video Technology 6, no. 3 (June 1996): 243–50. https://doi.org/10.1109/76.499834.

[4] Shapiro, J.M. “Embedded Image Coding Using Zerotrees of Wavelet Coefficients.” IEEE Transactions on Signal Processing 41, no. 12 (December 1993): 3445–62. https://doi.org/10.1109/78.258085.

[5] Strang, Gilbert, and Truong Nguyen. Wavelets and Filter Banks. Rev. ed. Wellesley, Mass: Wellesley-Cambridge Press, 1997.

[6] Walker, James S. "Wavelet-Based Image Compression." Sub-chapter in Transform and Data Compression. A Primer on Wavelets and Their Scientific Applications. Vol. 29. Studies in Advanced Mathematics. CRC Press, 1999. https://doi.org/10.1201/9781420050011.

Version History

Introduced in R2008b