This section provides additional information about working with
images in the Wavelet Toolbox™ software. It describes the types
of supported images and how the MATLAB^{®} environment represents
them, as well as techniques for analyzing color images.

The basic data structure in MATLAB is the rectangular* matrix*,
an ordered set of real or complex elements. This object is naturally
suited to the representation of *images*, which
are real-valued, ordered sets of color or intensity data. (This toolbox
does not support complex-valued images.)

The word *pixel* is derived from *picture
element** *and usually denotes a single
dot on a computer display, or a single element in an image matrix.
You can select a single pixel from an image matrix using normal matrix
subscripting. For example:

I(2,15)

returns the value of the pixel at row 2 and column 15 of the
image `I`

. By default, MATLAB scales images
to fill the display axes; therefore, an image pixel may use more than
a single pixel on the screen.

A typical color image requires two matrices: a colormap and
an image matrix. The *colormap* is an ordered set
of values that represent the colors in the image. For each image pixel,
the *image matrix* contains a corresponding index
into the colormap. (The elements of the image matrix are floating-point
integers, or *flints*, which MATLAB stores
as double-precision values.)

The size of the colormap matrix is `n`

-by-3
for an image containing `n`

colors. Each row of the
colormap matrix is a 1-by-3 red, green, blue (RGB) color vector

color = [R G B]

that specifies the intensity of the
red, green, and blue components of that color. `R`

, `G`

,
and `B`

are real scalars that range from 0.0 (black)
to 1.0 (full intensity). MATLAB translates these values into
display intensities when you display an image and its colormap.

When MATLAB displays an indexed image, it uses the values in the image matrix to look up the desired color in the colormap. For instance, if the image matrix contains the value 18 in matrix location (86,198), the color for pixel (86,198) is the color from row 18 of the colormap.

Outside MATLAB,
indexed images with `n`

colors often contain values
from 0 to n–1. These values are indices into a colormap with
0 as its first index. Since MATLAB matrices start with index
1, you must increment each value in the image, or *shift
up* the image, to create an image that you can manipulate
with toolbox functions.

*Indexed images* can be thought of as scaled
intensity images, with matrix elements containing only integers from
1 to `n`

, where `n`

is the number
of discrete shades in the image.

If the colormap is not provided, the graphical user interface
tools display the image and processing results using a monotonic colormap
with` `

`max(max(X))-min(min(X))+1`

colors.

Since the image colormap is only used for display purposes, some indexed images may need to be preprocessed to achieve the correct results from the wavelet decomposition.

In general, color indexed images do not have linear, monotonic colormaps and need to be converted to the appropriate gray-scale indexed image before performing a wavelet decomposition.

Note that the coefficients, approximations, and details produced by wavelet decomposition are not indexed image matrices.

To display these images in a suitable way, the graphical user interface tools follow these rules:

Reconstructed approximations are displayed using the colormap

`map`

.The coefficients and the reconstructed details are displayed using the colormap

`map`

applied to a rescaled version of the matrices.

An RGB image, sometimes referred to as a truecolor image, is
stored in MATLAB as an *m*-by-*n*-by-3
data array that defines red, green, and blue color components for
each individual pixel. RGB images do not use a palette. The color
of each pixel is determined by the combination of the red, green,
and blue intensities stored in each color plane at the pixel's location.
Graphics file formats store RGB images as 24-bit images, where the
red, green, and blue components are 8 bits each. This yields a potential
of 16 million colors.

The precision with which a real-life image can be replicated
led to the nickname "truecolor image." An RGB MATLAB array
can be of class `double`

, `single`

, `uint8`

,
or `uint16`

. In an RGB array of class `double`

,
each color component is a value between 0 and 1.

The color components of an 8-bit RGB image are integers in the range [0, 255] rather than floating-point values in the range [0, 1].

The truecolor images analyzed are *m*-by-*n*-by-3
arrays of `uint8`

. Each of the three-color components
is a matrix that is decomposed using the two-dimensional wavelet decomposition
scheme.

Wavelet Toolbox software lets you work with some other types
of images. Using the `imread`

function, the various
tools using images try to load indexed images from files that are
not MAT files (for example, PCX files).

These tools are:

Two-Dimensional Discrete Wavelet Analysis

Two-Dimensional Wavelet Packet Analysis

Two-Dimensional Stationary Wavelet Analysis

Two-Dimensional Extension tool

For more information on the supported file types, type ```
help
imread
```

.

Use the `imfinfo`

function to find the type
of image stored in the file. If the file does not contain an indexed
image, the load operation fails.

Image Processing Toolbox™ software provides a comprehensive set of functions that let you easily convert between image types. If you do not have Image Processing Toolbox software, the examples below demonstrate how this conversion may be performed using basic MATLAB commands.

load xpmndrll whos

Name | Size | Bytes | Class |
---|---|---|---|

`X2` | `192x200` | `307200` | `double array` |

`map` | `64x3` | `1536` | `double array` |

image(X2) title('Original Color Indexed Image') colormap(map); colorbar

The color bar to the right of the image is not smooth and does not monotonically progress from dark to light. This type of indexed image is not suitable for direct wavelet decomposition with the toolbox and needs to be preprocessed.

First, separate the color indexed image into its RGB components:

R = map(X2,1); R = reshape(R,size(X2)); G = map(X2,2); G = reshape(G,size(X2)); B = map(X2,3); B = reshape(B,size(X2));

Next, convert the RGB matrices into a gray-scale intensity image, using the standard perceptual weightings for the three-color components:

Xrgb = 0.2990*R + 0.5870*G + 0.1140*B;

Then, convert the gray-scale intensity image back to a gray-scale indexed image with 64 distinct levels and create a new colormap with 64 levels of gray:

n = 64; % Number of shades in new indexed image X = round(Xrgb*(n-1)) + 1; map2 = gray(n); figure image(X), title('Processed Gray Scale Indexed Image') colormap(map2), colorbar

The color bar of the converted image is now linear and has a smooth transition from dark to light. The image is now suitable for wavelet decomposition.

Finally, save the converted image in a form compatible with the Wavelet Toolbox graphical user interface:

baboon = X; map = map2; save baboon baboon map

Suppose the file `myImage.tif`

contains an
RGB image (noncompressed) of size `S1xS2`

. Use the
following commands to convert this image:

A = imread('myImage.tif'); % A is an S1xS2x3 array of uint8. A = double(A); Xrgb = 0.2990*A(:,:,1) + 0.5870*A(:,:,2) + 0.1140*A(:,:,3); NbColors = 255; X = wcodemat(Xrgb,NbColors); map = pink(NbColors);

The same program can be used to convert BMP or JPEG files.

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