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decorrstretch

Apply decorrelation stretch to multichannel image

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Syntax

S = decorrstretch(A)
S = decorrstretch(A,Name,Value)

Description

S = decorrstretch(A) applies a decorrelation stretch to RGB or multispectral image A and returns the result in S. The mean and variance in each band of S are the same as in A.

The primary purpose of decorrelation stretch is visual enhancement. Decorrelation stretching is a way to enhance the color differences in an image.

example

S = decorrstretch(A,Name,Value) uses name-value pairs to control aspects of the decorrelation stretch, such as the target mean and standard deviation of each band.

Examples

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Open Live Script

This example shows how to use decorrelation stretching to highlight elements in a forest image by exaggerating the color differences.

Read an image into the workspace.

[X, map] = imread('forest.tif');

Apply decorrelation stretching using decorrstretch.

S = decorrstretch(ind2rgb(X,map),'tol',0.01);

Display the original image and the enhanced image.

figure
imshow(X,map)
title('Original Image')

Figure contains an axes object. The axes object with title Original Image contains an object of type image.

figure
imshow(S)
title('Enhanced Image')

Figure contains an axes object. The axes object with title Enhanced Image contains an object of type image.

Input Arguments

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Image to be enhanced, specified as an RGB image or multispectral image of size m-by-n-by-nBands. For an RGB image, nBands = 3.

Data Types: single | double | int16 | uint8 | uint16

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: 'Mode','covariance'

Decorrelation method, specified as the comma-separated pair consisting of 'Mode' and of the following values.

  • 'correlation' — Uses the eigen decomposition of the band-to-band correlation matrix.

  • 'covariance' — Uses the eigen decomposition of the band-to-band covariance matrix.

Data Types: char | string

Target mean values of the output bands, specified as the comma-separated pair consisting of 'TargetMean' and a real scalar or vector of length nBands. By default, TargetMean is an 1-by-nBands vector containing the sample mean of each band, which preserves the band-wise means before and after the decorrelation stretch.

TargetMean must be of class double, but uses the same values as the pixels in the input image. For example, if A is class uint8, then 127.5 would be a reasonable value. If values need to be clamped to the standard range of the input/output image class, it can impact the results.

Data Types: double

Target standard deviation values of the output bands, specified as the comma-separated pair consisting of 'TargetSigma' and a positive scalar or vector of length nBands. By default, TargetSigma is an 1-by-nBands vector containing the sample standard deviation of each band, which preserves the band-wise variance before and after the decorrelation stretch. The target standard deviation is ignored for uniform (zero-variance) bands.

TargetSigma must be class double, but uses the same values as the pixels in the input image. For example, if A is of class uint8, then 50.0 would be a reasonable value.

Data Types: double

Linear contrast stretch following the decorrelation stretch, specified as the comma-separated pair consisting of 'Tol' and a numeric scalar or 2-element numeric vector of class double. Specifying a value of Tol overrides the value of TargetMean or TargetSigma. If you do not specify Tol, then by default decorrstretch does not perform linear contrast stretch.

Tol has the same meaning as in stretchlim, where Tol = [LOW_FRACT HIGH_FRACT] specifies the fraction of the image to saturate at low and high intensities. If you specify Tol as a scalar value, then LOW_FRACT = Tol and HIGH_FRACT = 1 - Tol, saturating equal fractions at low and high intensities.

Small adjustments to Tol can strongly affect the visual appearance of the output.

Data Types: double

Subset of A used to compute the band-means, covariance, and correlation, specified as a cell array containing two arrays of pixel subscripts {rowsubs, colsubs}. rowsubs and colsubs are vectors or matrices of matching size that contain row and column subscripts, respectively.

Use this option to reduce the amount of computation, to keep invalid or non-representative pixels from affecting the transformation, or both. For example, you can use rowsubs and colsubs to exclude areas of cloud cover. If not specified, decorrstretch uses all the pixels in A.

Data Types: double

Output Arguments

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Decorrelation stretched image, returned as a numeric array of the same size and class as the input image, A.

Tips

  • The results of a straight decorrelation (without the contrast stretch option) may include values that fall outside the numerical range supported by the class uint8 or uint16 (negative values, or values exceeding 255 or 65535, respectively). In these cases, decorrstretch clamps its output to the supported range.

  • For class double, decorrstretch clamps the output only when you provide a value for Tol, specifying a linear contrast stretch followed by clamping to the interval [0 1].

  • The optional parameters do not interact, except that a linear stretch usually alters both the band-wise means and band-wise standard deviations. Thus, while you can specify TargetMean and TargetSigma along with Tol, their effects will be modified.

Algorithms

A decorrelation stretch is a linear, pixel-wise operation in which the specific parameters depend on the values of actual and desired (target) image statistics. The vector a containing the value of a given pixel in each band of the input image A is transformed into the corresponding pixel b in output image B as follows:

b = T * (a - m) + m_target.

a and b are nBands-by-1 vectors, T is an nBands-by-nBands matrix, and m and m_target are nBands-by-1 vectors such that

  • m contains the mean of each band in the image, or in a subset of image pixels that you specify

  • m_target contains the desired output mean in each band. The default choice is m_target = m.

The linear transformation matrix T depends on the following:

  • The band-to-band sample covariance of the image, or of a subset of the image that you specify (the same subset as used for m), represented by matrix Cov

  • A desired output standard deviation in each band. This is conveniently represented by a diagonal matrix, SIGMA_target. The default choice is SIGMA_target = SIGMA, where SIGMA is the diagonal matrix containing the sample standard deviation of each band. SIGMA should be computed from the same pixels that were used for m and Cov, which means simply that:

    SIGMA(k,k) = sqrt(Cov(k,k), k = 1,..., nBands).

Cov, SIGMA, and SIGMA_target are nBands-by-nBands, as are the matrices Corr, LAMBDA, and V, defined below.

The first step in computing T is to perform an eigen-decomposition of either the covariance matrix Cov or the correlation matrix

Corr = inv(SIGMA) * Cov * inv(SIGMA).

  • In the correlation-based method, Corr is decomposed: Corr = V LAMBDA V'.

  • In the covariance-based method, Cov is decomposed: Cov = V LAMBDA V'.

LAMBDA is a diagonal matrix of eigenvalues and V is the orthogonal matrix that transforms either Corr or Cov to LAMBDA.

The next step is to compute a stretch factor for each band, which is the inverse square root of the corresponding eigenvalue. It is convenient to define a diagonal matrix S containing the stretch factors, such that:

S(k,k) = 1 / sqrt(LAMBDA(k,k)).

Finally, matrix T is computed from either

T = SIGMA_target V S V' inv(SIGMA) (correlation-based method)

or

T = SIGMA_target V S V' (covariance-based method).

The two methods yield identical results if the band variances are uniform.

Substituting T into the expression for b:

b = m_target + SIGMA_target V S V' inv(SIGMA) * (a - m)

or

b = m_target + SIGMA_target V S V' * (a - m)

and reading from right to left, you can see that the decorrelation stretch:

  1. Removes a mean from each band

  2. Normalizes each band by its standard deviation (correlation-based method only)

  3. Rotates the bands into the eigenspace of Corr or Cov

  4. Applies a stretch S in the eigenspace, leaving the image decorrelated and normalized in the eigenspace

  5. Rotates back to the original band-space, where the bands remain decorrelated and normalized

  6. Rescales each band according to SIGMA_target

  7. Restores a mean in each band.

Version History

Introduced before R2006a

See Also

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