Note: This page has been translated by MathWorks. Click here to see

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Apply decorrelation stretch to multichannel image

`S = decorrstretch(A)`

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

applies
a decorrelation stretch to RGB or multispectral image `S`

= decorrstretch(`A`

)`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.

uses name-value pairs to control aspects of the decorrelation stretch, such as the target mean
and standard deviation of each band.`S`

= decorrstretch(`A`

,`Name,Value`

)

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.

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:

Removes a mean from each band

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

Rotates the bands into the eigenspace of

`Corr`

or`Cov`

Applies a stretch

`S`

in the eigenspace, leaving the image decorrelated and normalized in the eigenspaceRotates back to the original band-space, where the bands remain decorrelated and normalized

Rescales each band according to

`SIGMA_target`

Restores a mean in each band.