cwtft2
2-D continuous wavelet transform
Description
specifies options using one or more name-value arguments in addition to the input
arguments in previous syntaxes.cwtstruct
= cwtft2(___,Name,Value
)
Examples
2-D CWT with Morlet Wavelet
Load and display the star image.
img = imread("star.jpg");
image(img)
Obtain the 2-D CWT of the star image using the default Morlet wavelet, scales 2.^(0:5)
, and an angle of 0. Visualize the 2-D CWT coefficient magnitudes at the finest scale.
cwtout = cwtft2(img); sca = 1; imagesc(abs(cwtout.cfs(:,:,1,1,sca)))
Plot 2-D CWT
Load an image of a woman, obtain the 2-D CWT using the default Morlet wavelet, and plot the CWT coefficients.
load woman cwtmorl = cwtft2(X,"plot");
Compare Isotropic and Anisotropic Wavelets
Shows how an isotropic wavelet does not discern the orientation of features while an anisotropic wavelet does. The example uses the Marr isotropic wavelet and the directional (anisotropic) Cauchy wavelet.
Load and view the hexagon image.
img = imread("hexagon.jpg");
imagesc(img)
Obtain the scale-one 2-D CWT with both the Marr and Cauchy wavelets. Specify a vector of angles going from 0 to in increments.
cwtAngles = 0:pi/8:2*pi-pi/8; cwtcauchy = cwtft2(img,wavelet="cauchy",scales=1, ... angles=cwtAngles); cwtmarr = cwtft2(img,wavelet="marr",scales=1, ... angles=cwtAngles);
There are 16 angles. Visualize the scale-one 2-D CWT coefficient magnitudes at any two consecutive angles. Confirm that using the Marr isotropic wavelet does not discern the orientation of features, but the Cauchy wavelet does.
angz = {"0", "pi/8", "pi/4", "3pi/8", "pi/2", "5pi/8", "3pi/4", ... "7pi/8","pi", "9pi/8", "5pi/4", "11pi/8", "3pi/2", ... "13pi/8" "7pi/4", "15pi/8"}; indexAngle1 = 7; indexAngle2 = 8; tiledlayout(2,2) for k=[indexAngle1 indexAngle2] nexttile imagesc(abs(cwtmarr.cfs(:,:,1,1,k))); title(["Marr Wavelet at " angz(k) "radians"]); nexttile imagesc(abs(cwtcauchy.cfs(:,:,1,1,k))); title(["Cauchy Wavelet at " angz(k) "radians"]); end
Visualize the scale-one 2-D CWT coefficient magnitudes obtained using the Marr isotropic wavelet at any two angles. Confirm the wavelet does not discern the orientation of features.
indexAngle1 = 2; indexAngle2 = 7; tiledlayout(1,2) for k=[indexAngle1 indexAngle2] nexttile imagesc(abs(cwtmarr.cfs(:,:,1,1,k))); title(["Marr Wavelet at " angz(k) "radians"]); end
Input Arguments
X
— Input data
array
Input data, specified as a numeric array. X
can be an
M-by-N array representing an
indexed image or an M-by-N-by-3 array
representing a truecolor image.
Data Types: double
| single
| uint8
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.
Example: wavelet="paul",scales=2.^(0:5)
specifies to use the
Paul wavelet and a vector of scales.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: "wavelet","paul","scales",2.^(0:5)
specifies to use the Paul
wavelet and a vector of scales.
angles
— Angles
0
(default) | scalar | vector
Angles in radians used in the 2-D CWT, specified as a scalar or a vector.
Example: angles=[0 pi/2 pi]
norm
— Normalization
"L2"
(default) | "L1"
| "L0"
Normalization used in the 2-D CWT, specified as one of these:
"L2"
— The Fourier transform of the analyzing wavelet at a given scale is multiplied by the corresponding scale."L2"
is the default normalization."L1"
— The Fourier transform of the analyzing wavelet is multiplied by 1 at all scales."L0"
— The Fourier transform of the analyzing wavelet at a given scale is multiplied by the square of the corresponding scale.
Example: norm="L1"
scales
— Scales
2.^(0:5)
(default) | scalar | vector
Scales, specified as a positive real-valued scalar or a vector of positive real numbers.
Example: scales=2.^(1:6)
wavelet
— Analyzing wavelet
"morlet"
(default) | character vector | string scalar | structure | cell array
Analyzing wavelet, specified as a character vector, a string scalar, a structure, or a cell
array. cwtftinfo2
provides a
comprehensive list of supported wavelets and associated
parameters.
If you specify wavelet
as a structure, the structure must contain two fields:
name
— character vector or string scalar corresponding to a supported wavelet.param
— cell array containing optional parameters, which depend on the wavelet. If you do not wish to specify optional parameters, use an empty cell array.
If you specify wavelet
as a cell array, wav
, the cell
array must contain two elements:
wav{1}
— character vector or string scalar corresponding to a supported wavelet.wav{2}
— cell array with the parameters of the wavelet.
Example: "wavelet",{"morlet",{6,1,1}}
specifies the Morlet wavelet as a cell
array.
Example: "wavelet",struct("name","paul","param",{{2}})
specifies the Paul
wavelet as a structure array.
Output Arguments
cwtstruct
— 2-D CWT
structure
The 2-D CWT, returned as a structure with the following fields:
wav
— Analyzing wavelet and parameters
structure
Analyzing wavelet and parameters, returned as a structure with the following fields:
wname
— Wavelet nameparam
— Wavelet parameters
wav_norm
— Normalization constants
matrix
Normalization constants, returned as an M-by-N matrix, where M is the number of scales and N is the number of angles.
cfs
— CWT coefficients
array
CWT coefficients, returned as an N-D array.
The row and column dimensions of the array equal the row and column dimensions of the input data.
The third page of the array is equal to 1 or 3 depending on whether the input data is a grayscale or truecolor image.
The fourth page of the array is equal to the number of scales.
The fifth page of the array is equal to the number of angles.
scales
— Scales
vector
Scales for the 2-D CWT, returned as a row vector.
angles
— Angles
vector
Angles for the 2-D CWT, returned as a row vector.
meanSIG
— Mean
scalar
Mean of the input data, returned as a scalar
Version History
Introduced in R2013b
Open Example
You have a modified version of this example. Do you want to open this example with your edits?
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)