ihaart2
Inverse 2-D Haar wavelet transform
Description
specifies
how the inverse 2-D Haar transform handles integer-valued data, using
any of the previous syntaxes.xrec
= ihaart2(___,integerflag
)
Examples
Inverse 2-D Haar Transform of an Image
Obtain the inverse 2-D Haar transform of image and view the reconstructed image.
Load the image and obtain its 2-D Haar transform.
im = imread('mandrill.png');
[a,h,v,d] = haart2(im);
Use the inverse 2-D Haar transform to reconstruct the image.
xrec = ihaart2(a,h,v,d);
Compare the original and reconstructed images.
imagesc(im)
title('Original RGB Image')
figure
imagesc(uint8(xrec))
title('Reconstructed RGB Image')
Inverse 2-D Haar Transform of Image Limited to Specified Level
Obtain the 2-D Haar transform of an image limiting the transform to 2 levels.
Load and view the image of a cameraman.
im = imread('cameraman.tif');
imagesc(im)
Obtain the 2-D Haar transform using the default maximum number of levels.
[a,h,v,d] = haart2(im);
Reconstruct the image using the inverse 2-D Haar transform and view the image. Notice the near-perfect reconstruction.
xrec = ihaart2(a,h,v,d); imagesc(xrec)
Reconstruct and view the image using the inverse 2-D Haar transform, limited to level 2. Level 2 corresponds to the fourth scale because scale is defined as , where j is the level.
xrec1 = ihaart2(a,h,v,d,2); imagesc(xrec1)
Using fewer levels returns the average of the original image at level 2.
Inverse 2-D Haar Transform of Image Limited to Integer Data
Obtain the 2-D Haar transform of an image limiting the transform to integer data.
Load the image of a cameraman.
im = imread('cameraman.tif');
Obtain the 2-D Haar transform using the 'integer'
flag.
[a,h,v,d]=haart2(im,'integer');
Reconstruct the image using the inverse 2-D Haar transform and view the image.
xrec = ihaart2(a,h,v,d,'integer');
imagesc(xrec)
Use integer data when you need to reduce the amount of memory used compared to noninteger data.
Input Arguments
a
— Approximation coefficients
scalar | matrix
Approximation coefficients, specified as a scalar or matrix
of coefficients, depending on the level to which the 2-D Haar transform
was calculated. a
is an output from the haart2
function. Approximation, or scaling,
coefficients are a lowpass representation of the input. If a
and
the elements of h
, v
, and d
,
are vectors, xrec
is a vector. If a
and
the elements of h
, v
, and d
are
matrices, xrec
is a matrix, where each column
is the inverse 2-D Haar transform of the corresponding columns in a
and h
, v
,
or d
.
Data Types: single
| double
h
— Horizontal detail coefficients
matrix | cell array
Horizontal detail coefficients by level, specified as a matrix
or cell array of matrices. h
is an output from
the haart2
function. If h
is
a matrix, the 2-D Haar transform was computed only down to one level
coarser in resolution.
Data Types: single
| double
v
— Vertical detail coefficients
matrix or | cell array
Vertical detail coefficients by level, specified as a matrix
or cell array of matrices. v
is an output from
the haart2
function. If v
is
a matrix, the 2-D Haar transform was computed only down to one level
coarser in resolution.
Data Types: single
| double
d
— Diagonal detail coefficients
matrix or | cell array
Diagonal detail coefficients by level, specified as a matrix
or cell array of matrices. d
is an output from
the haart2
function. If d
is
a matrix, the 2-D Haar transform was computed only down to one level
coarser in resolution.
Data Types: single
| double
level
— Maximum level
0
(default) | nonnegative integer
Maximum level to which to invert the Haar transform, specified
as a nonnegative integer. If h
is a cell array, level
is
less than or equal to length(h)-1
. If h
is
a vector or matrix, level
must equal 0
or
be unspecified.
integerflag
— Integer-valued data handling
'noninteger'
(default) | 'integer'
Integer-valued data handling, specified as either 'noninteger'
or
'integer'
. 'noninteger'
does not
preserve integer-valued data in the 2-D Haar transform, and
'integer'
preserves it. The
'integer'
option applies only if all elements of
inputs, a
, h
,
v
, and d
, are integer-valued.
The inverse 2-D Haar transform algorithm, however, uses floating-point
arithmetic.
Output Arguments
xrec
— Inverse 2-D Haar wavelet transform
matrix
2-D Haar wavelet transform, returned as a matrix.
Data Types: single
| double
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Version History
Introduced in R2016b
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