|
|
|
|
@ -1,5 +1,5 @@
|
|
|
|
|
import numpy as np
|
|
|
|
|
__all__ = ['dct', 'idct']
|
|
|
|
|
__all__ = ['dct', 'idct', 'dctn', 'idctn']
|
|
|
|
|
def dct(x, n=None):
|
|
|
|
|
"""
|
|
|
|
|
Discrete Cosine Transform
|
|
|
|
|
@ -105,3 +105,258 @@ def idct(x, n=None):
|
|
|
|
|
return y.real
|
|
|
|
|
else:
|
|
|
|
|
return y
|
|
|
|
|
|
|
|
|
|
def dctn(y, axis=None, w=None):
|
|
|
|
|
'''
|
|
|
|
|
DCTN N-D discrete cosine transform.
|
|
|
|
|
|
|
|
|
|
Y = DCTN(X) returns the discrete cosine transform of X. The array Y is
|
|
|
|
|
the same size as X and contains the discrete cosine transform
|
|
|
|
|
coefficients. This transform can be inverted using IDCTN.
|
|
|
|
|
|
|
|
|
|
DCTN(X,axis) applies the DCTN operation across the dimension axis.
|
|
|
|
|
|
|
|
|
|
Class Support
|
|
|
|
|
-------------
|
|
|
|
|
Input array can be numeric or logical. The returned array is of class
|
|
|
|
|
double.
|
|
|
|
|
|
|
|
|
|
Reference
|
|
|
|
|
---------
|
|
|
|
|
Narasimha M. et al, On the computation of the discrete cosine
|
|
|
|
|
transform, IEEE Trans Comm, 26, 6, 1978, pp 934-936.
|
|
|
|
|
|
|
|
|
|
Example
|
|
|
|
|
-------
|
|
|
|
|
RGB = imread('autumn.tif');
|
|
|
|
|
I = rgb2gray(RGB);
|
|
|
|
|
J = dctn(I);
|
|
|
|
|
imshow(log(abs(J)),[]), colormap(jet), colorbar
|
|
|
|
|
|
|
|
|
|
The commands below set values less than magnitude 10 in the DCT matrix
|
|
|
|
|
to zero, then reconstruct the image using the inverse DCT.
|
|
|
|
|
|
|
|
|
|
J(abs(J)<10) = 0;
|
|
|
|
|
K = idctn(J);
|
|
|
|
|
figure, imshow(I)
|
|
|
|
|
figure, imshow(K,[0 255])
|
|
|
|
|
|
|
|
|
|
See also
|
|
|
|
|
--------
|
|
|
|
|
idctn, dct, idct
|
|
|
|
|
'''
|
|
|
|
|
|
|
|
|
|
y = np.atleast_1d(y)
|
|
|
|
|
shape0 = y.shape
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
if axis is None:
|
|
|
|
|
y = y.squeeze() # Working across singleton dimensions is useless
|
|
|
|
|
dimy = y.ndim
|
|
|
|
|
if dimy==1:
|
|
|
|
|
y = np.atleast_2d(y)
|
|
|
|
|
y = y.T
|
|
|
|
|
# Some modifications are required if Y is a vector
|
|
|
|
|
# if isvector(y):
|
|
|
|
|
# if y.shape[0]==1:
|
|
|
|
|
# if axis==0:
|
|
|
|
|
# return y, None
|
|
|
|
|
# elif axis==1:
|
|
|
|
|
# axis=0
|
|
|
|
|
# y = y.T
|
|
|
|
|
# elif axis==1:
|
|
|
|
|
# return y, None
|
|
|
|
|
|
|
|
|
|
if w is None:
|
|
|
|
|
w = [0,] * dimy
|
|
|
|
|
for dim in range(dimy):
|
|
|
|
|
if axis is not None and dim!=axis:
|
|
|
|
|
continue
|
|
|
|
|
n = (dimy==1)*y.size + (dimy>1)*shape0[dim]
|
|
|
|
|
#w{dim} = exp(1i*(0:n-1)'*pi/2/n);
|
|
|
|
|
w[dim] = np.exp(1j * np.arange(n) * np.pi / (2 * n))
|
|
|
|
|
|
|
|
|
|
# --- DCT algorithm ---
|
|
|
|
|
if np.iscomplex(y).any():
|
|
|
|
|
y = np.complex(dctn(np.real(y),axis,w),dctn(np.imag(y),axis,w))
|
|
|
|
|
else:
|
|
|
|
|
for dim in range(dimy):
|
|
|
|
|
y = shiftdim(y,1)
|
|
|
|
|
if axis is not None and dim!=axis:
|
|
|
|
|
y = shiftdim(y, 1)
|
|
|
|
|
continue
|
|
|
|
|
siz = y.shape
|
|
|
|
|
n = siz[-1]
|
|
|
|
|
y = y[...,np.r_[0:n:2, 2*int(n//2)-1:0:-2]]
|
|
|
|
|
y = y.reshape((-1,n))
|
|
|
|
|
y = y*np.sqrt(2*n);
|
|
|
|
|
y = (np.fft.ifft(y, n=n, axis=1) * w[dim]).real
|
|
|
|
|
y[:,0] = y[:,0]/np.sqrt(2)
|
|
|
|
|
y = y.reshape(siz)
|
|
|
|
|
|
|
|
|
|
#end
|
|
|
|
|
#end
|
|
|
|
|
|
|
|
|
|
return y.reshape(shape0), w
|
|
|
|
|
|
|
|
|
|
def idctn(y, axis=None, w=None):
|
|
|
|
|
'''
|
|
|
|
|
IDCTN N-D inverse discrete cosine transform.
|
|
|
|
|
X = IDCTN(Y) inverts the N-D DCT transform, returning the original
|
|
|
|
|
array if Y was obtained using Y = DCTN(X).
|
|
|
|
|
|
|
|
|
|
IDCTN(X,DIM) applies the IDCTN operation across the dimension DIM.
|
|
|
|
|
|
|
|
|
|
Class Support
|
|
|
|
|
-------------
|
|
|
|
|
Input array can be numeric or logical. The returned array is of class
|
|
|
|
|
double.
|
|
|
|
|
|
|
|
|
|
Reference
|
|
|
|
|
---------
|
|
|
|
|
Narasimha M. et al, On the computation of the discrete cosine
|
|
|
|
|
transform, IEEE Trans Comm, 26, 6, 1978, pp 934-936.
|
|
|
|
|
|
|
|
|
|
Example
|
|
|
|
|
-------
|
|
|
|
|
RGB = imread('autumn.tif');
|
|
|
|
|
I = rgb2gray(RGB);
|
|
|
|
|
J = dctn(I);
|
|
|
|
|
imshow(log(abs(J)),[]), colormap(jet), colorbar
|
|
|
|
|
|
|
|
|
|
The commands below set values less than magnitude 10 in the DCT matrix
|
|
|
|
|
to zero, then reconstruct the image using the inverse DCT.
|
|
|
|
|
|
|
|
|
|
J(abs(J)<10) = 0;
|
|
|
|
|
K = idctn(J);
|
|
|
|
|
figure, imshow(I)
|
|
|
|
|
figure, imshow(K,[0 255])
|
|
|
|
|
|
|
|
|
|
See also
|
|
|
|
|
--------
|
|
|
|
|
dctn, idct, dct
|
|
|
|
|
|
|
|
|
|
-- Damien Garcia -- 2009/04, revised 2009/11
|
|
|
|
|
website: <a
|
|
|
|
|
href="matlab:web('http://www.biomecardio.com')">www.BiomeCardio.com</a>
|
|
|
|
|
|
|
|
|
|
----------
|
|
|
|
|
[Y,W] = IDCTN(X,DIM,W) uses and returns the weights which are used by
|
|
|
|
|
the program. If IDCTN is required for several large arrays of same
|
|
|
|
|
size, the weights can be reused to make the algorithm faster. A typical
|
|
|
|
|
syntax is the following:
|
|
|
|
|
w = [];
|
|
|
|
|
for k = 1:10
|
|
|
|
|
[y{k},w] = idctn(x{k},[],w);
|
|
|
|
|
end
|
|
|
|
|
The weights (w) are calculated during the first call of IDCTN then
|
|
|
|
|
reused in the next calls.
|
|
|
|
|
'''
|
|
|
|
|
|
|
|
|
|
y = np.atleast_1d(y)
|
|
|
|
|
shape0 = y.shape
|
|
|
|
|
|
|
|
|
|
if axis is None:
|
|
|
|
|
y = y.squeeze() # Working across singleton dimensions is useless
|
|
|
|
|
|
|
|
|
|
dimy = y.ndim
|
|
|
|
|
if dimy==1:
|
|
|
|
|
y = np.atleast_2d(y)
|
|
|
|
|
y = y.T
|
|
|
|
|
# Some modifications are required if Y is a vector
|
|
|
|
|
# if isvector(y):
|
|
|
|
|
# if y.shape[0]==1:
|
|
|
|
|
# if axis==0:
|
|
|
|
|
# return y, None
|
|
|
|
|
# elif axis==1:
|
|
|
|
|
# axis=0
|
|
|
|
|
# y = y.T
|
|
|
|
|
# elif axis==1:
|
|
|
|
|
# return y, None
|
|
|
|
|
#
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
if w is None:
|
|
|
|
|
w = [0,] * dimy
|
|
|
|
|
for dim in range(dimy):
|
|
|
|
|
if axis is not None and dim!=axis:
|
|
|
|
|
continue
|
|
|
|
|
n = (dimy==1)*y.size + (dimy>1)*shape0[dim]
|
|
|
|
|
#w{dim} = exp(1i*(0:n-1)'*pi/2/n);
|
|
|
|
|
w[dim] = np.exp(1j * np.arange(n) * np.pi / (2 * n))
|
|
|
|
|
# --- IDCT algorithm ---
|
|
|
|
|
if np.iscomplex(y).any():
|
|
|
|
|
y = np.complex(idctn(np.real(y),axis,w),idctn(np.imag(y),axis,w))
|
|
|
|
|
else:
|
|
|
|
|
for dim in range(dimy):
|
|
|
|
|
y = shiftdim(y,1)
|
|
|
|
|
if axis is not None and dim!=axis:
|
|
|
|
|
#y = shiftdim(y, 1)
|
|
|
|
|
continue
|
|
|
|
|
siz = y.shape
|
|
|
|
|
n = siz[-1]
|
|
|
|
|
|
|
|
|
|
y = y.reshape((-1,n)) * w[dim]
|
|
|
|
|
y[:,0] = y[:,0]/np.sqrt(2)
|
|
|
|
|
y = (np.fft.ifft(y, n=n, axis=1)).real
|
|
|
|
|
y = y * np.sqrt(2*n)
|
|
|
|
|
|
|
|
|
|
I = np.empty(n,dtype=int)
|
|
|
|
|
I.put(np.r_[0:n:2],np.r_[0:int(n//2)+np.remainder(n,2)])
|
|
|
|
|
I.put(np.r_[1:n:2],np.r_[n-1:int(n//2)-1:-1])
|
|
|
|
|
y = y[:,I]
|
|
|
|
|
|
|
|
|
|
y = y.reshape(siz)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
y = y.reshape(shape0);
|
|
|
|
|
return y, w
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def no_leading_ones(x):
|
|
|
|
|
first = 0
|
|
|
|
|
for i, xi in enumerate(x):
|
|
|
|
|
if xi != 1:
|
|
|
|
|
first = i
|
|
|
|
|
break
|
|
|
|
|
return x[first:]
|
|
|
|
|
|
|
|
|
|
def shiftdim(x, n=None):
|
|
|
|
|
if n is None:
|
|
|
|
|
# returns the array B with the same number of
|
|
|
|
|
# elements as X but with any leading singleton
|
|
|
|
|
# dimensions removed.
|
|
|
|
|
return x.reshape(no_leading_ones(x.shape))
|
|
|
|
|
elif n>=0:
|
|
|
|
|
# When n is positive, shiftdim shifts the dimensions
|
|
|
|
|
# to the left and wraps the n leading dimensions to the end.
|
|
|
|
|
return x.transpose(np.roll(range(x.ndim), -n))
|
|
|
|
|
else:
|
|
|
|
|
# When n is negative, shiftdim shifts the dimensions
|
|
|
|
|
# to the right and pads with singletons.
|
|
|
|
|
return x.reshape((1,)*-n+x.shape)
|
|
|
|
|
|
|
|
|
|
def test_dctn():
|
|
|
|
|
a = np.arange(12).reshape((3,-1))
|
|
|
|
|
#y = dct(a)
|
|
|
|
|
#x = idct(y)
|
|
|
|
|
#print(y)
|
|
|
|
|
#print(x)
|
|
|
|
|
|
|
|
|
|
print(a)
|
|
|
|
|
yn = dctn(a)[0]
|
|
|
|
|
xn = idctn(yn)[0]
|
|
|
|
|
|
|
|
|
|
print(yn)
|
|
|
|
|
print(xn)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def test_docstrings():
|
|
|
|
|
import doctest
|
|
|
|
|
doctest.testmod()
|
|
|
|
|
|
|
|
|
|
if __name__ == '__main__':
|
|
|
|
|
#test_docstrings()
|
|
|
|
|
test_dctn()
|
Per.Andreas.Brodtkorb
13 years ago