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## $Id$
## -*- coding: utf-8 -*-
# jpeg.dct
# ========
#
# .. module:: pysteg.jpeg.dct
#
# :Module: pysteg.jpeg.dct
# :Date: $Date$
# :Revision: $Revision$
# :Copyright: © 2010: University of Surrey, UK
# :Author: Hans Georg Schaathun <H.Schaathun@surrey.ac.uk> (2010)
#
# ::
from numpy import dot,linalg
import numpy
def auxcos(x,u):
return numpy.cos( (numpy.pi/8) * (x + 0.5) * u )
def cosmat(M=8,N=8):
C = numpy.array( [ [ auxcos(x,u) for u in range(N) ]
for x in range(M) ] ) / 2
C[:,0] = C[:,0] / numpy.sqrt(2)
# C[0,:] = C[0,:] / numpy.sqrt(2)
return C
auxM = cosmat(8,8)
invM = linalg.inv(auxM)
auxT = numpy.transpose(auxM)
invT = numpy.transpose(invM)
def dct2(g):
"""
Perform a 2D DCT transform on g, assuming that g is 8x8.
"""
assert (8,8) == numpy.shape( g )
return dot( auxT, dot( g, auxM ) )
def idct2(g):
"""
Perform a 2D inverse DCT transform on g, assuming that g is 8x8.
"""
assert (8,8) == numpy.shape( g )
# return dot( invM, dot( g, invT ) )
return dot( invT, dot( g, invM ) )
def bdct(C,f=dct2):
"""
Make a blockwise (8x8 blocks) 2D DCT transform on the matrix C.
The optional second parameter f specifies the DCT transform function.
The height and width of C have to be divisible by 8.
"""
(M,N) = numpy.shape(C)
assert M%8 == 0
assert N%8 == 0
S = numpy.ndarray((M,N))
for i in range(0,M,8):
for j in range(0,N,8):
S[i:(i+8),j:(j+8)] = f( C[i:(i+8),j:(j+8)] )
return S
def ibdct(C): return bdct(C,f=idct2)
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