def calc_log_avg_fft(x):
if len(x.shape) == 2:
return np.log(
fftshift(
np.abs(fftpack.fft2(x.reshape(x.shape[0], 32,
32))).mean(axis=0)))
else:
return np.log(fftshift(np.abs(fftpack.fft2(x.reshape(32, 32)))))
def wiener_filter(img, kernel, K = 10):
temp_img = np.copy(img)
kernel = np.pad(kernel, [(0, temp_img.shape[0] - kernel.shape[0]), (0, temp_img.shape[1] - kernel.shape[1])], 'constant')
# Fourier Transform
temp_img = fft2(temp_img)
kernel = fft2(kernel)
kernel = np.conj(kernel) / (np.abs(kernel) ** 2 + K)
temp_img = temp_img * kernel
temp_img = np.abs(ifft2(temp_img))
return np.uint8(temp_img)
def fft_convolve(im, filt):
t1 = time.clock()
shp_w = im.shape[0] + filt.shape[0]
shp_h = im.shape[1] + filt.shape[1]
f_c = fftpack.fft2(filt[::-1, ::-1], s=(shp_w, shp_h))
f_im = fftpack.fft2(im, s=(shp_w, shp_h))
res = np.real(fftpack.ifft2(f_c * f_im))
b = (filt.shape[0] - 1) // 2
res = res[b:-b - 1, b:-b - 1]
t2 = time.clock()
tt = t2 - t1
print("Elapsed time fft_convolve %fs" % tt)
return res, tt
def fft_convolve(im, filt):
t1 = time.clock()
shp_w = im.shape[0] + filt.shape[0]
shp_h = im.shape[1] + filt.shape[1]
f_c = fftpack.fft2(filt[::-1, ::-1], s=(shp_w, shp_h))
f_im = fftpack.fft2(im, s=(shp_w, shp_h))
res = np.real(fftpack.ifft2(f_c * f_im))
b = (filt.shape[0] - 1) // 2
res = res[b:-b - 1, b:-b - 1]
t2 = time.clock()
tt = t2 - t1
print("Elapsed time fft_convolve %fs" % tt)
return res, tt
def __init__(self):
self.fig = plt.figure()
originalImage = Image.open('Fourier.jpg')
(ow, oh) = originalImage.size
if ow > maxWidth:
monoImageArray = numpy.asarray(
originalImage.convert('L').resize(
(maxWidth, oh * maxWidth // ow)))
else:
monoImageArray = numpy.asarray(originalImage.convert('L'))
(self.imageHeight, self.imageWidth) = monoImageArray.shape
self.samples = numpy.zeros((self.imageHeight, self.imageWidth),
dtype=complex)
self.samplePoints = numpy.zeros((self.imageHeight, self.imageWidth, 4))
self.fftImage = fftpack.fft2(monoImageArray)
self.fftImageForPlot = numpy.roll(numpy.roll(numpy.real(self.fftImage),
self.imageHeight // 2,
axis=0),
self.imageWidth // 2,
axis=1)
self.fftMean = numpy.mean(self.fftImageForPlot)
self.fftStd = numpy.std(self.fftImageForPlot)
self.axes1 = plt.subplot(2, 3, 1)
plt.imshow(monoImageArray, cmap='gray')
self.axes2 = plt.subplot(2, 3, 2)
p = plt.imshow(self.fftImageForPlot, cmap='gray')
p.set_clim(self.fftMean - self.fftStd, self.fftMean + self.fftStd)
self.axes3 = plt.subplot(2, 3, 4)
self.axes3.set_aspect('equal')
self.axes3.set_xlim(0, self.imageWidth)
self.axes3.set_ylim(self.imageHeight, 0)
self.axes4 = plt.subplot(2, 3, 5)
self.axes4.set_aspect('equal')
self.axes4.set_xlim(0, self.imageWidth)
self.axes4.set_ylim(self.imageHeight, 0)
self.axes5 = plt.subplot(2, 3, 6)
self.axes5.set_aspect('equal')
self.axes5.set_xlim(0, self.imageWidth)
self.axes5.set_ylim(self.imageHeight, 0)
self.bMousePressed = False
self.mouseButton = 0
self.bCtrlPressed = False
self.fig.canvas.mpl_connect('motion_notify_event', self.onMove)
self.fig.canvas.mpl_connect('button_press_event', self.onButtonPress)
self.fig.canvas.mpl_connect('button_release_event',
self.onButtonRelease)
self.fig.canvas.mpl_connect('key_press_event', self.onKeyPress)
self.fig.canvas.mpl_connect('key_release_event', self.onKeyRelease)
plt.show()
def power_spectrum(pref, peak_val=1.0):
"""
Computes the FFT power spectrum of the orientation preference.
"""
fft_spectrum = abs(fftshift(fft2(pref-0.5, s=None, axes=(-2,-1))))
fft_spectrum = 1 - fft_spectrum # Inverted spectrum by convention
zero_min_spectrum = fft_spectrum - fft_spectrum.min()
spectrum_range = fft_spectrum.max() - fft_spectrum.min()
normalized_spectrum = (peak_val * zero_min_spectrum) / spectrum_range
return normalized_spectrum
def power_spectrum(pref, peak_val=1.0):
"""
Computes the FFT power spectrum of the orientation preference.
"""
fft_spectrum = abs(fftshift(fft2(pref - 0.5, s=None, axes=(-2, -1))))
fft_spectrum = 1 - fft_spectrum # Inverted spectrum by convention
zero_min_spectrum = fft_spectrum - fft_spectrum.min()
spectrum_range = fft_spectrum.max() - fft_spectrum.min()
normalized_spectrum = (peak_val * zero_min_spectrum) / spectrum_range
return normalized_spectrum
def _process(self, sheetview):
cr = sheetview.cyclic_range
data = sheetview.data if cr is None else sheetview.data/cr
fft_spectrum = abs(fftshift(fft2(data - 0.5, s=None, axes=(-2, -1))))
fft_spectrum = 1 - fft_spectrum # Inverted spectrum by convention
zero_min_spectrum = fft_spectrum - fft_spectrum.min()
spectrum_range = fft_spectrum.max() - fft_spectrum.min()
normalized_spectrum = (self.p.peak_val * zero_min_spectrum) / spectrum_range
l, b, r, t = sheetview.bounds.lbrt()
density = sheetview.xdensity
bb = BoundingBox(radius=(density/2)/(r-l))
return [SheetView(normalized_spectrum, bb,
metadata=sheetview.metadata,
label=sheetview.label+' FFT Power Spectrum')]
def OR_power_spectrum(image, toarray=True, peak_val=1.0):
""" Taken from current topographica code. Applies FFT power
spectrum to hue channel of OR maps (ie orientation). Accepts
RGB images or arrays."""
# Duplicates the line of code in command/pylabplot.py and tkgui.
# Unfortunately, there is no sensible way to reuse the existing code
if not toarray: peak_val = 255
if not image.shape[0] % 2:
hue = image[:-1, :-1]
else:
hue = image
fft_spectrum = abs(fftshift(fft2(hue - 0.5, s=None, axes=(-2, -1))))
fft_spectrum = 1 - fft_spectrum # Inverted spectrum by convention
zero_min_spectrum = fft_spectrum - fft_spectrum.min()
spectrum_range = fft_spectrum.max() - fft_spectrum.min()
normalized_spectrum = (peak_val * zero_min_spectrum) / spectrum_range
if not toarray:
return Image.fromarray(normalized_spectrum.astype('uint8'), mode='L')
return normalized_spectrum
def __call__(self, data, **params):
p = ParamOverrides(self, params)
fft_plot = 1 - np.abs(fftshift(fft2(data - 0.5, s=None,
axes=(-2, -1))))
return super(fftplot, self).__call__(fft_plot, **p)
def __call__(self, data, **params):
p = ParamOverrides(self, params)
fft_plot = 1 - np.abs(fftshift(fft2(data - 0.5, s=None, axes=(-2, -1))))
return super(fftplot, self).__call__(fft_plot, **p)
def get_angle(x):
return np.angle(fftpack.fft2(x.reshape(32, 32)))
def get_abs(x):
return np.abs(fftpack.fft2(x.reshape(32, 32)))
def phasecong100(im,
nscale=2,
norient=2,
minWavelength=7,
mult=2,
sigmaOnf=0.65):
#
# im # Input image
# nscale = 2; # Number of wavelet scales.
# norient = 2; # Number of filter orientations.
# minWaveLength = 7; # Wavelength of smallest scale filter.
# mult = 2; # Scaling factor between successive filters.
# sigmaOnf = 0.65; # Ratio of the standard deviation of the
# # Gaussian describing the log Gabor filter's
# # transfer function in the frequency domain
# # to the filter center frequency.
rows, cols = im.shape
imagefft = fft2(im)
zero = np.zeros(shape=(rows, cols))
EO = dict()
EnergyV = np.zeros((rows, cols, 3))
x_range = np.linspace(-0.5, 0.5, num=cols, endpoint=True)
y_range = np.linspace(-0.5, 0.5, num=rows, endpoint=True)
x, y = np.meshgrid(x_range, y_range)
radius = np.sqrt(x**2 + y**2)
theta = np.arctan2(-y, x)
radius = ifftshift(radius)
theta = ifftshift(theta)
radius[0, 0] = 1.
sintheta = np.sin(theta)
costheta = np.cos(theta)
lp = lowpass_filter((rows, cols), 0.45, 15)
logGabor = []
for s in range(1, nscale + 1):
wavelength = minWavelength * mult**(s - 1.)
fo = 1.0 / wavelength
logGabor.append(
np.exp((-(np.log(radius / fo))**2) / (2 * np.log(sigmaOnf)**2)))
logGabor[-1] *= lp
logGabor[-1][0, 0] = 0
# The main loop...
for o in range(1, norient + 1):
angl = (o - 1.) * np.pi / norient
ds = sintheta * np.cos(angl) - costheta * np.sin(angl)
dc = costheta * np.cos(angl) + sintheta * np.sin(angl)
dtheta = np.abs(np.arctan2(ds, dc))
dtheta = np.minimum(dtheta * norient / 2., np.pi)
spread = (np.cos(dtheta) + 1.) / 2.
sumE_ThisOrient = zero.copy()
sumO_ThisOrient = zero.copy()
for s in range(0, nscale):
filter_ = logGabor[s] * spread
EO[(s, o)] = ifft2(imagefft * filter_)
sumE_ThisOrient = sumE_ThisOrient + np.real(EO[(s, o)])
sumO_ThisOrient = sumO_ThisOrient + np.imag(EO[(s, o)])
EnergyV[:, :, 0] = EnergyV[:, :, 0] + sumE_ThisOrient
EnergyV[:, :, 1] = EnergyV[:, :, 1] + np.cos(angl) * sumO_ThisOrient
EnergyV[:, :, 2] = EnergyV[:, :, 2] + np.sin(angl) * sumO_ThisOrient
OddV = np.sqrt(EnergyV[:, :, 0]**2 + EnergyV[:, :, 1]**2)
featType = np.arctan2(EnergyV[:, :, 0], OddV)
return featType