def test_emd2d_linearBackground_simpleIMF_FIXE_H(self):
rows, cols = 128, 128
linear_background = 0.1*self._generate_linear_image(rows, cols)
# Sinusoidal IMF
X = np.arange(cols)[None,:].T
Y = np.arange(rows)
x_comp_1d = np.sin(X*0.5)
y_comp_1d = np.sin(Y*0.2)
comp_2d = 5*x_comp_1d*y_comp_1d
image = linear_background + comp_2d
emd2D = EMD2D()
emd2D.FIXE_H = 10
IMFs = emd2D.emd(image)
# Check that only two IMFs were extracted
self.assertTrue(IMFs.shape==(2,rows,cols), "Shape is "+str(IMFs.shape))
# First IMF should be sin
self.assertTrue(np.allclose(IMFs[0], comp_2d, atol=1.),
"Output: \n"+str(IMFs[0])+"\nInput: \n"+str(comp_2d))
# Second IMF should be linear trend
self.assertTrue(np.allclose(IMFs[1], linear_background, atol=1.))
def test_emd2d_passArgsViaDict(self):
FIXE = 10
params = {"FIXE": FIXE}
emd2D = EMD2D(**params)
self.assertTrue(emd2D.FIXE==FIXE,
"Received {}, Expceted {}".format(emd2D.FIXE, FIXE))
def test_default_call_EMD2d(self):
x = np.arange(50)
y = np.arange(50)
xv, yv = np.meshgrid(x,y)
pos = (10, 20)
std = 5
img = self._generate_Gauss(xv, yv, pos, std)
max_imf = 2
emd2d = EMD2D()
emd2d(img, max_imf)
class ImageEMDTest(unittest.TestCase):
emd2d = EMD2D()
def _generate_image(self, r=64, c=64):
return np.random.random((r,c))
def _generate_linear_image(self, r=16, c=16):
rows = np.arange(r)
return np.repeat(rows, c).reshape(r,c)
def _generate_Gauss(self, x, y, pos, std, amp=1):
x_s = x-pos[0]
y_s = y-pos[1]
x2 = x_s*x_s
y2 = y_s*y_s
exp = np.exp(-(x2+y2)/(2*std*std))
#exp[exp<1e-6] = 0
scale = amp/np.linalg.norm(exp)
return scale*exp
def test_default_call_EMD2d(self):
x = np.arange(50)
y = np.arange(50)
xv, yv = np.meshgrid(x,y)
pos = (10, 20)
std = 5
img = self._generate_Gauss(xv, yv, pos, std)
max_imf = 2
emd2d = EMD2D()
emd2d(img, max_imf)
def test_endCondition_perfectReconstruction(self):
c1 = self._generate_image()
c2 = self._generate_image()
IMFs = np.stack((c1,c2))
org_img = np.sum(IMFs, axis=0)
self.assertTrue(self.emd2d.end_condition(org_img, IMFs))
def test_findExtrema_singleMax(self):
x = np.arange(50)
y = np.arange(50)
xv, yv = np.meshgrid(x,y)
pos = (10, 20)
std = 5
img_max = self._generate_Gauss(xv, yv, pos, std)
idx_min, idx_max = self.emd2d.find_extrema(img_max)
x_min, y_min = xv[idx_min], yv[idx_min]
x_max, y_max = xv[idx_max], yv[idx_max]
self.assertTrue((x_max, y_max)==pos)
self.assertTrue(len(x_min)==0)
self.assertTrue(len(y_min)==0)
def test_findExtrema_singleMin(self):
x = np.arange(50)
y = np.arange(50)
xv, yv = np.meshgrid(x,y)
pos = (10, 20)
std = 5
img_max = (-1)*self._generate_Gauss(xv, yv, pos, std, 10)
idx_min, idx_max = self.emd2d.find_extrema(img_max)
x_min, y_min = xv[idx_min], yv[idx_min]
x_max, y_max = xv[idx_max], yv[idx_max]
self.assertTrue((x_min, y_min)==pos)
self.assertTrue(len(x_max)==0)
self.assertTrue(len(y_max)==0)
def test_findExtrema_general(self):
x = np.arange(50)
y = np.arange(50)
xv, yv = np.meshgrid(x,y)
min_peaks = [((5,40), 4, -1), ((34,10), 2, -3)]
max_peaks = [((10,20), 5, 2), ((25,25), 3, 1), ((40,5), 3, 3)]
# Construct image with few Gausses
img = np.zeros(xv.shape)
for peak in max_peaks+min_peaks:
img = img + self._generate_Gauss(xv, yv, peak[0], peak[1], peak[2])
# Extract extrema
idx_min, idx_max = self.emd2d.find_extrema(img)
x_min = xv[idx_min].tolist()
y_min = yv[idx_min].tolist()
x_max = xv[idx_max].tolist()
y_max = yv[idx_max].tolist()
# Confirm that all peaks found - number
self.assertTrue(len(x_min)==len(min_peaks))
self.assertTrue(len(y_min)==len(min_peaks))
self.assertTrue(len(x_max)==len(max_peaks))
self.assertTrue(len(y_max)==len(max_peaks))
for peak in min_peaks:
peak_pos = peak[0]
x_min.remove(peak_pos[0])
y_min.remove(peak_pos[1])
for peak in max_peaks:
peak_pos = peak[0]
x_max.remove(peak_pos[0])
y_max.remove(peak_pos[1])
# Confirm that all peaks found - exact position
self.assertTrue(len(x_min)==0)
self.assertTrue(len(y_min)==0)
self.assertTrue(len(x_max)==0)
self.assertTrue(len(y_max)==0)
def test_splinePoints_SBS_simpleGrid(self):
# Test points - leave space inbetween for interpolation
X = np.arange(5)*2
Y = np.arange(5)*2
xm, ym = np.meshgrid(X, Y)
xmf = xm.flatten()
ymf = ym.flatten()
# Constant value image
zf = np.ones(xmf.size)
# Interpolation grid
xi = np.arange(10)
yi = np.arange(10)
# interpolated_image == np.ones((5,5))
interpolated_image = self.emd2d.spline_points(xmf, ymf, zf, xi, yi)
# It is expected, that interpolation on constant will produce
# constant image
self.assertTrue(np.allclose(interpolated_image, 1))
def test_splinePoints_SBS_linearGrid(self):
X = np.arange(5)*2
Y = np.arange(5)*2
xm, ym = np.meshgrid(X, Y)
xmf = xm.flatten()
ymf = ym.flatten()
# Linear value image
z = np.repeat(np.arange(0,10,2)[None,:], 5, axis=0)
zf = z.flatten()
# Interpolation grid
xi = np.arange(9)
yi = np.arange(9)
# interpolated_image[row] == row
interpolated_image = self.emd2d.spline_points(xmf, ymf, zf, xi, yi)
# Since interpolation is on linear function, each row should have
# value equal to position, i.e. z[0]=(0...), ,,,, z[n] = (n...n).
for n in range(xi.size):
nth_row = interpolated_image[n]
self.assertTrue(np.allclose(nth_row, n))
def test_emd2d_noExtrema(self):
linear_image = self._generate_linear_image()
IMFs = self.emd2d.emd(linear_image)
self.assertTrue(np.all(linear_image == IMFs))
def test_emd2d_simpleIMF(self):
rows, cols = 128, 128
# Sinusoidal IMF
X = np.arange(cols)[None,:].T
Y = np.arange(rows)
sin_1d = np.sin(Y*0.3)
cos_1d = np.cos(X*0.4)
comp_2d = 10*cos_1d*sin_1d
comp_2d -= np.mean(comp_2d)
image = comp_2d
IMFs = self.emd2d.emd(image)
# Image = IMF + noise
self.assertTrue(IMFs.shape[0] <= 2,
"Depending on spline, there should be an IMF and possibly trend")
self.assertTrue(np.allclose(IMFs[0], image, atol=0.5),
"Output: \n"+str(IMFs[0])+"\nInput: \n"+str(comp_2d))
def test_emd2d_linearBackground_simpleIMF(self):
rows, cols = 128, 128
linear_background = 0.1*self._generate_linear_image(rows, cols)
# Sinusoidal IMF
X = np.arange(cols)[None,:].T
Y = np.arange(rows)
x_comp_1d = np.sin(X*0.5)
y_comp_1d = np.sin(Y*0.2)
comp_2d = 5*x_comp_1d*y_comp_1d
image = linear_background + comp_2d
IMFs = self.emd2d.emd(image)
# Check that only two IMFs were extracted
self.assertTrue(IMFs.shape==(2,rows,cols), "Shape is "+str(IMFs.shape))
# First IMF should be sin
self.assertTrue(np.allclose(IMFs[0], comp_2d, atol=1.),
"Output: \n"+str(IMFs[0])+"\nInput: \n"+str(comp_2d))
# Second IMF should be linear trend
self.assertTrue(np.allclose(IMFs[1], linear_background, atol=1.))
def test_emd2d_linearBackground_simpleIMF_FIXE(self):
rows, cols = 128, 128
linear_background = 0.1*self._generate_linear_image(rows, cols)
# Sinusoidal IMF
X = np.arange(cols)[None,:].T
Y = np.arange(rows)
x_comp_1d = np.sin(X*0.5)
y_comp_1d = np.sin(Y*0.2)
comp_2d = 5*x_comp_1d*y_comp_1d
image = linear_background + comp_2d
emd2d = EMD2D()
emd2d.FIXE = 10
IMFs = emd2d.emd(image)
# Check that only two IMFs were extracted
self.assertTrue(IMFs.shape==(2,rows,cols), "Shape is "+str(IMFs.shape))
# First IMF should be sin
self.assertTrue(np.allclose(IMFs[0], comp_2d, atol=1.),
"Output: \n"+str(IMFs[0])+"\nInput: \n"+str(comp_2d))
# Second IMF should be linear trend
self.assertTrue(np.allclose(IMFs[1], linear_background, atol=1.))
def test_emd2d_linearBackground_simpleIMF_FIXE_H(self):
rows, cols = 128, 128
linear_background = 0.1*self._generate_linear_image(rows, cols)
# Sinusoidal IMF
X = np.arange(cols)[None,:].T
Y = np.arange(rows)
x_comp_1d = np.sin(X*0.5)
y_comp_1d = np.sin(Y*0.2)
comp_2d = 5*x_comp_1d*y_comp_1d
image = linear_background + comp_2d
emd2D = EMD2D()
emd2D.FIXE_H = 10
IMFs = emd2D.emd(image)
# Check that only two IMFs were extracted
self.assertTrue(IMFs.shape==(2,rows,cols), "Shape is "+str(IMFs.shape))
# First IMF should be sin
self.assertTrue(np.allclose(IMFs[0], comp_2d, atol=1.),
"Output: \n"+str(IMFs[0])+"\nInput: \n"+str(comp_2d))
# Second IMF should be linear trend
self.assertTrue(np.allclose(IMFs[1], linear_background, atol=1.))
def test_emd2d_passArgsViaDict(self):
FIXE = 10
params = {"FIXE": FIXE}
emd2D = EMD2D(**params)
self.assertTrue(emd2D.FIXE==FIXE,
"Received {}, Expceted {}".format(emd2D.FIXE, FIXE))
def test_emd2d_limitImfNo(self):
# Create image
rows, cols = 128, 128
linear_background = 0.2*self._generate_linear_image(rows, cols)
# Sinusoidal IMF
X = np.arange(cols)[None,:].T
Y = np.arange(rows)
x_comp_1d = np.sin(X*0.3) + np.cos(X*2.9)**2
y_comp_1d = np.sin(Y*0.2)
comp_2d = 10*x_comp_1d*y_comp_1d
comp_2d = comp_2d
image = linear_background + comp_2d
# Limit number of IMFs
max_imf = 2
# decompose image
IMFs = self.emd2d.emd(image, max_imf=max_imf)
# It should have no more than 2 (max_imf)
self.assertTrue(IMFs.shape[0]==max_imf)
print("Generating image... ", end="")
rows, cols = 1024, 1024
row_scale, col_scale = 256, 256
x = np.arange(rows)/float(row_scale)
y = np.arange(cols).reshape((-1,1))/float(col_scale)
pi2 = 2*np.pi
img = np.zeros((rows,cols))
img = img + np.sin(2*pi2*x)*np.cos(y*4*pi2+4*x*pi2)
img = img + 3*np.sin(2*pi2*x)+2
img = img + 5*x*y + 2*(y-0.2)*y
print("Done")
# Perform decomposition
print("Performing decomposition... ", end="")
emd2d = EMD2D()
#emd2d.FIXE_H = 5
IMFs = emd2d.emd(img, max_imf=4)
imfNo = IMFs.shape[0]
print("Done")
print("Plotting results... ", end="")
import pylab as plt
# Save image for preview
plt.figure(figsize=(4,4*(imfNo+1)))
plt.subplot(imfNo+1, 1, 1)
plt.imshow(img)
plt.colorbar()
plt.title("Input image")