def findDerivatives(I_gray):
# 2D Gaussian kernel
G = utils.GaussianPDF_2D(0, 1, 10, 10)
# Deviation vectors/filter for horizontal and vertical direction (to compute gradient of Gaussian)
dx = [[1.0, 0.0, -1.0]]
dy = [[1.0], [0.0], [-1.0]]
# Perform convolution of Gaussian and filters, get gradient of Gaussian (10 by 10)
Gx = signal.convolve2d(G, dx, mode='same', boundary='symm')
Gy = signal.convolve2d(G, dy, mode='same', boundary='symm')
# Perform convolution of original image matrix and gradient matrix
ix = signal.convolve2d(I_gray, Gx, mode='same', boundary='symm')
iy = signal.convolve2d(I_gray, Gy, mode='same', boundary='symm')
# Compute magnitude of the gradient
im = np.sqrt(np.square(ix) + np.square(iy))
# Get gradient of the image
idx = signal.convolve2d(I_gray, dx, mode='same')
idy = signal.convolve2d(I_gray, dy, mode='same')
# Get orientation of the edge
orientation = np.arctan(np.divide(idy, idx))
return im, ix, iy, orientation
def findDerivatives(I_gray):
## ==========Filter out noise
img = ndimage.gaussian_filter(I_gray, sigma=1.5, order=0)
# plt.imshow(img, cmap='gray', vmin=0, vmax=255)
# plt.show()
## ==========Compute derivative
dx, dy = np.gradient(utils.GaussianPDF_2D(0, 0.5, 5, 5), axis=(1, 0))
Ix = signal.convolve2d(img, dx, 'same')
Iy = signal.convolve2d(img, dy, 'same')
# plt.imshow(Ix, cmap='gray')
# plt.show()
# plt.imshow(Iy, cmap='gray')
# plt.show()
## ==========Compute the magnitude
Mag = np.sqrt(Ix * Ix + Iy * Iy)
# plt.imshow(Mag, cmap='gray')
# plt.show()
## =========Compute orientation
Ori = np.arctan2(Iy, Ix + 0.0001)
return Mag, Ix, Iy, Ori
def findDerivatives(I_gray):
# TODO: your code here
Gausian = utils.GaussianPDF_2D(0.1, 0.5, 5, 5)
dx, dy = np.gradient(Gausian, axis=(1, 0))
Ix = signal.convolve2d(I_gray, dx, 'same')
Iy = signal.convolve2d(I_gray, dy, 'same')
Im = np.sqrt(Ix * Ix + Iy * Iy)
Ori = np.arctan(Iy / Ix)
return Im, Ix, Iy, Ori
def findDerivatives(I_gray):
#G_1D = utils.GaussianPDF_1D(0,0.5,10)
G_2D = utils.GaussianPDF_2D(0, 0.5, 10, 10)
dx, dy = np.gradient(G_2D)
Magx = signal.convolve2d(I_gray, dx, 'same')
Magy = signal.convolve2d(I_gray, dy, 'same')
Mag = np.sqrt(Magx * Magx + Magy * Magy)
Ori = np.arctan(Magy, Magx)
return Mag, Magx, Magy, Ori
def findDerivatives(I_gray): # TODO: your code here mu=0 sigma=2 G=utils.GaussianPDF_2D(mu, sigma, 3,3)#form 2d gussian dx,dy=np.gradient(G, axis=(1,0))#form 2d gussian derivative in x and y direction Magx=signal.convolve2d(I_gray,dx,'same') Magy=signal.convolve2d(I_gray,dy,'same') Mag=np.sqrt(Magx*Magx+Magy*Magy) Ori=np.arctan2(Magy,Magx,out=None) return [Mag,Magx,Magy,Ori]
def findDerivatives(I_gray):
# TODO: your code here
# Gaussian filter
#G = np.array([[2, 4, 5, 4, 2], [4, 9, 12, 9, 4], [5, 12, 15, 12, 5], [4, 9, 12, 9, 4], [2, 4, 5, 4, 2]])
#G = np.matrix('2,4,5,4,2; 4,9,12,9,4; 5,12,15,12,5; 4,9,12,9,4; 2,4,5,4,2') #sigma=1.4
#G = G/159;
#Ga = np.squeeze(np.asarray(G))
#less sigma, more blurred edge
mu = 0
sigma = 0.4 #0.4
Ga = utils.GaussianPDF_2D(mu, sigma, 5, 5)
# Filter
dx = np.array([[1, 0, -1]]) # Horizontal
dy = np.array([[1], [0], [-1]]) # Vertical
#dx = np.array([[1, -1]]) # Horizontal
#dy = np.array([[1],[-1]]) # Vertical
# Convolution of image
#Gx = np.convolve(G, dx, 'same')
#Gy = np.convolve(G, dy, 'same')
#lx = np.convolve(I_gray, Gx, 'same')
#ly = np.convolve(I_gray, Gy, 'same')
Gx = scipy.signal.convolve2d(Ga, dx, boundary='fill', mode='same')
Gy = scipy.signal.convolve2d(Ga, dy, boundary='fill', mode='same')
lx = scipy.signal.convolve2d(I_gray, Gx, boundary='fill', mode='same')
ly = scipy.signal.convolve2d(I_gray, Gy, boundary='fill', mode='same')
# Magnitude
Mag = np.sqrt(lx * lx + ly * ly)
# Angle
angle = np.arctan(ly / lx)
angle[angle < 0] = math.pi + angle[angle < 0]
angle[angle > 7 * math.pi / 8] = math.pi - angle[angle > 7 * math.pi / 8]
'''
# Edge angle discretization into 0, pi/4, pi/2, 3*pi/4
angle[angle>=0 and angle<math.pi/8] = 0
angle[angle>=math.pi/8 and angle<3*math.pi/8] = math.pi/4
angle[angle>=3*math.pi/8 and angle<5*math.pi/8] = math.pi/2
angle[angle>=5*math.pi/8 and angle<=7*math.pi/8] = 3*math.pi/4
'''
return Mag
def feat_desc(img, x, y):
pad = np.zeros([img.shape[0] + 80, img.shape[1] + 80])
mu = 0
sigma = 1 # 0.4
# gau = np.matrix([[2, 4, 5, 4, 2], [4, 9, 12, 9, 4], [5, 12, 15, 12, 5], [4, 9, 12, 9, 4], [2, 4, 5, 4, 2]])
# gau = np.asarray(gau)
gau = utils.GaussianPDF_2D(mu, sigma, 10, 10)
# gau = 1 / 159 * gau
'''dx = np.matrix([1, 0, -1])
dy = np.matrix([[1], [0], [-1]])
dx = np.asarray(dx)
dy = np.asarray(dy)
Gx = signal.convolve2d(gau, dx, 'same')
Gy = signal.convolve2d(gau, dy, 'same')'''
lx = signal.convolve2d(img, gau, 'same')
ly = signal.convolve2d(img, gau, 'same')
blurImg = lx + ly
#plt.imshow(blurImg)
# plt.show()
pad[40:img.shape[0] + 40, 40:img.shape[1] + 40] = blurImg
offset = 40
output = np.zeros([64, x.size])
for i in range(x.size):
windowB = pad[x[i][0] + offset - 20:x[i][0] + offset + 20, y[i][0] + offset - 20:y[i][0] + offset + 20]
for j in range(0, 64):
row = (j + 1) // 8
if (j + 1) % 8 == 0:
row = (j + 1) // 8 - 1
col = (j + 1) % 8 - 1
if col == -1:
col = 7
subB = windowB[0 + row*5:row*5 + 4, 0 + col*5:col*5+4]
output[j, i] = subB.max()
output_mean = np.sum(output[:, i]) / 64
output_var = np.std(output[:, i])
if output_var != 0:
output[:, i] = (output[:, i] - output_mean) / output_var
else:
output[:, i] = 0
return output
def findDerivatives(I_gray): g=utils.GaussianPDF_2D(0.1,1,5,5) #print(g) x=np.array([[0,0,0],[1,0,-1],[0,0,0]]) y=np.array([[0,1,0],[0,0,0],[0,-1,0]]) #print(x.shape) #I_gray1=signal.convolve2d(I_gray,g,mode='same') dx=signal.convolve2d(g,x,mode='same') dy=signal.convolve2d(g,y,mode='same') i_gx=signal.convolve2d(I_gray,dx,'same') i_gy=signal.convolve2d(I_gray,dy,'same') #plt.imshow(i_gy,cmap='gray') M=np.sqrt(i_gx*i_gx + i_gy*i_gy) ang1=np.arctan2(i_gy,i_gx) return M,i_gx,i_gy,ang1