def feat_desc(img, x, y):
N = x.size
descs = np.zeros((64, N))
edges = filters.sobel(img)
for i in range(N):
x_temp = np.arange(x[i] - 19, x[i] + 21, 1)
x_i = np.tile(x_temp, (40, 1))
y_temp = np.arange(y[i] - 19, y[i] + 21, 1)
y_temp = y_temp.reshape(-1, 1)
y_i = np.tile(y_temp, (1, 40))
interp = interp2(edges, x_i, y_i)
final = np.zeros((320, 5))
final[0:40, 0:5] = interp[0:40, 0:5]
final[40:80, 0:5] = interp[0:40, 5:10]
final[80:120, 0:5] = interp[0:40, 10:15]
final[120:160, 0:5] = interp[0:40, 15:20]
final[160:200, 0:5] = interp[0:40, 20:25]
final[200:240, 0:5] = interp[0:40, 25:30]
final[240:280, 0:5] = interp[0:40, 30:35]
final[280:320, 0:5] = interp[0:40, 35:40]
final = final.reshape((64, 25))
final_max = np.amax(final, axis=1)
descs_i = preprocessing.scale(final_max)
descs[0:64, i:i + 1] = descs_i.reshape((64, 1))
return descs
def estimateFeatureTranslation(startX, startY, Ix, Iy, img1, img2):
I_gray_1, I_gray_2 = rgb2gray(img1), rgb2gray(img2)
X_old, Y_old = generatePatch(startX, startY)
X_old, Y_old = X_old.astype(np.int32), Y_old.astype(np.int32)
Ix_temp, Iy_temp = Ix[Y_old, X_old], Iy[Y_old, X_old]
x0, y0 = startX, startY
min_error = 999999
error_thresh = 1
iteration = 5
for i in range(iteration):
X_new, Y_new = generatePatch(x0, y0)
old_coor = np.array((x0, y0)).reshape(-1, 1)
It_temp = interp2(I_gray_2, X_new, Y_new) - I_gray_1[Y_old, X_old]
error = np.linalg.norm(It_temp)
if error < min_error:
min_error = error
newX, newY = x0, y0
if error < error_thresh:
break
A = np.hstack((Ix_temp.reshape(-1, 1), Iy_temp.reshape(-1, 1)))
b = -It_temp.reshape(-1, 1)
flow_temp = np.linalg.solve(np.dot(A.T, A), np.dot(A.T, b))
new_coor = old_coor + flow_temp
x0, y0 = new_coor[0, 0], new_coor[1, 0]
return newX, newY
def estimateAllTranslation(startXs, startYs, origXs, origYs, img1, img2, bbox,
params):
import numpy as np
from helpers import rgb2gray
from helpers import interp2
from scipy import signal
from calculateError import calculateError
# ---------- Part 1: Setup ---------- #
# Get images computed to grayscale
# For now I'm going to pad the images symmetrically to get W for edges and corners
# It will just be important to remember that padding's there when solving for pixel locations
window = 11
pad = int((window - 1) / 2)
# Blur the images to get better optical flow results
Gx = signal.gaussian(window, 1.4).reshape(1, window)
Gy = signal.gaussian(window, 1.4).reshape(window, 1)
gray1 = signal.convolve2d(rgb2gray(img1), Gx, mode="full", boundary="symm")
gray1 = signal.convolve2d(gray1, Gy, mode="full", boundary="symm")
gray2 = signal.convolve2d(rgb2gray(img2), Gx, mode="full", boundary="symm")
gray2 = signal.convolve2d(gray2, Gy, mode="full", boundary="symm")
# Pull out parameters for looping
F = len(startXs)
# Initialize our outputs
newXs = np.zeros(F, dtype=object)
newYs = np.zeros(F, dtype=object)
# Calculate the gradients
kx = np.array([[1, -1]])
ky = np.array([[1], [-1]])
Ix = signal.convolve2d(gray1, kx, mode="same")
Iy = signal.convolve2d(gray1, ky, mode="same")
# ---------- Part 2: Caluclate the feature translations ---------- #
# Use these gradients to find the new locations of the feature points
# I'm not going to put this into a second function to reduce runtime
A = np.zeros((window**2, 2))
b = np.zeros((window**2, 1))
# Iterate for each bounding box as necessary
for i in range(F):
error = np.nan_to_num(np.Inf)
min_error = error.copy()
iters = 0
tempOrigXs = np.copy(origXs[i])
tempOrigYs = np.copy(origYs[i])
# Run for a max of 5 iterations or until the average squared distance between ea feat pt value is less than 5k
while error > 5000 and iters < 5:
N = len(startXs[i])
potXs = np.zeros(N)
potYs = np.zeros(N)
It = gray2 - gray1
iters += 1
for j in range(N):
# Get our feature location
fx = startXs[i][j]
fy = startYs[i][j]
# Generate a meshgrid for interpolating
meshx, meshy = np.meshgrid(np.arange(window),
np.arange(window))
meshx = meshx + fx
meshy = meshy + fy
# Build A and b from A*[u; v] = b centered around the feature location
A[:, 0] = interp2(Ix, meshx, meshy).reshape(
window**2
) # Ix[fy - pad: fy + pad + 1, fx - pad: fx + pad + 1].reshape(window**2)
A[:, 1] = interp2(Iy, meshx, meshy).reshape(
window**2
) # Iy[fy - pad: fy + pad + 1, fx - pad: fx + pad + 1].reshape(window**2)
b[:, 0] = interp2(It, meshx, meshy).reshape(
window**2
) # It[fy - pad: fy + pad + 1, fx - pad: fx + pad + 1].reshape(window**2)
# Solve for [u; v]
try:
translation = np.matmul(
np.matmul(np.linalg.inv(np.matmul(A.T, A)), A.T), -b)
except np.linalg.LinAlgError:
translation = np.array([0, 0])
# Save our result into our output
potXs[j] = startXs[i][j] + translation[0]
potYs[j] = startYs[i][j] + translation[1]
# Calculate the error
error, gray1, indexer, Ix, Iy, potXs, potYs = calculateError(
startXs[i], startYs[i], potXs, potYs, np.copy(gray1),
np.copy(gray2), Ix, Iy, np.copy(bbox[i]), params)
startXs[i] = np.copy(potXs)
startYs[i] = np.copy(potYs)
tempOrigXs = tempOrigXs[indexer]
tempOrigYs = tempOrigYs[indexer]
# If we did better this time, save the results
if error < min_error:
min_error = error.copy()
newXs[i] = np.copy(potXs)
newYs[i] = np.copy(potYs)
origXs[i] = np.copy(tempOrigXs)
origYs[i] = np.copy(tempOrigYs)
return newXs, newYs, origXs, origYs
def calculateError(startXs, startYs, newXs, newYs, img1, img2, Ix, Iy, box,
params):
import numpy as np
from helpers import rgb2gray
from helpers import interp2
from scipy import signal
from scipy.optimize import least_squares
from helpers import inlier_cost_func
from helpers import warp_image
# Extract parameters
max_dist = params[0]
k1 = params[1]
k2 = params[2]
k3 = params[3]
k4 = params[4]
pad = 5
source = rgb2gray(img1)
target = rgb2gray(img2)
source_warped = np.copy(source)
h, w = source.shape
# Get the boundaries of bounding box
xmin = max([np.amin(box[:, 0]) - pad, 0])
xmax = min([np.amax(box[:, 0]) + pad + 1, w])
ymin = max([np.amin(box[:, 1]) - pad, 0])
ymax = min([np.amax(box[:, 1]) + pad + 1, h])
# Outlier handling
indexer = np.all(np.stack([
newXs > xmin + pad, newXs < xmax - pad, newYs > ymin + pad,
newYs < ymax - pad
],
axis=0),
axis=0)
distances = np.sqrt(
np.square(newXs - startXs) + np.square(newYs - startYs))
avg_dist = np.mean(distances)
std_dist = np.std(distances)
if avg_dist != 0:
indexer = np.logical_and(
indexer,
np.logical_and(
distances < min([k1 * avg_dist + k2 * std_dist, max_dist]),
distances > k3 * avg_dist - k4 * std_dist))
# Generate vectors of inliers for calculating the transformation
ux = startXs[indexer]
uy = startYs[indexer]
vx = newXs[indexer]
vy = newYs[indexer]
# Form our initial and final feature points in homogeneous coordinates
N = len(ux)
u = np.stack([ux, uy, np.ones(N)])
v = np.stack([vx, vy, np.ones(N)])
# Calculate the transformation via least squares
T = least_squares(inlier_cost_func,
np.identity(3)[:2].reshape(6),
args=(u, v))["x"].reshape(2, 3)
T = np.concatenate((T, np.array([[0, 0, 1]])))
newXs = np.matmul(T, u)[0]
newYs = np.matmul(T, u)[1]
# Warp img1, Ix and Iy based on calculated transformation
target_area = target[ymin:ymax, xmin:xmax]
source_area = source[ymin:ymax, xmin:xmax]
warped_area = warp_image(source, T, xmin, xmax, ymin, ymax)
source_warped[ymin:ymax, xmin:xmax] = warped_area
Ix_area = warp_image(Ix, T, xmin, xmax, ymin, ymax)
Ix[ymin:ymax, xmin:xmax] = Ix_area
Iy_area = warp_image(Iy, T, xmin, xmax, ymin, ymax)
Iy[ymin:ymax, xmin:xmax] = Iy_area
# Calculate the error per feature point
interpx = np.array([newXs])
interpy = np.array([newYs])
values_this = interp2(source_warped, interpx, interpy).reshape(len(newXs))
values_next = interp2(target, interpx, interpy).reshape(len(newXs))
error = np.sum(np.square(values_next - values_this)) / len(newXs)
return error, source_warped, indexer, Ix, Iy, newXs, newYs
def generate_warp(size_H, size_W, Tri, A_Inter_inv_set, A_im_set, image):
# generate x,y meshgrid
x, y = np.meshgrid(np.arange(size_W), np.arange(size_H))
x = x.flatten()
y = y.flatten()
# all points in img (size_H*size_W, 2) as x,y system
empty_points = np.array(list(zip(x, y)))
# print(empty_points)
assert empty_points.shape == (size_H * size_W, 2)
# find the tris where these points live in
find_simplex_tris = Tri.find_simplex(empty_points)
# compute alpha, beta, gamma
all_Inter_inv_A = A_Inter_inv_set[find_simplex_tris]
all_img_A = A_im_set[find_simplex_tris]
# aug_empty_points = np.hstack((empty_points,np.ones((empty_points.shape[0], 1))))
alpha = all_Inter_inv_A[:, 0, 0] * empty_points[:, 0].flatten() + \
all_Inter_inv_A[:, 0, 1] * empty_points[:, 1].flatten() + \
all_Inter_inv_A[:, 0, 2] * 1
beta = all_Inter_inv_A[:, 1, 0] * empty_points[:, 0] + \
all_Inter_inv_A[:, 1, 1] * empty_points[:, 1] + \
all_Inter_inv_A[:, 1, 2] * 1
gamma = all_Inter_inv_A[:, 2, 0] * empty_points[:, 0] + \
all_Inter_inv_A[:, 2, 1] * empty_points[:, 1] + \
all_Inter_inv_A[:, 2, 2] * 1
assert beta.size == empty_points[:, 0].flatten().size
# print(all_Inter_inv_A[:, 2, 0].shape)
all_x_coor = all_img_A[:, 0, 0] * alpha + \
all_img_A[:, 0, 1] * beta + \
all_img_A[:, 0, 2] * gamma
all_y_coor = all_img_A[:, 1, 0] * alpha + \
all_img_A[:, 1, 1] * beta + \
all_img_A[:, 1, 2] * gamma
# analytical result
all_z_coor = np.ones(beta.size)
all_x_coor_regularized = all_x_coor / all_z_coor
all_y_coor_regularized = all_y_coor / all_z_coor
# generate warp img
generated_pic = np.zeros((size_H, size_W, 3), dtype=np.uint8)
generated_pic[:, :, 0] = np.reshape(
interp2(image[:, :, 0], all_x_coor_regularized,
all_y_coor_regularized), [size_H, size_W])
generated_pic[:, :, 1] = np.reshape(
interp2(image[:, :, 1], all_x_coor_regularized,
all_y_coor_regularized), [size_H, size_W])
generated_pic[:, :, 2] = np.reshape(
interp2(image[:, :, 2], all_x_coor_regularized,
all_y_coor_regularized), [size_H, size_W])
# LOOP VERSION: SLOW
#
#
# # generate a empty matrix to store the warp img
# generated_pic = np.zeros((size_H, size_W, 3), dtype=np.uint8)
#
# # go through every point's coor in the inter-generated-pic
# for i in np.arange(size_H):
# for j in np.arange(size_W):
# # find its belonging triangle,
# # find_simplex according to x,y system
# fea_index = Tri.find_simplex(np.array([i, j]))
# # print(fea_index)
# # pull out the A_inter_inv matrix of Tri index
# A_Inter_inv = A_Inter_inv_set[fea_index, :, :]
#
# # pull out the coor of the point
# b_target = np.array([i, j, 1])
#
# # compute the barycentric coor
# barycentric = np.dot(A_Inter_inv, b_target)
#
# # pull out the A_im matrix of the Tir index
# b_source = np.dot(A_im_set[fea_index, :, :], barycentric)
# assert len(b_source) == 3
# print(b_source[2])
#
# b_source = b_source/b_source[2]
# b_source_map = np.round(b_source).astype(int)[0:2]
#
# generated_pic[i, j, 0] = image[b_source_map[0], b_source_map[1], 0]
# generated_pic[i, j, 1] = image[b_source_map[0], b_source_map[1], 1]
# generated_pic[i, j, 2] = image[b_source_map[0], b_source_map[1], 2]
return generated_pic
x1, y1 = xs1, ys1
x2, y2 = xs2, ys2
X_old = np.array(
[[x1 - 1, x1, x1 + 1], [x1 - 1, x1, x1 + 1], [x1 - 1, x1, x1 + 1]],
dtype=np.int32)
Y_old = np.array([[0, 0, 0], [1, 1, 1], [2, 2, 2]], dtype=np.int32)
ix_temp = ix[Y_old, X_old]
iy_temp = iy[Y_old, X_old]
for i in range(5):
X_new = np.array([[x1 - 1, x1, x1 + 1], [x1 - 1, x1, x1 + 1],
[x1 - 1, x1, x1 + 1]])
Y_new = np.array([[0, 0, 0], [1, 1, 1], [2, 2, 2]])
old_coor = np.array((x1, y1)).reshape(-1, 1)
it_temp = interp2(i2, X_new, Y_new) - i1[Y_old, X_old]
error = np.linalg.norm(it_temp)
A = np.hstack((ix_temp.reshape(-1, 1), iy_temp.reshape(-1, 1)))
b = -it_temp.reshape(-1, 1)
flow_temp = np.linalg.solve(np.dot(A.T, A), np.dot(A.T, b))
new_coor = old_coor + flow_temp
x1, y1 = new_coor[0, 0], new_coor[1, 0]
xe1, ye1 = x1, y1
print("result point 1:", (xe1, ye1))
X_old = np.array(
[[x2 - 1, x2, x2 + 1], [x2 - 1, x2, x2 + 1], [x2 - 1, x2, x2 + 1]],
dtype=np.int32)
Y_old = np.array([[0, 0, 0], [1, 1, 1], [2, 2, 2]], dtype=np.int32)
ix_temp = ix[Y_old, X_old]
iy_temp = iy[Y_old, X_old]
def morph_tri(im1, im2, im1_pts, im2_pts, warp_frac, dissolve_frac):
# TODO: Your code here
# Tips: use Delaunay() function to get Delaunay triangulation;
# Tips: use tri.find_simplex(pts) to find the triangulation index that pts locates in.
dissolve_frac = 1-dissolve_frac
warp_frac = 1-warp_frac
images = []
if im2.shape != im1.shape:
im2 = Image.fromarray(im2)
im2 = im2.resize((im1.shape[1],im1.shape[0]))
im2 = np.asarray(im2)
imFF = np.zeros(([len(warp_frac),im1.shape[0],im1.shape[1],3]))
imgc = 0
for t in warp_frac:
im_mpts = (t*im1_pts + (1-t)*im2_pts)
D = Delaunay(im_mpts)
x = range(im1.shape[0])
y = range(im1.shape[1])
xv, yv = np.meshgrid(x, y)
r = im1.shape[0]
c = im1.shape[1]
co_ords = np.zeros([im1.shape[1],im1.shape[0],3])
co_ords[:,:,0] = yv
co_ords[:,:,1] = xv
co_ords[:,:,2] = np.ones(yv.shape)
points = co_ords.reshape([1,r*c,3])
triangles = D.find_simplex(points[:,:,:2])
act_tri = np.transpose(triangles.reshape(co_ords[:,:,0].shape))
tri_pt = D.simplices
A_pt = tri_pt[:,0]
B_pt = tri_pt[:,1]
C_pt = tri_pt[:,2]
A_ptc = im_mpts[A_pt]
B_ptc = im_mpts[B_pt]
C_ptc = im_mpts[C_pt]
A_ptc = np.pad(A_ptc,[(0,0),(0,1)],mode = 'constant')
A_ptc[:,2] = A_ptc[:,2]+1
B_ptc = np.pad(B_ptc,[(0,0),(0,1)],mode = 'constant')
B_ptc[:,2] = B_ptc[:,2]+1
C_ptc = np.pad(C_ptc,[(0,0),(0,1)],mode = 'constant')
C_ptc[:,2] = C_ptc[:,2]+1
A_ptc = np.transpose(A_ptc)
B_ptc = np.transpose(B_ptc)
C_ptc = np.transpose(C_ptc)
D1 = np.transpose(A_ptc.copy())
E1 = np.transpose(B_ptc.copy())
F1 = np.transpose(C_ptc.copy())
D12 = D1.reshape([A_ptc.shape[1],3,1])
E12 = E1.reshape([B_ptc.shape[1],3,1])
F12 = F1.reshape([C_ptc.shape[1],3,1])
tri_mat = np.concatenate((D12,E12,F12),axis=2)
tri_inv = np.linalg.inv(tri_mat)
tri_inv_ordered = tri_inv[triangles,:,:]
tri_inv_ordered = tri_inv_ordered[0,:,:,:]
points1 = points[0,:,:]
points1 = points.reshape([points.shape[1],3,1])
BC = np.matmul(tri_inv_ordered,points1)
As_ptc = im1_pts[A_pt]
Bs_ptc = im1_pts[B_pt]
Cs_ptc = im1_pts[C_pt]
As_ptc = np.pad(As_ptc,[(0,0),(0,1)],mode = 'constant')
As_ptc[:,2] = As_ptc[:,2]+1
Bs_ptc = np.pad(Bs_ptc,[(0,0),(0,1)],mode = 'constant')
Bs_ptc[:,2] = Bs_ptc[:,2]+1
Cs_ptc = np.pad(Cs_ptc,[(0,0),(0,1)],mode = 'constant')
Cs_ptc[:,2] = Cs_ptc[:,2]+1
As_ptc = np.transpose(As_ptc)
Bs_ptc = np.transpose(Bs_ptc)
Cs_ptc = np.transpose(Cs_ptc)
D1s = np.transpose(As_ptc.copy())
E1s = np.transpose(Bs_ptc.copy())
F1s = np.transpose(Cs_ptc.copy())
D12s = D1s.reshape([As_ptc.shape[1],3,1])
E12s = E1s.reshape([Bs_ptc.shape[1],3,1])
F12s = F1s.reshape([Cs_ptc.shape[1],3,1])
tris_mat = np.concatenate((D12s,E12s,F12s),axis=2)
tris_mat_ordered = tris_mat[triangles,:,:]
tris_mat_ordered = tris_mat_ordered[0,:,:,:]
sxyz = np.matmul(tris_mat_ordered,BC)
sxy = sxyz[:,:2,0]
sxy = sxy.reshape([im1.shape[1],im1.shape[0],2])
x_1 = sxy[:,:,0]
y_1 = sxy[:,:,1]
im1R = interp2(im1[:,:,0],x_1,y_1)
im1G = interp2(im1[:,:,1],x_1,y_1)
im1B = interp2(im1[:,:,2],x_1,y_1)
At_ptc = im2_pts[A_pt]
Bt_ptc = im2_pts[B_pt]
Ct_ptc = im2_pts[C_pt]
At_ptc = np.pad(At_ptc,[(0,0),(0,1)],mode = 'constant')
At_ptc[:,2] = At_ptc[:,2]+1
Bt_ptc = np.pad(Bt_ptc,[(0,0),(0,1)],mode = 'constant')
Bt_ptc[:,2] = Bt_ptc[:,2]+1
Ct_ptc = np.pad(Ct_ptc,[(0,0),(0,1)],mode = 'constant')
Ct_ptc[:,2] = Ct_ptc[:,2]+1
At_ptc = np.transpose(At_ptc)
Bt_ptc = np.transpose(Bt_ptc)
Ct_ptc = np.transpose(Ct_ptc)
D1t = np.transpose(At_ptc.copy())
E1t = np.transpose(Bt_ptc.copy())
F1t = np.transpose(Ct_ptc.copy())
D12t = D1t.reshape([At_ptc.shape[1],3,1])
E12t = E1t.reshape([Bt_ptc.shape[1],3,1])
F12t = F1t.reshape([Ct_ptc.shape[1],3,1])
trit_mat = np.concatenate((D12t,E12t,F12t),axis=2)
trit_mat_ordered = trit_mat[triangles,:,:]
trit_mat_ordered = trit_mat_ordered[0,:,:,:]
txyz = np.matmul(trit_mat_ordered,BC)
txy = txyz[:,:2,0]
txy = txy.reshape([im1.shape[1],im1.shape[0],2])
x_2 = txy[:,:,0]
y_2 = txy[:,:,1]
im2R = interp2(im2[:,:,0],x_2,y_2)
im2G = interp2(im2[:,:,1],x_2,y_2)
im2B = interp2(im2[:,:,2],x_2,y_2)
imFR = (dissolve_frac[imgc]*im1R + (1-dissolve_frac[imgc])*im2R).T
imFG = (dissolve_frac[imgc]*im1G + (1-dissolve_frac[imgc])*im2G).T
imFB = (dissolve_frac[imgc]*im1B + (1-dissolve_frac[imgc])*im2B).T
imF = im1.copy()
imF[:,:,0] = imFR
imF[:,:,1] = imFG
imF[:,:,2] = imFB
# plt.imshow(imF)
# plt.show()
imFF[imgc,:,:,0] = imFR
imFF[imgc,:,:,1] = imFG
imFF[imgc,:,:,2] = imFB
images.append(imF)
imgc = imgc +1
morphed_im = imFF
io.mimsave('Morph.gif', images, duration = 0.05)
# print(morphed_im.shape)
return morphed_im
def findStuff(xx, yy, img, pts_avg, pts_orig, tri, tri_arr):
corr_tri = tri_arr[yy * 300 + xx]
trig_pts_avg = pts_avg[tri.simplices]
trig_pts_orig = pts_orig[tri.simplices]
Ax_avg = trig_pts_avg[corr_tri, 0, 0]
Bx_avg = trig_pts_avg[corr_tri, 1, 0]
Cx_avg = trig_pts_avg[corr_tri, 2, 0]
Ay_avg = trig_pts_avg[corr_tri, 0, 1]
By_avg = trig_pts_avg[corr_tri, 1, 1]
Cy_avg = trig_pts_avg[corr_tri, 2, 1]
Ax_orig = trig_pts_orig[corr_tri, 0, 0]
Bx_orig = trig_pts_orig[corr_tri, 1, 0]
Cx_orig = trig_pts_orig[corr_tri, 2, 0]
Ay_orig = trig_pts_orig[corr_tri, 0, 1]
By_orig = trig_pts_orig[corr_tri, 1, 1]
Cy_orig = trig_pts_orig[corr_tri, 2, 1]
ones = np.zeros((300, 300))
ones.fill(1)
ones_horiz = np.zeros((1, 90000))
ones_horiz.fill(1)
Ax_avg_flat = Ax_avg.flatten()
Bx_avg_flat = Bx_avg.flatten()
Cx_avg_flat = Cx_avg.flatten()
Ay_avg_flat = Ay_avg.flatten()
By_avg_flat = By_avg.flatten()
Cy_avg_flat = Cy_avg.flatten()
Ax_orig_flat = Ax_orig.flatten()
Bx_orig_flat = Bx_orig.flatten()
Cx_orig_flat = Cx_orig.flatten()
Ay_orig_flat = Ay_orig.flatten()
By_orig_flat = By_orig.flatten()
Cy_orig_flat = Cy_orig.flatten()
# big fat chunk to get Avg into 90000 * 3 * 3 matrix
tempABCx = np.vstack((Ax_avg_flat, Bx_avg_flat, Cx_avg_flat))
tempx = tempABCx.T
tempx = np.vsplit(tempx, 90000)
tempx = np.hstack(tempx)
tempx = np.squeeze(tempx, axis=0)
tempABCy = np.vstack((Ay_avg_flat, By_avg_flat, Cy_avg_flat))
tempy = tempABCy.T
tempy = np.vsplit(tempy, 90000)
tempy = np.hstack(tempy)
tempy = np.squeeze(tempy, axis=0)
ones_flat = np.zeros(270000, dtype='float64')
ones_flat.fill(1)
temp_avg = np.vstack((tempx, tempy, ones_flat))
temp_avg = np.hsplit(temp_avg, 90000)
temp_avg = np.vstack(temp_avg)
temp_avg = np.vsplit(temp_avg, 90000)
# big fat chunk to get orig into 90000 * 3 * 3 matrix
tempABCxo = np.vstack((Ax_orig_flat, Bx_orig_flat, Cx_orig_flat))
tempxo = tempABCxo.T
tempxo = np.vsplit(tempxo, 90000)
tempxo = np.hstack(tempxo)
tempxo = np.squeeze(tempxo, axis=0)
tempABCyo = np.vstack((Ay_orig_flat, By_orig_flat, Cy_orig_flat))
tempyo = tempABCyo.T
tempyo = np.vsplit(tempyo, 90000)
tempyo = np.hstack(tempyo)
tempyo = np.squeeze(tempyo, axis=0)
temp_o = np.vstack((tempxo, tempyo, ones_flat))
temp_o = np.hsplit(temp_o, 90000)
temp_o = np.vstack(temp_o)
temp_o = np.vsplit(temp_o, 90000)
xx_flat = xx.flatten()
yy_flat = yy.flatten()
ones_flat_2 = np.zeros(90000, dtype='float64')
ones_flat_2.fill(1)
xy1_stack = np.vstack((xx_flat, yy_flat, ones_flat_2))
xy1 = np.hsplit(xy1_stack, 90000)
xy1 = np.vstack(xy1)
xy1 = np.vsplit(xy1, 90000)
solutiontMtx = np.linalg.solve(temp_avg, xy1)
solution_pts = np.matmul(temp_o, solutiontMtx)
solution_pts = np.squeeze(solution_pts, axis=2)
solution_pts = np.hsplit(solution_pts, 3)
sol_x = solution_pts[0]
sol_y = solution_pts[1]
sol_x = sol_x.flatten()
sol_y = sol_y.flatten()
sol_x_r = sol_x.reshape((300, 300))
sol_y_r = sol_y.reshape((300, 300))
img_r = img[:, :, 0]
img_g = img[:, :, 1]
img_b = img[:, :, 2]
im1_morph_r = interp2(img_r, sol_x_r, sol_y_r)
im1_morph_g = interp2(img_g, sol_x_r, sol_y_r)
im1_morph_b = interp2(img_b, sol_x_r, sol_y_r)
return im1_morph_r, im1_morph_g, im1_morph_b
def morph_tri(im1, im2, im1_pts, im2_pts, warp_frac, dissolve_frac):
# Tips: use Delaunay() function to get Delaunay triangulation;
# Tips: use tri.find_simplex(pts) to find the triangulation index that pts locates in.
num_of_frames = warp_frac.shape[0]
row, col, ch = im1.shape
# create meshgrid of x,y coordinate
x, y = np.meshgrid(np.arange(col), np.arange(row))
y = y.flatten()
x = x.flatten()
# create pixel coordinate in (x,y)
pixel = np.stack((x,y), axis=1)
# initialize morphing image
morph_im = np.zeros([num_of_frames, row, col, ch], dtype='uint8')
warp_src = np.zeros([num_of_frames, row, col, ch], dtype='uint8')
warp_trg = np.zeros([num_of_frames, row, col, ch], dtype='uint8')
for i in range(num_of_frames):
# find interpolated points for Delaunay triangulation
interp_pts = (1 - warp_frac[i]) * im1_pts + warp_frac[i] * im2_pts
tri = Delaunay(interp_pts)
# find the triangulation index that interp_pts locates in
location = tri.find_simplex(pixel)
# location = location.reshape(row, col)
for j in range(np.shape(tri.simplices)[0]):
# loop through every Delaunay triangles
coor = pixel[np.where(location == j)] # pixels that belongs to triangle j
x = coor[:,0]
y = coor[:,1]
pixel_coor = np.row_stack((x, y, np.ones(x.shape[0])))
# vertices of Delaunay triangles
vertices = interp_pts[tri.simplices[j]]
vertices = np.transpose(vertices)
vertices = np.row_stack((vertices, np.ones([1,3])))
inv_vertices = np.linalg.inv(vertices)
# barycentric coordinates for each pixel
bary_coor = np.dot(inv_vertices, pixel_coor)
# vertices of Delaunay triangles from source picture
vertices_src = im1_pts[tri.simplices[j]]
vertices_src = np.transpose(vertices_src)
vertices_src = np.row_stack((vertices_src, np.ones([1, 3])))
source_coor = np.dot(vertices_src, bary_coor)
# vertices of Delaunay triangles from target picture
vertices_trg = im2_pts[tri.simplices[j]]
vertices_trg = np.transpose(vertices_trg)
vertices_trg = np.row_stack((vertices_trg, np.ones([1, 3])))
target_coor = np.dot(vertices_trg, bary_coor)
# interpolate through every pixel in source and target
for k in range(ch):
warp_src[i, y, x, k] = interp2(im1[:, :, k], source_coor[0, :], source_coor[1, :])
warp_trg[i, y, x, k] = interp2(im2[:, :, k], target_coor[0, :], target_coor[1, :])
morph_im[i, :, :, :] = (1-dissolve_frac[i]) * warp_src[i,:,:,:] + dissolve_frac[i] * warp_trg[i,:,:,:]
# pixel value should be between [0,255]
morph_im = np.clip(morph_im, 0, 255)
return morph_im