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rtv_smooth.py
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rtv_smooth.py
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import numpy as np
from numba import njit, prange
from scipy.sparse import dia_array
from scipy.sparse.linalg import bicgstab
from skimage.color import rgb2xyz
from skimage.filters import gaussian
def cross_sum(a, out):
a = np.pad(a, ((1, 1), (1, 1), (0, 0)))
out[:] = a[2:, 1:-1] + a[:-2, 1:-1] + a[1:-1, 2:] + a[1:-1, :-2]
@njit
def cross_sum_unroll(a, out, mask):
for i in prange(1, a.shape[0] - 1):
for j in range(1, a.shape[1] - 1):
if mask[i, j]:
continue
out[i, j] = 4 * a[i, j]
out[i, j] += a[i - 1, j]
out[i, j] += a[i + 1, j]
out[i, j] += a[i, j - 1]
out[i, j] += a[i, j + 1]
for i in range(1, a.shape[0] - 1):
j = 0
if not mask[i, j]:
out[i, j] = 4 * a[i, j]
out[i, j] += a[i - 1, j]
out[i, j] += a[i + 1, j]
out[i, j] += a[i, j + 1]
j = a.shape[1] - 1
if not [i, j]:
out[i, j] = 4 * a[i, j]
out[i, j] += a[i - 1, j]
out[i, j] += a[i + 1, j]
out[i, j] += a[i, j - 1]
for j in range(1, a.shape[1] - 1):
i = 0
if not mask[i, j]:
out[i, j] = 4 * a[i, j]
out[i, j] += a[i + 1, j]
out[i, j] += a[i, j - 1]
out[i, j] += a[i, j + 1]
i = a.shape[0] - 1
if not mask[i, j]:
out[i, j] = 4 * a[i, j]
out[i, j] += a[i - 1, j]
out[i, j] += a[i, j - 1]
out[i, j] += a[i, j + 1]
i = 0
j = 0
if not mask[i, j]:
out[i, j] = 4 * a[i, j]
out[i, j] += a[i + 1, j]
out[i, j] += a[i, j + 1]
i = 0
j = a.shape[1] - 1
if not mask[i, j]:
out[i, j] = 4 * a[i, j]
out[i, j] += a[i + 1, j]
out[i, j] += a[i, j - 1]
i = a.shape[0] - 1
j = 0
if not mask[i, j]:
out[i, j] = 4 * a[i, j]
out[i, j] += a[i - 1, j]
out[i, j] += a[i, j + 1]
i = a.shape[0] - 1
j = a.shape[1] - 1
if not mask[i, j]:
out[i, j] = 4 * a[i, j]
out[i, j] += a[i - 1, j]
out[i, j] += a[i, j - 1]
def tv_smooth(img, mask, max_iter=10**3, tol=1e-6):
assert mask.ndim == 2
mask_0 = mask[:, :, None]
mask = mask_0.astype(img.dtype)
img_new = np.zeros_like(img)
mask_new = np.zeros_like(mask)
for _ in range(max_iter):
cross_sum(mask * img, img_new)
cross_sum(mask, mask_new)
mask = mask_new
img_new /= np.maximum(mask, 1e-7).astype(mask.dtype)
img_new = np.where(mask_0, img, img_new)
norm = ((img_new - img) ** 2).max()
if norm < tol:
break
img, img_new = img_new, img
mask = (mask > 0).astype(mask.dtype)
return img_new
# uwx: (H - 1, W)
# uwy: (H, W - 1)
def compute_texture_weights(img, sigma, sharpness=0.02, sharpness_lf=1e-3):
img = rgb2xyz(img)
gx = img[1:, :] - img[:-1, :]
gy = img[:, 1:] - img[:, :-1]
wx = 1 / (np.sqrt((gx**2).sum(axis=2)) + sharpness)
wy = 1 / (np.sqrt((gy**2).sum(axis=2)) + sharpness)
# print('wx', wx.min(), wx.max(), wx.mean(), wx.std())
# print('wy', wy.min(), wy.max(), wy.mean(), wy.std())
gx_lf = gaussian(gx, sigma, channel_axis=2)
gy_lf = gaussian(gy, sigma, channel_axis=2)
ux = 1 / (np.sqrt((gx_lf**2).sum(axis=2)) + sharpness_lf)
uy = 1 / (np.sqrt((gy_lf**2).sum(axis=2)) + sharpness_lf)
ux = gaussian(ux, sigma)
uy = gaussian(uy, sigma)
# print('ux', ux.min(), ux.max(), ux.mean(), ux.std())
# print('uy', uy.min(), uy.max(), uy.mean(), uy.std())
uwx = ux * wx
uwy = uy * wy
# print('uwx', uwx.min(), uwx.max(), uwx.mean(), uwx.std())
# print('uwy', uwy.min(), uwy.max(), uwy.mean(), uwy.std())
return uwx, uwy
def solve_img(img, uwx, uwy, lam=0.01):
H, W, C = img.shape
size = H * W
e = np.pad(uwx, ((0, 1), (0, 0)))
e = -lam * e.flatten()
w = np.pad(e[:-W], ((W, 0),))
s = np.pad(uwy, ((0, 0), (0, 1)))
s = -lam * s.flatten()
n = np.pad(s[:-1], ((1, 0),))
d = 1 - (e + w + s + n)
A = dia_array(([d, s, n, e, w], [0, -1, 1, -W, W]), shape=(size, size))
A = A.tocsr()
out = np.empty_like(img)
for i in range(C):
b = img[:, :, i].flatten()
x, info = bicgstab(A, b, tol=1e-2, atol=1e-2, maxiter=10**3)
if info != 0:
print("info", info)
out[:, :, i] = x.reshape((H, W))
return out
def rtv_smooth(img, sigma=3, max_iter=10, tol=1e-4):
for i in range(max_iter):
print("rtv_smooth", i)
uwx, uwy = compute_texture_weights(img, sigma)
img_new = solve_img(img, uwx, uwy)
norm = ((img_new - img) ** 2).mean()
if norm < tol:
break
img = img_new
return img_new