\u5728 3D \u6e32\u67d3\u4e0e\u73af\u5883\u7f8e\u672f\u7ba1\u7ebf\u4e2d，\u5730\u8868\u3001\u7816\u5899\u3001\u5ca9\u77f3\u7b49\u5927\u9762\u79ef\u6750\u8d28\u90fd\u9700\u8981\u8fdb\u884c\u5e73\u94fa（Tiling）\u3002\u65e0\u8bba\u662f\u901a\u8fc7 AI \u6269\u6563\u6a21\u578b（\u5982 Stable Diffusion）\u751f\u6210\u7684\u8d34\u56fe，\u8fd8\u662f\u65e0\u4eba\u673a\u822a\u62cd\u5b9e\u91c7\u7684\u7eb9\u7406，\u76f4\u63a5\u5e73\u94fa\u90fd\u4f1a\u5728\u56db\u5468\u8fb9\u6846\u51fa\u73b0\u523a\u773c\u7684\u51e0\u4f55\u7f1d\u9699\u4e0e\u8272\u8c03\u65ad\u5c42\u3002<\/p>\n
\u4f20\u7edf Photoshop \u4e2d\u7684\u201c\u4f4d\u79fb + \u4eff\u5236\u56fe\u7ae0\u201d\u4f9d\u8d56\u4eba\u5de5\u624b\u52a8\u4fee\u8865，\u65e0\u6cd5\u96c6\u6210\u5230\u5168\u81ea\u52a8 PCG \u6216\u5b9e\u65f6\u6750\u8d28\u751f\u6210\u7ba1\u7ebf\u4e2d\u3002\u4ece\u7b97\u6cd5\u89d2\u5ea6\u51fa\u53d1，\u6d88\u9664\u8d34\u56fe\u63a5\u7f1d\u6709\u4e24\u79cd\u6838\u5fc3\u601d\u8def：\u57fa\u4e8e\u51e0\u4f55\u52a0\u6743\u7684\u8fb9\u7f18\u6e10\u53d8\u6269\u6563（Alpha Feathered Wrap Blending），\u4ee5\u53ca\u57fa\u4e8e\u68af\u5ea6\u57df\u4f18\u5316\u7684\u6cca\u677e\u56fe\u50cf\u878d\u5408（Poisson Image Blending）\u3002<\/p>\n
\u63a5\u7f1d\u4ea7\u751f\u7684\u6839\u672c\u539f\u56e0\u662f\u56fe\u50cf\u5de6\u53f3\u8fb9\u7f18 $I(0, y)$ \u4e0e $I(W-1, y)$\u3001\u4e0a\u4e0b\u8fb9\u7f18 $I(x, 0)$ \u4e0e $I(x, H-1)$ \u5b58\u5728\u50cf\u7d20\u503c\u4e0e\u68af\u5ea6\u5dee\u3002<\/p>\n
\u901a\u8fc7\u5bf9\u56fe\u50cf\u8fdb\u884c\u534a\u5bbd\u534a\u9ad8\u4f4d\u79fb（Wrap Offset），\u5c06\u539f\u672c\u5728\u56db\u5468\u7684\u56db\u6761\u5916\u8fb9\u754c\u5e73\u79fb\u5230\u56fe\u50cf\u6b63\u4e2d\u592e\u5448\u5341\u5b57\u5f62\u5341\u5b57\u4ea4\u53c9\u7ebf：<\/p>\n
$$(x', y') = ((x + W\/2) \\\\pmod W, (y + H\/2) \\\\pmod H)$$<\/p>\n
\u63a5\u7f1d\u4fee\u590d\u7684\u76ee\u6807，\u5c31\u662f\u5728\u4fdd\u6301\u56db\u5468\u8fb9\u6cbf\u7edd\u5bf9\u8fde\u7eed\u7684\u524d\u63d0\u4e0b，\u5c06\u5341\u5b57\u4ea4\u53c9\u63a5\u7f1d\u5904\u7684\u8fc7\u6e21\u5904\u7406\u5f97\u5e73\u6ed1\u65e0\u75d5\u3002<\/p>\n
\u8fb9\u7f18\u6269\u6563\u6cd5\u901a\u8fc7\u5728\u5341\u5b57\u63a5\u7f1d\u5904\u5b9a\u4e49\u4e00\u4e2a\u8fc7\u6e21\u5bbd\u5ea6（Band Width $B$），\u5229\u7528\u7ebf\u6027\u6216\u4f59\u5f26\u63d2\u503c\u6743\u91cd\u5c06\u8fb9\u7f18\u50cf\u7d20\u4e0e\u5bf9\u5e94\u5185\u4fa7\u50cf\u7d20\u8fdb\u884c\u52a0\u6743\u5e73\u5747\u3002<\/p>\n
\u8fd9\u79cd\u65b9\u6cd5\u7684\u4f18\u70b9\u662f\u8ba1\u7b97\u6781\u5feb，\u4ec5\u9700\u51e0\u4e2a\u7247\u5143\u6307\u4ee4\u5373\u53ef\u5728 GPU \u4e0a\u5b8c\u6210；\u7f3a\u70b9\u662f\u5728\u9ad8\u9891\u7ec6\u8282\u7eb9\u7406（\u5982\u9e45\u5375\u77f3\u3001\u88c2\u7eb9\u7816\u77f3）\u4e0a，\u7ebf\u6027\u53e0\u52a0\u4f1a\u4ea7\u751f\u660e\u663e\u7684\u534a\u900f\u660e\u91cd\u5f71\u4e0e\u6a21\u7cca\u8f6f\u5316\u3002<\/p>\n
import numpy as np<\/p>\n
def make_seamless_feather(image: np.ndarray, overlap: float = 0.15) -> np.ndarray:
\n """
\n \u57fa\u4e8e\u4f59\u5f26\u6743\u91cd\u7684\u8fb9\u7f18\u65e0\u7f1d\u878d\u5408
\n :param image: \u8f93\u5165\u56fe\u50cf (H, W, C), float32 [0, 1]
\n :param overlap: \u91cd\u53e0\u8fc7\u6e21\u533a\u57df\u5360\u6bd4 (0.0 – 0.5)
\n """
\n h, w, c = image.shape
\n ow = int(w * overlap)
\n oh = int(h * overlap)<\/p>\n
# \u6784\u9020\u6c34\u5e73\u4e0e\u5782\u76f4\u5e73\u6ed1\u6743\u91cd\u77e9\u9635
\n x = np.linspace(0, 1, ow)
\n w_weight = 0.5 * (1 – np.cos(np.pi * x)) # \u4f59\u5f26\u5e73\u6ed1\u66f2\u7ebf<\/p>\n
y = np.linspace(0, 1, oh)
\n h_weight = 0.5 * (1 – np.cos(np.pi * y))<\/p>\n
# \u5148\u505a Wrap Offset \u5c06\u8fb9\u7f18\u79fb\u5230\u4e2d\u5fc3
\n shifted = np.roll(np.roll(image, shift=w \/\/ 2, axis=1), shift=h \/\/ 2, axis=0)<\/p>\n
# \u5bf9\u5341\u5b57\u4ea4\u53c9\u533a\u57df\u8fdb\u884c\u6743\u91cd\u5e73\u6ed1\u6df7\u5408
\n # … \u5728\u8fc7\u6e21\u533a\u6df7\u5408\u539f\u59cb\u8fb9\u6cbf\u4fe1\u606f …
\n return shifted<\/p>\n
\u4e3a\u4e86\u907f\u514d\u878d\u5408\u533a\u57df\u53d8\u6a21\u7cca，\u5fc5\u987b\u5728**\u68af\u5ea6\u57df（Gradient Domain）**\u8fdb\u884c\u6c42\u89e3\u3002\u6cca\u677e\u878d\u5408\u7684\u6838\u5fc3\u601d\u60f3\u662f：\u4fdd\u6301\u5f85\u4fee\u8865\u533a\u57df\u5185\u7684\u7ec6\u8282\u7eb9\u7406\u68af\u5ea6 $\\\\mathbf{v} = \\\\nabla I$ \u4e0d\u53d8，\u540c\u65f6\u5f3a\u884c\u7ea6\u675f\u4fee\u8865\u533a\u57df\u8fb9\u754c\u4e0e\u76ee\u6807\u80cc\u666f\u5b8c\u5168\u543b\u5408\u3002<\/p>\n
\u6570\u5b66\u4e0a，\u8fd9\u7b49\u4ef7\u4e8e\u6c42\u89e3\u5e26\u6709\u72c4\u5229\u5229\u6761\u4ef6（Dirichlet Boundary Conditions）\u7684\u6cca\u677e\u504f\u5fae\u5206\u65b9\u7a0b：<\/p>\n
$$\\\\Delta f = \\\\operatorname{div} \\\\mathbf{v} \\\\quad \\\\text{over } \\\\Omega, \\\\quad \\\\text{with } f|{\\\\partial \\\\Omega} = f^*|{\\\\partial \\\\Omega}$$<\/p>\n
\u5176\u4e2d：<\/p>\n
\u5728\u79bb\u6563\u7f51\u683c\u4e0a，\u62c9\u666e\u62c9\u65af\u65b9\u7a0b\u8868\u73b0\u4e3a\u4e00\u4e2a\u5de8\u5927\u7684\u7a00\u758f\u7ebf\u6027\u65b9\u7a0b\u7ec4 $A \\\\mathbf{x} = \\\\mathbf{b}$，\u6bcf\u4e2a\u5185\u90e8\u50cf\u7d20\u6ee1\u8db3\u4e94\u70b9\u79bb\u6563\u5dee\u5206\u683c\u5f0f：<\/p>\n
$$4 f_{i,j} – f_{i-1,j} – f_{i+1,j} – f_{i,j-1} – f_{i,j+1} = \\\\operatorname{div} \\\\mathbf{v}(i, j)$$<\/p>\n
\u4e0b\u9762\u7ed9\u51fa\u5229\u7528 SciPy \u7a00\u758f\u77e9\u9635\u6c42\u89e3\u5668\u5b9e\u73b0\u7684\u65e0\u7f1d\u8d34\u56fe\u4fee\u8865\u6d41\u6c34\u7ebf：<\/p>\n
import numpy as np
\nimport scipy.sparse as sp
\nimport scipy.sparse.linalg as splinalg
\nimport cv2<\/p>\n
def make_seamless_poisson(img: np.ndarray, blend_width: int = 32) -> np.ndarray:
\n """
\n \u4f7f\u7528\u6cca\u677e\u878d\u5408\u6d88\u9664\u4f4d\u79fb\u540e\u7684\u5341\u5b57\u63a5\u7f1d
\n :param img: \u8f93\u5165\u56fe\u50cf float32, \u8303\u56f4 [0, 1]
\n :param blend_width: \u5341\u5b57\u63a5\u7f1d\u5904\u7684\u4fee\u8865\u5e26\u534a\u5bbd (\u50cf\u7d20)
\n """
\n h, w, c = img.shape<\/p>\n
# 1. \u73af\u7ed5\u4f4d\u79fb，\u4f7f\u5916\u8fb9\u6846\u5bf9\u9f50\u5230\u5185\u90e8
\n shifted = np.roll(np.roll(img, shift=w \/\/ 2, axis=1), shift=h \/\/ 2, axis=0)<\/p>\n
# 2. \u6784\u5efa\u5341\u5b57\u63a5\u7f1d\u4fee\u8865 Mask (1 \u4ee3\u8868\u5f85\u4fee\u8865\u533a\u57df，0 \u4ee3\u8868\u7edd\u5bf9\u4fdd\u6301\u533a\u57df)
\n mask = np.zeros((h, w), dtype=np.uint8)
\n cx, cy = w \/\/ 2, h \/\/ 2
\n mask[:, max(0, cx – blend_width):min(w, cx + blend_width)] = 1
\n mask[max(0, cy – blend_width):min(h, cy + blend_width), :] = 1<\/p>\n
# 3. \u8ba1\u7b97\u5f15\u5bfc\u68af\u5ea6\u573a (\u91c7\u7528\u539f\u56fe\u672a\u4f4d\u79fb\u65f6\u7684\u8fb9\u754c\u65e0\u7f1d\u68af\u5ea6)
\n # \u4e3a\u6bcf\u4e2a\u901a\u9053\u72ec\u7acb\u6c42\u89e3\u6cca\u677e\u65b9\u7a0b
\n result = np.zeros_like(shifted)<\/p>\n
# \u5efa\u7acb\u672a\u77e5\u6570\u50cf\u7d20\u7d22\u5f15\u6620\u5c04
\n unknown_indices = np.where(mask == 1)
\n num_unknowns = len(unknown_indices[0])<\/p>\n
coord_to_idx = -np.ones((h, w), dtype=np.int32)
\n for idx, (y, x) in enumerate(zip(unknown_indices[0], unknown_indices[1])):
\n coord_to_idx[y, x] = idx<\/p>\n
# \u6784\u5efa\u7a00\u758f\u62c9\u666e\u62c9\u65af\u77e9\u9635 A
\n A = sp.lil_matrix((num_unknowns, num_unknowns), dtype=np.float32)<\/p>\n
for idx, (y, x) in enumerate(zip(unknown_indices[0], unknown_indices[1])):
\n A[idx, idx] = 4.0
\n neighbors = [(y – 1, x), (y + 1, x), (y, x – 1), (y, x + 1)]
\n for ny, nx in neighbors:
\n ny = ny % h
\n nx = nx % w
\n if mask[ny, nx] == 1:
\n n_idx = coord_to_idx[ny, nx]
\n A[idx, n_idx] = -1.0<\/p>\n
A = A.tocsr()<\/p>\n
# \u6c42\u89e3\u6bcf\u4e2a\u989c\u8272\u901a\u9053
\n for ch in range(c):
\n b = np.zeros(num_unknowns, dtype=np.float32)
\n channel_data = shifted[:, :, ch]<\/p>\n
# \u8ba1\u7b97\u79bb\u6563\u6563\u5ea6\u4e0e\u8fb9\u754c\u6761\u4ef6
\n for idx, (y, x) in enumerate(zip(unknown_indices[0], unknown_indices[1])):
\n # \u4ece\u4f4d\u79fb\u539f\u56fe\u4e2d\u8ba1\u7b97\u76ee\u6807\u62c9\u666e\u62c9\u65af\u503c
\n div = 4.0 * channel_data[y, x] – (
\n channel_data[(y – 1) % h, x] +
\n channel_data[(y + 1) % h, x] +
\n channel_data[y, (x – 1) % w] +
\n channel_data[y, (x + 1) % w]
\n )<\/p>\n
# \u8fb9\u754c\u56fa\u5b9a\u503c\u7ea6\u675f
\n neighbors = [(y – 1, x), (y + 1, x), (y, x – 1), (y, x + 1)]
\n for ny, nx in neighbors:
\n ny = ny % h
\n nx = nx % w
\n if mask[ny, nx] == 0:
\n div += channel_data[ny, nx]<\/p>\n
b[idx] = div<\/p>\n
# \u4f7f\u7528\u5171\u8f6d\u68af\u5ea6\u6cd5\u5feb\u901f\u6c42\u89e3\u7a00\u758f\u7cfb\u7edf
\n x_sol, _ = splinalg.cg(A, b, maxiter=200, tol=1e-5)<\/p>\n
reconstructed = channel_data.copy()
\n for idx, (y, x) in enumerate(zip(unknown_indices[0], unknown_indices[1])):
\n reconstructed[y, x] = x_sol[idx]<\/p>\n
result[:, :, ch] = np.clip(reconstructed, 0.0, 1.0)<\/p>\n
return result<\/p>\n
| \u8ba1\u7b97\u590d\u6742\u5ea6<\/td>\n | $O(N)$，\u7b80\u5355\u7ebf\u6027\u63d2\u503c<\/td>\n | $O(N^{1.5})$，\u7a00\u758f\u7ebf\u6027\u7cfb\u7edf\u6c42\u89e3<\/td>\n<\/tr>\n |
| GPU \u5b9e\u65f6\u6027<\/td>\n | \u6781\u4f73（\u53ef\u5728\u7247\u5143\u7740\u8272\u5668 0.05ms \u5185\u5b8c\u6210）<\/td>\n | \u8f83\u91cd（\u901a\u5e38\u5728\u79bb\u7ebf\u70d8\u7119\u6216 Compute Shader \u591a\u7f51\u683c\u8fed\u4ee3）<\/td>\n<\/tr>\n |
| \u9ad8\u9891\u8fb9\u7f18\u4fdd\u6301<\/td>\n | \u6613\u4ea7\u751f\u6a21\u7cca\u5149\u6655\u4e0e\u53cc\u91cd\u91cd\u5f71<\/td>\n | \u6781\u4f73，\u5b8c\u6574\u4fdd\u7559\u7802\u77f3\u3001\u7816\u7f1d\u7b49\u9ad8\u9891\u62d3\u6251<\/td>\n<\/tr>\n |
| \u5927\u5c3a\u5ea6\u5149\u7167\u5e73\u6ed1<\/td>\n | \u65e0\u6cd5\u6d88\u9664\u5168\u5c40\u660e\u6697\u6e10\u53d8\u8272\u5dee<\/td>\n | \u81ea\u52a8\u6269\u6563\u4f4e\u9891\u8272\u5f69，\u6d88\u9664\u9634\u9633\u8138<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u5728\u73b0\u4ee3\u8d44\u4ea7\u81ea\u52a8\u5316\u6d41\u6c34\u7ebf\u4e2d，\u5bf9\u4e8e\u6cd5\u7ebf\u8d34\u56fe（Normal Map）\u548c\u7c97\u7cd9\u5ea6\u8d34\u56fe（Roughness Map），\u7531\u4e8e\u6cd5\u7ebf\u5411\u91cf\u5177\u6709\u5f52\u4e00\u5316\u51e0\u4f55\u7ea6\u675f，\u901a\u5e38\u91c7\u7528\u6269\u6563\u4e0e\u5207\u7ebf\u91cd\u5f52\u4e00\u5316；\u800c\u5bf9\u4e8e\u9ad8\u52a8\u6001\u6f2b\u53cd\u5c04\u8d34\u56fe（Albedo \/ Base Color），\u6cca\u677e\u878d\u5408\u5219\u662f\u6d88\u9664\u5149\u7167\u4e0d\u5747\u4e0e\u8fb9\u7f18\u8272\u5dee\u7684\u5de5\u4e1a\u6807\u51c6\u5229\u5668\u3002<\/p>\n","protected":false},"excerpt":{"rendered":" \u65e0\u7f1d\u5e73\u7f1d\u8d34\u56fe\u7684\u751f\u6210\u4e0e\u63a5\u7f1d\u4fee\u8865：\u4ece\u8fb9\u7f18\u6269\u6563\u5230\u6cca\u677e\u878d\u5408 |