如何在 python 中进行 alpha 抠图

如何在 python 中进行 alpha 抠图？

更具体地说，如何提取图像的 alpha 通道，给定一个将像素标记为

• 100% 前景（白色）
• 100% 背景（黑色）
• 或未知（灰色）

输入图像

输入三元图

使用库进行 alpha 抠图

这里有两个选项，都基于论文“自然图像抠图的封闭式解决方案”莱文和利辛斯基。

• https://github.com/MarcoForte/close-form-matting
• https://github.com/99991/matting

其背后的数学原理

1. 计算矩阵L基于图像I它描述了相邻像素的相似程度：

1. 使用约束矩阵求解 alpha 的线性系统D和矢量b修复已知的 alpha 值：

python 中的实现

import numpy as np
import numpy.linalg
import scipy.sparse
import scipy.sparse.linalg
from PIL import Image
from numba import njit

def main():
    # configure paths here
    image_path  = "cat_image.png"
    trimap_path = "cat_trimap.png"
    alpha_path  = "cat_alpha.png"
    cutout_path = "cat_cutout.png"

    # load and convert to [0, 1] range
    image  = np.array(Image.open( image_path).convert("RGB"))/255.0
    trimap = np.array(Image.open(trimap_path).convert(  "L"))/255.0

    # make matting laplacian
    i,j,v = closed_form_laplacian(image)
    h,w = trimap.shape
    L = scipy.sparse.csr_matrix((v, (i, j)), shape=(w*h, w*h))

    # build linear system
    A, b = make_system(L, trimap)

    # solve sparse linear system
    print("solving linear system...")
    alpha = scipy.sparse.linalg.spsolve(A, b).reshape(h, w)

    # stack rgb and alpha
    cutout = np.concatenate([image, alpha[:, :, np.newaxis]], axis=2)

    # clip and convert to uint8 for PIL
    cutout = np.clip(cutout*255, 0, 255).astype(np.uint8)
    alpha  = np.clip( alpha*255, 0, 255).astype(np.uint8)

    # save and show
    Image.fromarray(alpha ).save( alpha_path)
    Image.fromarray(cutout).save(cutout_path)
    Image.fromarray(alpha ).show()
    Image.fromarray(cutout).show()

@njit
def closed_form_laplacian(image, epsilon=1e-7, r=1):
    h,w = image.shape[:2]
    window_area = (2*r + 1)**2
    n_vals = (w - 2*r)*(h - 2*r)*window_area**2
    k = 0
    # data for matting laplacian in coordinate form
    i = np.empty(n_vals, dtype=np.int32)
    j = np.empty(n_vals, dtype=np.int32)
    v = np.empty(n_vals, dtype=np.float64)

    # for each pixel of image
    for y in range(r, h - r):
        for x in range(r, w - r):

            # gather neighbors of current pixel in 3x3 window
            n = image[y-r:y+r+1, x-r:x+r+1]
            u = np.zeros(3)
            for p in range(3):
                u[p] = n[:, :, p].mean()
            c = n - u

            # calculate covariance matrix over color channels
            cov = np.zeros((3, 3))
            for p in range(3):
                for q in range(3):
                    cov[p, q] = np.mean(c[:, :, p]*c[:, :, q])

            # calculate inverse covariance of window
            inv_cov = np.linalg.inv(cov + epsilon/window_area * np.eye(3))

            # for each pair ((xi, yi), (xj, yj)) in a 3x3 window
            for dyi in range(2*r + 1):
                for dxi in range(2*r + 1):
                    for dyj in range(2*r + 1):
                        for dxj in range(2*r + 1):
                            i[k] = (x + dxi - r) + (y + dyi - r)*w
                            j[k] = (x + dxj - r) + (y + dyj - r)*w
                            temp = c[dyi, dxi].dot(inv_cov).dot(c[dyj, dxj])
                            v[k] = (1.0 if (i[k] == j[k]) else 0.0) - (1 + temp)/window_area
                            k += 1
        print("generating matting laplacian", y - r + 1, "/", h - 2*r)

    return i, j, v

def make_system(L, trimap, constraint_factor=100.0):
    # split trimap into foreground, background, known and unknown masks
    is_fg = (trimap > 0.9).flatten()
    is_bg = (trimap < 0.1).flatten()
    is_known = is_fg | is_bg
    is_unknown = ~is_known

    # diagonal matrix to constrain known alpha values
    d = is_known.astype(np.float64)
    D = scipy.sparse.diags(d)

    # combine constraints and graph laplacian
    A = constraint_factor*D + L
    # constrained values of known alpha values
    b = constraint_factor*is_fg.astype(np.float64)

    return A, b

if __name__ == "__main__":
    main()

输出阿尔法

输出断流