SuperPixel
Gonzalez R. C. and Woods R. E. Digital Image Processing (Forth Edition).
单个像素的意义其实很小, 于是有了superpixel的概念, 即一簇pixels的集合(且这堆pixels共用一个值), 这会导致图片有非常有趣的艺术风格(下图便是取不同的superpixel大小形成的效果, 有种抽象画的感觉?):
经过superpixel的预处理后, 图片可以变得更加容易提取edge, region, 毕竟superpixel已经率先提取过一次了.
SLIC Superpixel algorithm
SLIC (simple linear iterative clustering) 算法是基于k-means的一种聚类算法.
Given: 需要superpixels的个数\(n_{sp}\); 图片\(f(x, y) = (r, g, b), x = 1,2,\cdots M, y = 1, 2, \cdots, N\);
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根据图片以及其位置信息生成数据:
\[\bm{z} = [r, g, b, x, y]^T, \]其中\(r, g, b\)是颜色编码, \(x, y\)是位置信息.
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令\(n_{tp} = MN\)表示pixels的个数, 并计算网格大小:
\[s = [n_{tp} / n_{sp}]^{1/2}. \] -
将图片均匀分割为大小\(s\)的网格, 初始化superpixels的中心:
\[\bm{m}_i = [r_i, g_i, b_i, x_i, y_i]^T, i=1,2,\cdots, n_{sp}, \]为网格的中心. 或者, 为了防止噪声的影响, 选择中心\(3 \times 3\)领域内梯度最小的点.
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将图片的每个pixel的类别标记为\(L(p) = -1\), 距离\(d(p) = \infty\);
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重复下列步骤直到收敛:
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对于每个像素点\(p\), 计算其与\(2s \times 2s\)邻域内的中心点\(\bm{m}_i\)之间的距离\(D_i(p)\), 倘若\(D_i(p) < d(p)\):
\[d(p) = D_i, L(p) = i. \] -
令\(C_i\)表示\(L(p) = i\)的像素点的集合, 更新superpixels的中心:
\[\bm{m}_i = \frac{1}{|C_i|} \sum_{\bm{z} \in C_i} \bm{z}, i=1, 2, \cdots, n_{sp}. \]
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将以\(\bm{m}_i\)为中心的区域中的点的(r, g, b)设定为与\(\bm{m}_i\)一致.
距离函数的选择
倘若\(D\)采用的是和普通K-means一样的\(\|\cdot\|_2\)显然是不合适的, 因为\((r, g, b)\)和\((x, y)\)显然不是一个尺度的. 故采用如下的距离函数:
其中\(d_{cm}, d_{sm}\)分别是\(d_c, d_s\)可能取到的最大值, 相当于标准化了.
代码
import numpy as np
def _generate_data(img):
img = img.astype(np.float64)
if len(img.shape) == 2:
img = img[..., None]
M, N = img.shape[0], img.shape[1]
loc = np.stack(np.meshgrid(range(M), range(N), indexing='ij'), axis=-1)
classes = -np.ones((M, N))
distances = np.ones((M, N)) * np.float('inf')
data = np.concatenate((img, loc), axis=-1)
return data, classes, distances
def _generate_means(data, size: int):
M, N = data.shape[0], data.shape[1]
x_splits = np.arange(0, M + size, size)
y_splits = np.arange(0, N + size, size)
means = []
for i in range(len(x_splits) - 1):
for j in range(len(y_splits) - 1):
r1, r2 = x_splits[i:i+2]
c1, c2 = y_splits[j:j+2]
region = data[r1:r2, c1:c2]
means.append(region.mean(axis=(0, 1)))
return np.array(means)
def _unit_step(data, means, classes, distances, size, dis_fn):
M, N = data.shape[0], data.shape[1]
size = 2 * size
for i, m in enumerate(means):
# ..., x, y
x, y = np.round(m[-2:])
x, y = int(x), int(y)
xl, xr = max(0, x - size), min(x + size, M)
yb, yt = max(0, y - size), min(y + size, N)
p = data[xl:xr, yb:yt]
_dis = dis_fn(p, m)
indices = _dis < distances[xl:xr, yb:yt]
distances[xl:xr, yb:yt][indices] = _dis[indices]
classes[xl:xr, yb:yt][indices] = i
# update
for i in range(len(means)):
x_indices, y_indices = np.where(classes == i)
if len(x_indices) == 0:
continue
means[i] = data[x_indices, y_indices].mean(axis=0)
def slic(img, size, max_iters=10, compactness=10):
data, classes, distances = _generate_data(img)
means = _generate_means(data, size)
dsm = size
dcm = (img.max(axis=(0, 1)) - img.min(axis=(0, 1))) * compactness
dsc = np.concatenate((dcm, [dsm] * 2))
def dis_func(p, m):
_dis = ((p - m) / dsc) ** 2
return _dis.sum(axis=-1)
for _ in range(max_iters):
_unit_step(data, means, classes, distances, size, dis_func)
new_img = np.zeros_like(img, dtype=np.float)
for i, m in enumerate(means):
x_indices, y_indices = np.where(classes == i)
if len(x_indices) == 0:
continue
new_img[x_indices, y_indices] = m[:-2]
return new_img.astype(img.dtype)
from skimage import io, segmentation, filters
from freeplot.base import FreePlot
img = io.imread(r"Lenna.png")
ours = slic(img, size=50, compactness=0.5)
def mask2img(mask, img):
new_img = img.astype(np.float)
masks = np.unique(mask)
for m in masks:
x, y = np.where(mask == m)
mcolor = new_img[x, y].mean(axis=0)
new_img[x, y] = mcolor
return new_img.astype(img.dtype)
mask = segmentation.slic(img)
yours = mask2img(mask, img)
fp = FreePlot((1, 3), (10.3, 5), titles=('Lenna', 'ours', 'skimage.segmentation.slic'))
fp.imageplot(img, index=(0, 0))
fp.imageplot(ours, index=(0, 1))
fp.imageplot(yours, index=(0, 2))
fp.set_title()
fp.show()
skimage上实现的代码还有强制连通性, 我想这个是为什么它看起来这么流畅的原因. Compactness 越大, 聚类越倾向于空间信息, 所以越容易出现块状结构.
