2.1 Harris角点检测器
第二章讲局部图像描述子，旨在寻找图像间的对应点和对应区域。可以通过图像匹配的方式完成创建全景图、增强现实技术以及计算图像的三维重建等工作。
Harris角点检测算法（也称Harris或Stephens角点检测器）），主要思想：如果像素周围显示存在多于一个方向的边，就认为该点为兴趣点。称为角点。
# 2.1 Harris角点检测器
from pylab import *
from numpy import *
from PIL import Image
from numpy import random
from scipy.ndimage import filters
from imageio import imwrite
def computer_harris_response(im, sigma = 3):
"""在一幅灰度图像中，对每个像素计算Harris角点检测器响应函数"""
# 计算导数
imx = zeros(im.shape)
filters.gaussian_filter(im, (sigma, sigma), (0, 1), imx)
imy = zeros(im.shape)
filters.gaussian_filter(im, (sigma, sigma), (1, 0), imy)
# 计算Harris矩阵的分量
Wxx = filters.gaussian_filter(imx*imx, sigma)
Wxy = filters.gaussian_filter(imx * imy, sigma)
Wyy = filters.gaussian_filter(imy * imy, sigma)
# 计算特征值和迹
Wdet = Wxx*Wyy-Wxy**2
Wtr = Wxx + Wyy
return Wdet/Wtr
def get_harris_points(harrisim, min_dist=10, threshold=0.1):
"""从一幅Harris响应图像中返回角点。min_dist为分割角点和图像边界的最小像素数目"""
# 寻找高于阈值的候选角点
corner_threshold = harrisim.max()*threshold
harrisim_t = (harrisim > corner_threshold)*1
# 得到候选点的坐标
coords = array(harrisim_t.nonzero()).T
# 以及它们的Harris响应值
candidate_values = [harrisim[c[0], c[1]] for c in coords]
# 对候选点按照Harris响应值进行排序
index = argsort(candidate_values)
# 将可行点的位置保存到数组中
allowed_locations = zeros(harrisim.shape)
allowed_locations[min_dist:-min_dist, min_dist:-min_dist] = 1
# 按照min_distance原则，选择最佳Harris点
filtered_coords = []
for i in index:
if allowed_locations[coords[i,0], coords[i,1]] == 1:
filtered_coords.append(coords[i])
allowed_locations[(coords[i,0]-min_dist):(coords[i,0]+min_dist),
(coords[i,1]-min_dist):(coords[i,1]+min_dist)] = 0
return filtered_coords
def plot_harris_points(image, filtered_coords):
"""绘制图像中检测到的角点"""
figure()
gray()
imshow(image)
plot([p[1] for p in filtered_coords], [p[0] for p in filtered_coords], '*')
axis('off')
show()
im = array(Image.open('empire.jpg').convert('L'))
harrisim = computer_harris_response(im)
filtered_coords = get_harris_points(harrisim, threshold=0.2)
plot_harris_points(im, filtered_coords)以上为一个Harris角点检测算法实现的例子。如果想要了解角点检测的不同方法，包括Harris角点检测器的改进和进一步的开发应用，可以查找资源，如下面：
网站
在图像间寻找对应点
from pylab import *
from numpy import *
from PIL import Image
from numpy import random
from scipy.ndimage import filters
from imageio import imwrite
def get_descriptors(image, filtered_coords, wid=5):
"""
对于每个返回的点，返回点周围2*wid+1个像素的值
（假设选取点的min_distance>wid)
"""
desc = []
for coords in filtered_coords:
patch = image[coords[0] - wid:coords[0] + wid + 1,
coords[1] - wid:coords[1] + wid + 1].flatten()
desc.append(patch)
return desc
def match(desc1, desc2, threshold=0.5):
"""对于第一幅图像中的每个角点描述子，使用归一化互相关，
选取它在第二幅图像中的匹配角点"""
n = len(desc1[0])
# 点对的距离
d = -ones((len(desc1), len(desc2)))
for i in range(len(desc1)):
for j in range(len(desc2)):
d1 = (desc1[i]-mean(desc1[i]))/std(desc1[i])
d2 = (desc2[j]-mean(desc2[j]))/std(desc2[j])
ncc_value = sum(d1*d2)/(n-1) # 归一化的互相关矩阵
if ncc_value > threshold:
d[i, j] = ncc_value
ndx = argsort(-d) # Returns the indices that would sort an array. 从小到大
matchscores = ndx[:, 0]
return matchscores
def match_twosided(desc1, desc2, threshold=0.5):
"""两边对称版本的match()"""
matches_12 = match(desc1, desc2, threshold)
matches_21 = match(desc2, desc1, threshold)
ndx_12 = where(matches_12 >= 0)[0]
# 去除非对称的匹配
for n in ndx_12:
if matches_21[matches_12[n]] != n:
matches_12[n] = -1
return matches_12
def appendimages(im1, im2):
"""返回将两幅图像并排拼接成的一幅新图像"""
# 选取具有最少行数的图像，然后填充足够的空行
rows1 = im1.shape[0]
rows2 = im2.shape[0]
if rows1 < rows2:
im1 = concatenate((im1, zeros((rows2-rows1, im1.shape[1]))), axis=0)
elif rows1 > rows2:
im2 = concatenate((im1, zeros((rows1 - rows2, im2.shape[1]))), axis=0)
# 如果这些情况都没有，那么它们的行数相同，不需要进行填充
return concatenate((im1, im2), axis=1)
def plot_matches(im1, im2, locs1, locs2, matchscores, show_below=True):
"""显示一幅带有连接匹配之间连线的图片
输入：im1，im2（数组图像），locs1，locs2（特征位置），matchscores（match（）的输出）
show_below（如果图像应该显示在匹配的下方"""
im3 = appendimages(im1, im2)
if show_below:
im3 = vstack((im3, im3)) # ?
imshow(im3)
cols1 = im1.shape[1]
for i, m in enumerate(matchscores):
if m > 0:
plot([locs1[i][1], locs2[m][1]+cols1], [locs1[i][0], locs2[m][0]], 'c')
axis('off')
def computer_harris_response(im, sigma=3):
"""在一幅灰度图像中，对每个像素计算Harris角点检测器响应函数"""
# 计算导数
imx = zeros(im.shape)
filters.gaussian_filter(im, (sigma, sigma), (0, 1), imx)
imy = zeros(im.shape)
filters.gaussian_filter(im, (sigma, sigma), (1, 0), imy)
# 计算Harris矩阵的分量
Wxx = filters.gaussian_filter(imx * imx, sigma)
Wxy = filters.gaussian_filter(imx * imy, sigma)
Wyy = filters.gaussian_filter(imy * imy, sigma)
# 计算特征值和迹
Wdet = Wxx * Wyy - Wxy ** 2
Wtr = Wxx + Wyy
return Wdet / Wtr
def get_harris_points(harrisim, min_dist=10, threshold=0.1):
"""从一幅Harris响应图像中返回角点。min_dist为分割角点和图像边界的最小像素数目"""
# 寻找高于阈值的候选角点
corner_threshold = harrisim.max() * threshold
harrisim_t = (harrisim > corner_threshold) * 1
# 得到候选点的坐标
coords = array(harrisim_t.nonzero()).T
# 以及它们的Harris响应值
candidate_values = [harrisim[c[0], c[1]] for c in coords]
# 对候选点按照Harris响应值进行排序
index = argsort(candidate_values)
# 将可行点的位置保存到数组中
allowed_locations = zeros(harrisim.shape)
allowed_locations[min_dist:-min_dist, min_dist:-min_dist] = 1
# 按照min_distance原则，选择最佳Harris点
filtered_coords = []
for i in index:
if allowed_locations[coords[i, 0], coords[i, 1]] == 1:
filtered_coords.append(coords[i])
allowed_locations[(coords[i, 0] - min_dist):(coords[i, 0] + min_dist),
(coords[i, 1] - min_dist):(coords[i, 1] + min_dist)] = 0
return filtered_coords
wid = 5
im1 = array(Image.open('crans_1_small.jpg').convert('L'))
harrisim = computer_harris_response(im1, 5)
filtered_coords1 = get_harris_points(harrisim, wid+1)
d1 = get_descriptors(im1, filtered_coords1, wid)
im2 = array(Image.open('crans_2_small.jpg').convert('L'))
harrisim = computer_harris_response(im2, 5)
filtered_coords2 = get_harris_points(harrisim, wid+1)
d2 = get_descriptors(im2, filtered_coords2, wid)
print("starting matching")
matches = match_twosided(d1, d2)
figure()
gray()
plot_matches(im1, im2, filtered_coords1, filtered_coords2, matches[:100])
show()
该方法存在不正确匹配，因为图像像素块的互相关矩阵具有较弱的描述性。此外，这些描述符不具有尺度不变性和旋转不变性，且算法中像素块的大小也会影响对应匹配的结果。