原理
Otsu 的原理是最小化类间方差，从像素分布直方图的角度来看就是在像素分布直方图的峰值之间找一个点，使得两个类之间的方差最大，类内方差最小。
Screen Shot 2019-01-28 at 12.02.02 PM.png
image.png
这个算法可以用于OCR, 车牌分割等等
实现
- 这个实现是遍历每一个分割值，然后求解全局最优解，具体到工程应用也有一些优化算法。
img = cv.imread('noisy2.png',0)
blur = cv.GaussianBlur(img,(5,5),0)
# find normalized_histogram, and its cumulative distribution function
hist = cv.calcHist([blur],[0],None,[256],[0,256])
hist_norm = hist.ravel()/hist.max()
Q = hist_norm.cumsum()
bins = np.arange(256)
fn_min = np.inf
thresh = -1
for i in range(1,256):
p1,p2 = np.hsplit(hist_norm,[i]) # probabilities
q1,q2 = Q[i],Q[255]-Q[i] # cum sum of classes
b1,b2 = np.hsplit(bins,[i]) # weights
# finding means and variances
m1,m2 = np.sum(p1*b1)/q1, np.sum(p2*b2)/q2
v1,v2 = np.sum(((b1-m1)**2)*p1)/q1,np.sum(((b2-m2)**2)*p2)/q2
# calculates the minimization function
fn = v1*q1 + v2*q2
if fn < fn_min:
fn_min = fn
thresh = i
# find otsu's threshold value with OpenCV function
ret, otsu = cv.threshold(blur,0,255,cv.THRESH_BINARY+cv.THRESH_OTSU)
print( "{} {}".format(thresh,ret) )
