Implementing Otsu binarization from scratch python
Solution 1
I dont know if my implementation is alright. But this is what I got:
def otsu(gray):
pixel_number = gray.shape[0] * gray.shape[1]
mean_weigth = 1.0/pixel_number
his, bins = np.histogram(gray, np.array(range(0, 256)))
final_thresh = -1
final_value = -1
for t in bins[1:-1]: # This goes from 1 to 254 uint8 range (Pretty sure wont be those values)
Wb = np.sum(his[:t]) * mean_weigth
Wf = np.sum(his[t:]) * mean_weigth
mub = np.mean(his[:t])
muf = np.mean(his[t:])
value = Wb * Wf * (mub - muf) ** 2
print("Wb", Wb, "Wf", Wf)
print("t", t, "value", value)
if value > final_value:
final_thresh = t
final_value = value
final_img = gray.copy()
print(final_thresh)
final_img[gray > final_thresh] = 255
final_img[gray < final_thresh] = 0
return final_img
Solution 2
I used the implementation @Jose A in posted answer, which tries to maximize the interclass variance. It looks like jose has forgotten to multiply intensity level to their respective intensity pixel counts (in order to calculate mean), So I corrected the calculation of background mean mub and foreground mean muf. I am posting this as an answer and also trying to edit the accepted answer.
def otsu(gray):
pixel_number = gray.shape[0] * gray.shape[1]
mean_weight = 1.0/pixel_number
his, bins = np.histogram(gray, np.arange(0,257))
final_thresh = -1
final_value = -1
intensity_arr = np.arange(256)
for t in bins[1:-1]: # This goes from 1 to 254 uint8 range (Pretty sure wont be those values)
pcb = np.sum(his[:t])
pcf = np.sum(his[t:])
Wb = pcb * mean_weight
Wf = pcf * mean_weight
mub = np.sum(intensity_arr[:t]*his[:t]) / float(pcb)
muf = np.sum(intensity_arr[t:]*his[t:]) / float(pcf)
#print mub, muf
value = Wb * Wf * (mub - muf) ** 2
if value > final_value:
final_thresh = t
final_value = value
final_img = gray.copy()
print(final_thresh)
final_img[gray > final_thresh] = 255
final_img[gray < final_thresh] = 0
return final_img
Moondra
email: amitmoon2017[at]gmail[dot]com I like exploring different fields to see what problems haven't been solved, and to gain a better understanding of what we have accomplished so far (as well as appreciate). Currently working on a computer vision related app (slowly), exploring neural networks, trying to improve my programming skills from a scripter to a better scripter, learning about genetics, synthetic biology, and biohacking, anti-aging and always trying to improve my well-being. For those that have been programmers for a long time, I would love to hear how much exercise you guys do to stay healthy. Do you take breaks every x minutes? 1hr a day of weights and cardio? Below are some knowledgeable folks in the listed frameworks. Python Superstars Pandas : @coldspeed @maxU, @piRSquared Regex: @anubhava Numpy: @Divakar Webscraping: Tensorflow: @Maxim Keras: Swift
Updated on June 22, 2022Comments
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Moondra almost 2 years
It seems my implementation is incorrect and not sure what exactly I'm doing wrong:
Here is the histogram of my image:
So the threshold should be around 170 ish? I'm getting the threshold as 130.
Here is my code:
#Otsu in Python import numpy as np from PIL import Image import matplotlib.pyplot as plt def load_image(file_name): img = Image.open(file_name) img.load() bw = img.convert('L') bw_data = np.array(bw).astype('int32') BINS = np.array(range(0,257)) counts, pixels =np.histogram(bw_data, BINS) pixels = pixels[:-1] plt.bar(pixels, counts, align='center') plt.savefig('histogram.png') plt.xlim(-1, 256) plt.show() total_counts = np.sum(counts) assert total_counts == bw_data.shape[0]*bw_data.shape[1] return BINS, counts, pixels, bw_data, total_counts def within_class_variance(): ''' Here we will implement the algorithm and find the lowest Within- Class Variance: Refer to this page for more details http://www.labbookpages.co.uk /software/imgProc/otsuThreshold.html''' for i in range(1,len(BINS), 1): #from one to 257 = 256 iterations prob_1 = np.sum(counts[:i])/total_counts prob_2 = np.sum(counts[i:])/total_counts assert (np.sum(prob_1 + prob_2)) == 1.0 mean_1 = np.sum(counts[:i] * pixels[:i])/np.sum(counts[:i]) mean_2 = np.sum(counts[i:] * pixels[i:] )/np.sum(counts[i:]) var_1 = np.sum(((pixels[:i] - mean_1)**2 ) * counts[:i])/np.sum(counts[:i]) var_2 = np.sum(((pixels[i:] - mean_2)**2 ) * counts[i:])/np.sum(counts[i:]) if i == 1: cost = (prob_1 * var_1) + (prob_2 * var_2) keys = {'cost': cost, 'mean_1': mean_1, 'mean_2': mean_2, 'var_1': var_1, 'var_2': var_2, 'pixel': i-1} print('first_cost',cost) if (prob_1 * var_1) +(prob_2 * var_2) < cost: cost =(prob_1 * var_1) +(prob_2 * var_2) keys = {'cost': cost, 'mean_1': mean_1, 'mean_2': mean_2, 'var_1': var_1, 'var_2': var_2, 'pixel': i-1} #pixels is i-1 because BINS is starting from one return keys if __name__ == "__main__": file_name = 'fish.jpg' BINS, counts, pixels, bw_data, total_counts =load_image(file_name) keys =within_class_variance() print(keys['pixel']) otsu_img = np.copy(bw_data).astype('uint8') otsu_img[otsu_img > keys['pixel']]=1 otsu_img[otsu_img < keys['pixel']]=0 #print(otsu_img.dtype) plt.imshow(otsu_img) plt.savefig('otsu.png') plt.show()
Resulting otsu image looks like this:
Here is the fish image (It has a shirtless guy holding a fish so may not be safe for work):
Link : https://i.stack.imgur.com/EDTem.jpg
EDIT:
It turns out that by changing the threshold to 255 (The differences are more pronounced)