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Update otsu.md
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ad33edub authored Jan 14, 2025
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Expand Up @@ -34,13 +34,13 @@ Otsu's method works by maximizing the **between class variance** σ<sub>B</sub>

with

P~1~(&theta;) = $\sum_{i = 0}^{\theta} h(i)$ (&#8793; number of pixels below the threshold (background))
P<sub>1</sub>(&theta;) = $\sum_{i = 0}^{\theta} h(i)$ (&#8793; number of pixels below the threshold (background))

P~2~(&theta;) = 1 - P~1~(&theta;) = $\sum_{i = \theta +1}^{L-1} h(i)$ (&#8793; number of pixels above the threshold (foreground))
P<sub>2</sub>(&theta;) = 1 - P<sub>1</sub>(&theta;) = $\sum_{i = \theta +1}^{L-1} h(i)$ (&#8793; number of pixels above the threshold (foreground))

&mu;~1~(&theta;) = $\frac{1}{P1(\theta)}$ $\cdot$ $\sum_{i = 0}^{\theta} (i+1)h(i)$ (&#8793; mean intensity of the background)
&mu;<sub>1</sub>(&theta;) = $\frac{1}{P1(\theta)}$ $\cdot$ $\sum_{i = 0}^{\theta} (i+1)h(i)$ (&#8793; mean intensity of the background)

&mu;~2~(&theta;) = $\frac{1}{P2(\theta)}$ $\cdot$ $\sum_{i = \theta +1}^{L-1} (i+1)h(i)$ (&#8793; mean intensity of the foreground)
&mu;<sub>2</sub>(&theta;) = $\frac{1}{P2(\theta)}$ $\cdot$ $\sum_{i = \theta +1}^{L-1} (i+1)h(i)$ (&#8793; mean intensity of the foreground)
</div>

with __h(i)__ being the normalized histogram of the image, __&theta;__ being the current threshold and __L__ being the length of the histogram-array.
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