From 018eab70403d52a823486c9e3cdd3acc3056e4bc Mon Sep 17 00:00:00 2001 From: vishwesh5 Date: Thu, 14 Jun 2018 12:30:06 +0530 Subject: [PATCH] Corrected formula Corrected formula for weighted within-class variance --- doc/py_tutorials/py_imgproc/py_thresholding/py_thresholding.markdown | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/py_tutorials/py_imgproc/py_thresholding/py_thresholding.markdown b/doc/py_tutorials/py_imgproc/py_thresholding/py_thresholding.markdown index 1326bc5..896b5f7 100644 --- a/doc/py_tutorials/py_imgproc/py_thresholding/py_thresholding.markdown +++ b/doc/py_tutorials/py_imgproc/py_thresholding/py_thresholding.markdown @@ -183,7 +183,7 @@ minimizes the **weighted within-class variance** given by the relation : where -\f[q_1(t) = \sum_{i=1}^{t} P(i) \quad \& \quad q_1(t) = \sum_{i=t+1}^{I} P(i)\f]\f[\mu_1(t) = \sum_{i=1}^{t} \frac{iP(i)}{q_1(t)} \quad \& \quad \mu_2(t) = \sum_{i=t+1}^{I} \frac{iP(i)}{q_2(t)}\f]\f[\sigma_1^2(t) = \sum_{i=1}^{t} [i-\mu_1(t)]^2 \frac{P(i)}{q_1(t)} \quad \& \quad \sigma_2^2(t) = \sum_{i=t+1}^{I} [i-\mu_1(t)]^2 \frac{P(i)}{q_2(t)}\f] +\f[q_1(t) = \sum_{i=1}^{t} P(i) \quad \& \quad q_2(t) = \sum_{i=t+1}^{I} P(i)\f]\f[\mu_1(t) = \sum_{i=1}^{t} \frac{iP(i)}{q_1(t)} \quad \& \quad \mu_2(t) = \sum_{i=t+1}^{I} \frac{iP(i)}{q_2(t)}\f]\f[\sigma_1^2(t) = \sum_{i=1}^{t} [i-\mu_1(t)]^2 \frac{P(i)}{q_1(t)} \quad \& \quad \sigma_2^2(t) = \sum_{i=t+1}^{I} [i-\mu_2(t)]^2 \frac{P(i)}{q_2(t)}\f] It actually finds a value of t which lies in between two peaks such that variances to both classes are minimum. It can be simply implemented in Python as follows: -- 2.7.4