formula for comparing histograms using the Chi-Squared method is incorrect (Patch #1263)

Added by Nicu Stiurca over 13 years ago. Updated almost 13 years ago.

Status:	Done	Start date:
Priority:	High	Due date:
Assignee:	Vadim Pisarevsky	% Done:	0%
Category:	imgproc, video
Target version:	2.4.0
Affected version:		Operating System:
Difficulty:		HW Platform:
Pull request:

Description

One of the input histograms (say H1) should be denoted the histogram of expected values (henceforth, E), and the other (H2) should be denoted the histogram of observed values (henceforth, O). Then, the numerator of the summation terms becomes
(O(I) - E(I))^2

(numerically the same, but renamed variables), while the denominator SHOULD BE simply
E(I)
NOT
E(I) + O(I)

See, eg, http://en.wikipedia.org/wiki/Pearson%27s_chi-square_test#Calculating_the_test-statistic

Trivial patch included. Note: it may break unit tests if the tests used the wrong formula for the expected value.

histogram.cpp.patch - patch to fix chi squared formula (717 Bytes) Nicu Stiurca, 2011-07-28 04:03 am