Finding a centroid of an area ( y coord. ) under discrete valued 2D function

Hello,

I have a set of discrete pairs ( x , y ) - keys and values - 2D discrete function's samples - a histogram of input digital image that I need to process. ( y = f(x) )

I need to find y coordinate of a centroid of an area under a discrete 2D function ( histogram ) for special image processing after . I found next formulas for continues functions centroid: http://www.intmath.com/applications-integration/5-centroid-area.php

I've tried to calculate y coord. of a centroid using average method for discrete function integration but I'm not sure about computation of y , how to identify x = f-1(y) ( inverted ) and an intervals for computation in discrete case.

How to do that : from having (x,y) discrete pairs set to find the y coordinate of centroid of an area under the function y = f(x) for the given interval [a , b] ( size N )? I need pseudo code or C or Matlab code of calculation of the y:

something like ( pseudocode ):

function find_centroid ( map<Key,Value>input_hist ) returns int y;

Can anybody post a link for such problem solved , such function implemented or description of the algorithm ?

Thanks in advance

Answer 1

[Doug Hull]

I think I did something kinda similar to this in my book. The code is here.

http://www.mathworks.com/matlabcentral/fileexchange/2170

It was for finding centroids of shapes made by compositing circles, rectangles and triangles.

[Pavl M.]

Hello Doug.Thank you for the answer , I've took a look at the .m files , -> yes you calculate centroid in several functions:

hortrap,rectube,tbeam,titleblock,twovector,vertrap,vertia.In next way:

xcentroid=hortrap(b,Origh,a,p,'centx');

ycentroid=hortrap(b,Origh,a,p,'centy');

xcentroid=rectube(ob,oh,ib,ih,'centx');

ycentroid=rectube(ob,oh,ib,ih,'centy');

It seems there are recoursive calls in all of the function to compute centroid. Also it seems you use there trapezoidal partition for integration. But I do not understand yet what is the algorithm for computing ycentroid from x = f(y) 2D discrete function samples ,how to find inverse y = f^-1(x) function from discrete samples there is no one to one mapping as in case of histogram , intergrational partition ? Thanks.