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Image Analyst
on 29 Nov 2013

Image Analyst
on 30 Nov 2013

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Roger Stafford
on 29 Nov 2013

Edited: Roger Stafford
on 29 Nov 2013

Chitresh, I can tell you what kind of mathematical problem your expression is a solution to. Let us have n x and y pairs

x = [x1,x2,x3,...,xn]

y = [y1,y2,y3,...,yn]

and suppose we want to find the line of regression through them - that is, to find constants a and b such that

sum((a*x+b-y).^2)

is a minimum. This is a least squares problem and the solution for the constant b is

b = (sum(x.^2)*sum(y)-sum(x)*sum(x.*y))/(n*sum(x.^2)-sum(x)^2)

which is precisely your expression.

I can only guess how this might apply to the fingerprint image you display. If the xi and yi pairs refer to pixel coordinates of the black areas, and if the coordinate origin is at the lower left corner of the image, then b would be the vertical distance above the bottom at the left side where the line of regression crosses. On the other hand if the origin is located in the center of the image, b would be the vertical distance above or below this origin where the regression line crosses a vertical line through that origin. I would have thought the expression for a would have at least as much significance in the image as with b, since it would give the slope of that line of regression.

There are probably several other possible meanings that the x and y pairs might possess with regard to the image. I think that is a puzzle you will have to crack. Note that when you do solve your puzzle, the above expression shows you how to implement it in matlab in one line.

Image Analyst
on 30 Nov 2013

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