Dear Mr. Telagarapu

I don't understand (polarity change), exactly. Could you explain it?

If it means you change background and foreground to one another in both ground truth and segmented image, you're right.

If it means you change background and foreground to one another just in segmented image, first TP equals to second FN.

If it means you change background and foreground to one another just in ground truth, first TP equals to second FP.

I hope that I helped you.

At first glance and mathematically speaking, it could be correct. Unless, there is something else that we don't know it.

That what you are saying it makes seance. The TP fraction (TPF) is calculated when the expert detects a target (when a target is present), and the computerized method identifies. The FP fraction (FPF)  is calculated when the expert detects no target, and the computerized method incorrectly detects that there is a target present. The true-negative fraction (TNF) is calculated when the expert identifies no target and the computerized method identifies it as so (absent), whereas the false-negative fraction (FNF) is calculated when the expert identifies target presence, and the computerized method incorrectly identifies target absence. 

For additional details see also:

C.P. Loizou, C.S. Pattichis, M. Pantzaris, and A.N. Nicolaides, "An Integrated System for the Segmentation of Atherosclerotic Carotid Plaque", IEEE Transactions on Information Technology in Biomedicine, vol. 11, issue 6, pp. 661-667, November 2007

Can any one Provide formulas of TP,TN,FP and FN.

so that I can write matlab code.

Dear Prabhakar, you may implement all these using "union", "intersection" and "difference", functions from the morphology toolbox in matlab (i.e. add, subtract, etc). If you search in matlab help under the above you will find the appropriate functions that you may use. They are included in the morphology toolbox. You should apply the function on bw images (i.e. you should first transform the images to binary). See also explanation/s for the TPF, TNF, FPF and FNF in my above paper.

suppose I1 is the ground truth and K1 is the segmented image, then you can compute TP, TN, FN and FP using the following Equation:

TP =  I1 ∩ K1

FN = I1\ K1

FP =  K1\ I1

TN = ~I1∩ ~K1

convert your images into binary format (by considering one class in the image) then use the following Matlab code:

image=I1 & K1;

tp=sum(double(image));

image=K1 & (~I1);

fp=sum(double(image));

image=~K1 & ~I1;

tn=sum(double(image));

image=I1 & (~K1);

fn=sum(double(image));