Fit line on an edge of datapoints area

Not the best title but I didn't know a better one.

My question, I have some datapoints of 0 and 1 and I would like to know if (probably yes) and how I can fit lines through these datapoints on the edge. For example, I have the following plot from an analitycal solution:

And I have some data from simulations that exist of 0 and 1 that looks like this with contourf:

The first one is with 21x21 datapoints, the second with 41x41 datapoints. Yellow is 1 purple is 0. In the attachment are the datapoints of the 21x21 figure. (But I'll be working with 41x41 (or more) datapoints)

Plot is made with:

xaxis = [-0.5:0.1:1.5];
yaxis = [-0.5:0.1:1.5];

figure
contourf(xaxis,yaxis,STABLE,[0 1])

How can I get a fit over the edges of 0 to 1 to create a figure like the analytical one.?

edit: I see I uploaded the data file of another simulation. The question remains the same, but the data file is not exactly the same as the pictures I posted above. I'll try to find the proper file but it isn't really necessary because I just want to know how to make a fit. The pictures and data file is just as an example.

Answer 1

[KSSV]

[c,h] = contourf(xaxis,yaxis,STABLE,[0 1]) ; 

The above gives you the points of the countour lines. SPlit them into two parts, use polyfit to fit a line.

[MM]

But then polyfit will try to fit a line through all the 0's in the datapoints or all the 1's in the datapoints right? I want to fit a line on the edge of those two area's of 0's and 1's

Answer 2

[MM]

It isn't possible what I'm trying to do?