Plotting where two arrays meet

Hi there,

I am hoping to create an array that can be plotted. This array should just simply show the 2D parabola created where two arrays meet. For instance, I have two arrays: z and zpaper. These two arrays meet at a certain spot in space and create sort of a parabola at their intersection. I would like to create an array that just holds these values so the information can be analyzed as a 2D plot. Considering the code, I ran it for two images, so zpaper is for 1 image, whereas z is for the other. This was not coded in, I simply changed the variable name z to zpaper after running the first image and after running the second image, I left the variable as z. Here is the code:

raw_image = imread(filename)';


figure() 
mesh(raw_image)
avg = sum(sum(raw_image))/nnz(raw_image);
M1 = raw_image < avg;
[y1,x1] = ndgrid(1:size(M1, 1), 1:size(M1, 2));
centroid = mean([x1(M1),y1(M1)]);
x1 = nnz(M1(floor(centroid(1)),:));
y1 = nnz(M1(:,floor(centroid(2))));
avg = mean(mean(raw_image(centroid(1)-x1/2:centroid(1)+x1/2,centroid(2)-y1/2:centroid(2)+y1/2)));
std = std2(raw_image(centroid(1)-x1/2:centroid(1)+x1/2,centroid(2)-y1/2:centroid(2)+y1/2));
var = std.^2;

threshold = avg + 2.3*std;
M = raw_image < threshold;
raw_image = raw_image.*uint8(M);

figure()
mesh(raw_image)

figure()
imshow(raw_image*5)


fractionofdisc = 0.1:.01:1.0;
ny = length(fractionofdisc);

mult = double(prctile(raw_image(raw_image ~= 0),[5 95], 'all'));
multiplier = linspace(mult(1),mult(2),ny);
nx = length(multiplier);


if nx ~= ny
    error('In house error. The length of the multiplier and fraction of disc must be the same!')
end

[X,Y] = meshgrid(fractionofdisc, multiplier);

z = zeros(nx,ny);
for i = 1 : ny
    y = fractionofdisc(i);
    for k = 1 : nx
        x = multiplier(k); % have to create a variable for the x axis of plot
        %n = mean(mean(raw_image(raw_image ~= 0)))*x; % changing data type may not be necessary
        Mp2 = raw_image > x;
        sum_Mp2 = sum(Mp2);
        sum_sum_Mp2 = sum(sum_Mp2); % algorithm stops at a fraction of this number
        
        
        cumsum = 0;
    
        % While loop needed to sweep across the x values until it reaches
        % cumsum
        while cumsum < y*sum_sum_Mp2
            z(i,k) = z(i,k) + 1;      % column index
            cumsum = cumsum + sum_Mp2(z(i,k));
            
        end
    end
end


figure()
mesh(X,Y,z,'edgecolor','r')
hold on
mesh(X,Y,zpaper,'edgecolor','b')
hold off

% equal = zpaper == z;
equal = ismembertol(zpaper,z);%,'DataScale',0);
figure()
mesh(equal)

At the bottom here, I was attempting to see if I could grab the places where the two arrays met and maybe with a tolerance to create a curve without jumps. The figures in question as well as the raw images are attached.

Thank you ahead of time!!