How to find the midpoint between two curves in an image

I have attached the image of the curve, I would like to extract the midpoint between the curve. (Ideally, the thickness of the given curve is constant). I tried extracting the gradient direction and using the line along the gradient direction to extract the midpoint, but the gradient direction is not perfectly tangential due to the discrete nature of the iimage

for (points in the upper line)

%get the gradient

gx=(bw(i+1,j)-bw(i-1,j))/2;

gy=(bw(i,j+1)-bw(i,j-1))/2;

theta=atan(gy/gx);

m = sin(theta); %slope of the line

%use the slope and known initial point (and assumption that thickness is constant to get a midpoint)

%issue is gradient can only take a few directions, hence getting wrong results

Wanted to know if there is any better way of doing this

Answer 1

[Akira Agata]

How abou the following?

% Load image
I = imread('https://jp.mathworks.com/matlabcentral/answers/uploaded_files/1079075/curve.PNG');

% Binarize the image
I = rgb2gray(I);
BW = imbinarize(I);

% Apply bwdist
J = bwdist(~BW);

% Find maximum position for each row
[~, pt] = max(J, [], 2);

% Create the output image
pt_ind = sub2ind(size(BW), 1:size(BW, 1), pt');
BW2 = false(size(BW));
BW2(pt_ind) = true;

% Let's check!
figure
imshowpair(BW, BW2)

[Suraj Sudhakar]

This works, but it will not work if the curve is nearing a 'U' shaped curve (I only showed an extremely simple case here)

Edit: I will accept this as an answer, if II do not get any other as it does solve my original question

[yanqi liu]

yes，sir，if we make to U shape，may be just use

I = imread('curve2.png');

I = rgb2gray(I);
BW = imbinarize(I);

J = bwdist(~BW);
BW2 = J>max(J(:))*0.8;

figure
imshowpair(BW, BW2)

[Suraj Sudhakar]

That works, thanks