measure valley width 2d, matlab - matlab

Question

I have a 2d image, I have locations where local minimas occurs.
I want to measure the width of the valleys "leading" to those minimas.
I need either the radii of the circles or ellipses fitted to these valley.
An example attached here, dark red lines on the peaks contours is what I wish to find.
Thanks.

Answer 1

I am partially extending the answer of #Lucas.
Given a threshold t I would consider the points P_m that are below t and closer to a certain point m of minimum of your f (given a characteristic scale length r).
(You said your data are noisy; to distinguish minima and talk about wells, you need to estimate such r. In your example it can be for instance r=4, i.e. half the distance between the minima).
Then you have to consider a metric for each well region P_m, say for example
metric(P_m) = .5 * mean{ maximum vertical diameter of P_m ,
maximum horizontal diameter of P_m}.
In your picture metric(P_m) = 2 for both wells.
On the whole, in terms of pseudo-code you may consider
M := set of local minima of f
for_each(minimum m in M){
P_m += {p : d(p,m) < r and f(r)<t} % say that += is the push operation in a Stack
}
radius_of_region_around(m) = metric(P_m); %

Answer 2

I would suggest making a list of points that describe the values at the edge of your ellipse, perhaps by finding all the points where it crosses a threshold.
above = data > threshold
apply a simple edge detector
edges = EdgeDetector(above)
find coordinates of edges
[row,col] = find(edges)
Then apply this ellipse fitter http://www.mathworks.com/matlabcentral/fileexchange/3215-fitellipse

Answer 3

I'm assuming here you have access to the x, y and z data and are not processing a given JPG (or so) image. Then, you can use the function contourc to your advantage:
% plot some example function
figure(1), clf, hold on
[x,y,z] = peaks;
surf(x,y,z+10,'edgecolor', 'none')
grid on, view(44,24)
% generate contour matrix. The last entry is a 2-element vector, the last
% element of which is to ensure the right algorithm gets called (so leave
% it untouched), and the first element is your threshold.
C = contourc(x(1,:), y(:,1), z, [-4 max(z(:))+1]);
% plot the selected points
plot(C(1,2:end), C(2,2:end), 'r.')
Then use this superfast ellipse fitting tool to fit an ellipse through those points and find all the parameters of the ellipse you desire.
I suggest you read help contourc and doc contourc to find out why the above works, and what else you can use it for.