Find contour/edge in pcolor in Matlab

Question

I'm trying to make a contour that follows the edges of the 'pixels' in a pcolor plot in Matlab. This is probably best explained in pictures. Here is a plot of my data. There is a distinct boundary between the yellow data (data==1) and the blue data (data==0):

Note that this is a pcolor plot so each 'square' is essentially a pixel. I want to return a contour that follows the faces of the yellow data pixels, not just the edge of the yellow data.

So the output contour (green line) passes through the mid-points of the face (red dots) of the pixels.

Note that I don't want the contour to follow the centre points of the data (black dots), which would do something like this green line. This could be achieved easily with contour.

Also, if it's any help, I have a few grids which may be useful. I have the points in the middle of the pixels (obviously, as that's what I've plotted here), I also have the points on the corners, AND I have the points on the west/east faces and the north/south faces. IF you're familiar with Arakawa grids, this is an Arakawa-C grid, so I have the rho-, u-, v- and psi- points.

I've tried interpolation, interweaving grids, and a few other things but I'm not having any luck. Any help would be HUGELY appreciated and would stop me going crazy.

Cheers, Dave

EDIT:

Sorry, I simplified the images to make what I was trying to explain more obvious, but here is a larger (zoomed out) image of the region I'm trying to separate:

As you can see, it's a complex outline which heads in a "southwest" direction before wrapping around and moving back "northeast". And here is the red line that I'd like to draw, through the black points:

Answer 1

You can solve this with a couple of modifications to a solution I posted to a related question. I used a section of the sample image mask in the question for data. First, you will need to fill the holes in the mask, which you can do using imfill from the the Image Processing Toolbox:

x = 1:15;  % X coordinates for pixels
y = 1:17;  % Y coordinates for pixels
mask = imfill(data, 'holes');

Next, apply the method from my other answer to compute an ordered set of outline coordinates (positioned on the pixel corners):

% Create raw triangulation data:
[cx, cy] = meshgrid(x, y);
xTri = bsxfun(@plus, [0; 1; 1; 0], cx(mask).');
yTri = bsxfun(@plus, [0; 0; 1; 1], cy(mask).');
V = [xTri(:) yTri(:)];
F = reshape(bsxfun(@plus, [1; 2; 3; 1; 3; 4], 0:4:(4*nnz(mask)-4)), 3, []).';

% Trim triangulation data:
[V, ~, Vindex] = unique(V, 'rows');
V = V-0.5;
F = Vindex(F);

% Create triangulation and find free edge coordinates:
TR = triangulation(F, V);
freeEdges = freeBoundary(TR).';
xOutline = V(freeEdges(1, [1:end 1]), 1);  % Ordered edge x coordinates
yOutline = V(freeEdges(1, [1:end 1]), 2);  % Ordered edge y coordinates

Finally, you can get the desired coordinates at the centers of the pixel edges like so:

ex = xOutline(1:(end-1))+diff(xOutline)./2;
ey = yOutline(1:(end-1))+diff(yOutline)./2;

And here's a plot showing the results:

imagesc(x, y, data);
axis equal
set(gca, 'XLim', [0.5 0.5+size(mask, 2)], 'YLim', [0.5 0.5+size(mask, 1)]);
hold on;
plot(ex([1:end 1]), ey([1:end 1]), 'r', 'LineWidth', 2);
plot(ex, ey, 'k.', 'LineWidth', 2);

Answer 2

Take a look at the following code:

% plotting some data:
data = [0 0 0 0 0 0 1 1
    0 0 0 0 0 1 1 1
    0 0 0 0 1 1 1 1
    0 0 0 0 0 1 1 1
    0 0 0 0 1 1 1 1
    0 0 0 0 1 1 1 1
    0 0 0 0 1 1 1 1];
p = pcolor(data);
axis ij
% compute the contour
x = size(data,2)-cumsum(data,2)+1;
x = x(:,end);
y = (1:size(data,1));
% compute the edges shift
Y = get(gca,'YTick');
y_shift = (Y(2)-Y(1))/2;
% plot it:
hold on
plot(x,y+y_shift,'g','LineWidth',3,'Marker','o',...
    'MarkerFaceColor','r','MarkerEdgeColor','none')

It produces this:

Is this what you look for?

The most important lines above is:

x = size(data,2)-cumsum(data,2)+1;
x = x(:,end);

which finds the place of shifting between 0 to 1 for every row (assuming there is only one in a row).

Then, within the plot I shift y by half of the distance between two adjacent y-axis tick, so they will be placed at the center of the edge.

---

EDIT:

After some trials with this kind of data, I have got this result:

imagesc(data);
axis ij
b = bwboundaries(data.','noholes');
x = b{1}(:,1);
y = b{1}(:,2);
X = reshape(bsxfun(@plus,x,[0 -0.5 0.5]),[],1);
Y = reshape(bsxfun(@plus,y,[0 0.5 -0.5]),[],1);
k = boundary(X,Y,1);
hold on
plot(X(k),Y(k),'g','LineWidth',3,'Marker','o',...
    'MarkerFaceColor','r','MarkerEdgeColor','none')

It's not perfect, but may get you closer to what you want in a more simple approach:

Answer 3

OK, I think I've solved it... well close enough to be happy.

First I take the original data (which I call mask_rho and use this to make masks mask_u, mask_v, which is similar to mask_rho but is shifted slightly in the horizontal and vertical directions, respectively.

%make mask_u and mask_v  
for i = 2:size(mask_rho,2)
for j = 1:size(mask_rho,1)
    mask_u(j, i-1) = mask_rho(j, i) * mask_rho(j, i-1);
end
end
for i = 1:size(mask_rho,2)
for j = 2:size(mask_rho,1)
    mask_v(j-1, i) = mask_rho(j, i) * mask_rho(j-1, i);
end
end

I then make modified masks mask_u1 and mask_v1 which are the same as mask_rho but averaged with the neighbouring points in the horizontal and vertical directions, respectively.

%make mask which is shifted E/W (u) and N/S (v)
mask_u1 = (mask_rho(1:end-1,:)+mask_rho(2:end,:))/2;
mask_v1 = (mask_rho(:,1:end-1)+mask_rho(:,2:end))/2;

Then I use the difference between the masks to locate places where the masks change from 0 to 1 and 1 to 0 in the horizontal direction (in the u mask) and in the vertical direction (in the v mask).

% mask_u-mask_u1 gives the NEXT row with a change from 0-1.
diff_mask_u=logical(mask_u-mask_u1);
lon_u_bnds=lon_u.*double(diff_mask_u);
lon_u_bnds(lon_u_bnds==0)=NaN;
lat_u_bnds=lat_u.*double(diff_mask_u);
lat_u_bnds(lat_u_bnds==0)=NaN;
lon_u_bnds(isnan(lon_u_bnds))=[];
lat_u_bnds(isnan(lat_u_bnds))=[];
%now same for changes in mask_v
diff_mask_v=logical(mask_v-mask_v1);
lon_v_bnds=lon_v.*double(diff_mask_v);
lon_v_bnds(lon_v_bnds==0)=NaN;
lat_v_bnds=lat_v.*double(diff_mask_v);
lat_v_bnds(lat_v_bnds==0)=NaN;
lon_v_bnds(isnan(lon_v_bnds))=[];
lat_v_bnds(isnan(lat_v_bnds))=[];
bnd_coords_cat = [lon_u_bnds,lon_v_bnds;lat_u_bnds,lat_v_bnds]'; %make into 2 cols, many rows

And the result grabs all the coordinates at the edges of the boundary:

Now my answer goes a bit awry. If I plot the above vector as points plot(bnd_coords_cat(:,1),bnd_coords_cat(:,2),'kx' I get the above image, which is fine. However, if I join the line, as in: plot(bnd_coords_cat(:,1),bnd_coords_cat(:,2),'-' then the line jumps around, as the points aren't sorted. When I do the sort (using sort and pdist2) to sort by closest points, Matlab sometimes chooses odd points... nevertheless I figured I'd include this code as an appendix, and optional extra. Someone may know a better way to sort the output vectorbnds_coords_cat:

% now attempt to sort
[~,I]=sort([lon_u_bnds,lon_v_bnds]);
bnd_coords_inc1 = bnd_coords_cat(I,1);
bnd_coords_inc2 = bnd_coords_cat(I,2);
bnd_coords = [bnd_coords_inc1,bnd_coords_inc2];
bnd_coords_dist = pdist2(bnd_coords,bnd_coords);
bnd_coords_sort = nan(1,size(bnd_coords,1));
bnd_coords_sort(1)=1;
for ii=2:size(bnd_coords,1)
 bnd_coords_dist(:,bnd_coords_sort(ii-1)) = Inf; %don't go backwards?
 [~,closest_idx] = min(bnd_coords_dist(bnd_coords_sort(ii-1),:));
 bnd_coords_sort(ii)=closest_idx;
end
bnd_coords_final(:,1)=bnd_coords(bnd_coords_sort,1);
bnd_coords_final(:,2)=bnd_coords(bnd_coords_sort,2);

Note that the pdist2 method was suggested by a colleague and also from this SO answer, Sort coordinates points in matlab. This is the final result:

To be honest, plotting without the line is fine. So as far as I'm concerned this is close enough to be answered!