All your objects are lines, but one has a rounded shape because the ends are close together. What I'd do is to compute the areas and endpoints and see if the endpoints are farther away or closer than some ratio, like 0.2 or 0.5 or whatever. Something like (untested, off the top of my head):
keepers = [];
props = regionprops(binaryImage, 'area', 'PixelList');
for k = 1 : length(props)
thisArea = props(k).Area; % Get length of line.
x1 = props(k).PixelList(1,1); % Get endpoints.
y1 = props(k).PixelList(1,2);
x2 = props(k).PixelList(2,1);
y2 = props(k).PixelList(2,2);
separationDistance = sqrt((x2-x1)^2+(y2-y1)^2); % Compute distance.
if separationDistance < 0.5 * thisArea
% Ends are close together. Keep it.
keepers = [keepers, k];
end
end
% Get new binary image.
binaryImage = ismember(binaryImage, keepers);
Adjust the 0.5 to be smaller if you want the ends to be closer together.
Then call bwconvhull() to "fill it in" and call regionprops() again, this time asking for centroid.
binaryImage = bwconvhull(binaryImage, 'objects');
props = regionprops(binaryImage, 'Centroid', 'Area');
allAreas = [props.Area];
allCentroids = [props.Centroid];
xCentroids = allCentroids (1:2:end);
yCentroids = allCentroids (2:2:end);
