%// Read in image and convert to a binary one
im = imread('Line.jpg');
bw = im2bw(im);

%// There seems to be a thin white boundary across the image, make it false(black)
bw1 = false(size(bw));
bw1(5:end-5,5:end-5) = bw(5:end-5,5:end-5);

bw1(biggest_blob(bw1)) = 0; %// remove biggest blob (bottom left corner one)

SE = strel('disk', 11, 8); %// structuring element for dilation
bw2 = imdilate(bw1,SE); %// dilate the image
bw3 = bwmorph(bw2,'thin',Inf); %// thin it
out = biggest_blob(bw3); %// out of many thinned lines, select the biggest one

function out = biggest_blob(BW)

%// Find and labels blobs in the binary image BW
[L, num] = bwlabel(BW, 8);

%// Count of pixels in each blob, basically this should give the area of each blob
counts = sum(bsxfun(@eq,L(:),1:num));

%// Get the label(ind) cooresponding to blob with the maximum area
%// which would be the biggest blob
[~,ind] = max(counts);

%// Get only the logical mask of the biggest blob by comparing all labels
%// to the label(ind) of the biggest blob
out = (L==ind);

return;