help with image processing

I have a sequence of images whose area properties I wish to obtain. For this, I have to find the envelope of the object. In the 'samples.jpg' image attached here, we can see on the left column 4 grayscale images and on the right column the corresponding binary images. However, this almost gives me the area I need but not exactly. The area actually desired is that highlighted in the blue boundary, drawn by hand, in 'required.jpg'. I have provided 'L10_T1_A0.zip' which contain more such samples.

This is what I have been doing to get the area (more importantly the B/W binary image of the required shape). How can I get a better 'Ioppened' image?

half_Imr --> is the grayscale image on the left column of 'samples.jpg'

Iopenned --> is the binary image on the right column of 'samples.jpg'

get_area_from_image --> another custom function to get the area using 'regionprops' MATLAB function

level    = 0.3;  
I_BW  = imbinarize(half_Imr,level); %binary image seen on right column of 'samples.jpg'

morph_rect = [4 39];
Ifill      = imfill(I_BW,'holes');
se         = strel('rectangle',morph_rect);
Iopenned   = imopen(Ifill,se); 

% evaluating area swept by ribbon
pixel2mm = 19/60;                                  % Calibration from pixel to mm
Aimage   = get_area_from_image(Iopenned, pixel2mm);
----------------------------------------------------------------------------------
function Aimage = get_area_from_image(Iopenned, pixels2mm)
%%This function gives the area

Iregion_temp = regionprops(Iopenned, 'Area');
[sz,~]       = size(Iregion_temp);
temp         = struct2cell(Iregion_temp);
temp1        = cell2mat(temp);

if sz > 1 %multiple clusters of white area in image giving multiple areas
    Aimm2 = max(temp1 );
elseif isempty(temp1) == 0
    Aimm2 = temp1 ;
else
    Aimm2 = 0;
end

Aimm2   = Aimm2*pixels2mm^2;
Aimage  = Aimm2*1e-6; %m^2

end