calculate the enclosed area within an image

I have a set of experiment images and need to analyse base on that.

with image, I have to calculate the area that are enclosed, which is 1 and 2, and neglect the area of 3,4 as it touches the boundary.

So is there way find the black area that touches the boundary?

Here is what I have done so far.

I am thinking of finding a area of 3 and 4 by setting a condition and subtract them from total black area (1,2,3,4).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Area calculation%

a=imread ('rose.jpg'); % read image

b= reb2gray (a); %chagne to gray image

c= im2bw(b) % change to black and white image

total = bwarea(c)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Answer 1

[Image Analyst]

Not quite. You have to invert c and call imclearborder

regions1and2 = imclearborder(~c);
area = bwarea(regions1and2);  % or sum(regions1and2(:)) - slightly different calculation.