MATLAB Image Processing - Find Edge and Area of Image

Question

As a preface: this is my first question - I've tried my best to make it as clear as possible, but I apologise if it doesn't meet the required standards.

As part of a summer project, I am taking time-lapse images of an internal melt figure growing inside a crystal of ice. For each of these images I would like to measure the perimeter of, and area enclosed by the figure formed. Linked below is an example of one of my images:

The method that I'm trying to use is the following:

1. Load image, crop, and convert to grayscale
2. Process to reduce noise
3. Find edge/perimeter
4. Attempt to join edges
5. Fill perimeter with white
6. Measure Area and Perimeter using regionprops

This is the code that I am using:

clear; close all;

% load image and convert to grayscale
tyrgb = imread('TyndallTest.jpg');
ty    = rgb2gray(tyrgb);
figure; imshow(ty)

% apply a weiner filter to remove noise.
% N is a measure of the window size for detecting coherent features
N=20;
tywf  = wiener2(ty,[N,N]);
tywf = tywf(N:end-N,N:end-N);

% rescale the image adaptively to enhance contrast without enhancing noise
tywfb = adapthisteq(tywf);

% apply a canny edge detection
tyedb = edge(tywfb,'canny');

%join edges
diskEnt1 = strel('disk',8); % radius of 4
tyjoin1 = imclose(tyedb,diskEnt1);
figure; imshow(tyjoin1)

It is at this stage that I am struggling. The edges do not quite join, no matter how much I play around with the morphological structuring element. Perhaps there is a better way to complete the edges? Linked is an example of the figure this code outputs:

The reason that I am trying to join the edges is so that I can fill the perimeter with white pixels and then use regionprops to output the area. I have tried using the imfill command, but cannot seem to fill the outline as there are a large number of dark regions to be filled within the perimeter.

Is there a better way to get the area of one of these melt figures that is more appropriate in this case?

As background research: I can make this method work for a simple image consisting of a black circle on a white background using the below code. However I don't know how edit it to handle more complex images with edges that are less well defined.

clear all
close all
clc

%% Read in RGB image from directory
RGB1 = imread('1.jpg')   ;

%% Convert RPG image to grayscale image
I1 = rgb2gray(RGB1)       ;

%% Transform Image
%CROP
IC1 = imcrop(I1,[74 43 278 285]);

%BINARY IMAGE 
BW1 = im2bw(IC1); %Convert to binary image so the boundary can be traced

%FIND PERIMETER
BWP1 = bwperim(BW1); 
%Traces perimeters of objects & colours them white (1). 
%Sets all other pixels to black (0)
%Doing the same job as an edge detection algorithm?

%FILL PERIMETER WITH WHITE IN ORDER TO MEASURE AREA AND PERIMETER
BWF1 = imfill(BWP1); %This opens  figure and allows you to select the areas to fill with white.

%MEASURE PERIMETER
D1 = regionprops(BWF1, 'area', 'perimeter'); 
%Returns an array containing the properties area and perimeter. 
%D1(1) returns the perimeter of the box and an area value identical to that
%perimeter? The box must be  bounded by a perimeter.
%D1(2) returns the perimeter and area of the section filled in BWF1

%% Display Area and Perimeter data
D1(2)

Answer 1

I think you might have room to improve the effect of edge detection in addition to the morphological transformations, for instance the following resulted in what appeared to me a relatively satisfactory perimeter.

tyedb = edge(tywfb,'sobel',0.012);

%join edges

diskEnt1 = strel('disk',7); % radius of 4
tyjoin1 = imclose(tyedb,diskEnt1);

In addition I used bwfill interactively to fill in most of the interior. It should be possible to fill the interior programatically but I did not pursue this.

% interactively fill internal regions

[ny nx] = size(tyjoin1);
figure; imshow(tyjoin1)
tyjoin2=tyjoin1;
titl = sprintf('click on a region to fill\nclick outside window to stop...')
while 1
   pts=ginput(1)
   tyjoin2 = bwfill(tyjoin2,pts(1,1),pts(1,2),8);
   imshow(tyjoin2)
   title(titl)
   if (pts(1,1)<1 | pts(1,1)>nx | pts(1,2)<1 | pts(1,2)>ny), break, end
end

This was the result I obtained

The "fractal" properties of the perimeter may be of importance to you however. Perhaps you want to retain the folds in your shape.