How can I deform the boundary of a 2D shape with two layers in order to achieve a smooth transition between pixels, and generate different shapes in a randomized process?

I want to generate a 2D shape with two layers. To accomplish this, I have created a 2D matrix.

img = 10 * ones(100,100);

img(1:10,:) = 5;

Currently, the boundary of the layers is a straight line, but I intend to deform the boundary to achieve a shape for example similar to the one shown in the picture.

My current approach involves generating random integer numbers to select specific pixels and then using a loop to modify the values of those pixels. However, this approach presents two challenges.

Firstly, the random numbers can lead to significant fluctuations in the value changes between adjacent pixels. I aim to achieve a smooth transition instead.

Secondly, I intend to repeat this process 1000 times, each time obtaining a different shape. I am trying to figure out how to introduce randomness into this process.

Any guidance on addressing these issues would be greatly appreciated.

Answer 1

[Udit06]

Hi,

You can approach the problem as follows:

Step 1: Create a line using sum of m sine and n cosine functions. An example using one sine function and one cosine function is shown below.

% Define image size
width = 1000;
height = 1000;

% Create a white background image
image = ones(height, width, 3);

% Define the height of the superposition from the bottom
h = 200;

% Generate x-coordinates for the image
x = 1:width;

% Calculate the y-coordinates for the sine and cosine functions
scale = 300; % Scaling factor for the functions
y_sine = h + scale * sin(x / scale); % Scaled sine function
y_cosine = h + scale * cos(x / scale); % Scaled cosine function

y= y_sine + 0.6*y_cosine;

% Set the color of the superposition to black
color = [0, 0, 0];

% Draw the superposition on the image
for i = 1:width
    image(round(y(i)), i, :) = color;
end

% Display the image
imshow(image);

Step 2: Now color each pixel according to which region (upper or bottom) they belong to.

% Define image size
width = 1000;
height = 1000;

% Create a white background image
image = ones(height, width, 3);

% Define the height of the superposition from the bottom
h = 200;

% Generate x-coordinates for the image
x = 1:width;

% Calculate the y-coordinates for the sine and cosine functions
scale = 300; % Scaling factor for the functions
y_sine = h + scale * sin(x / scale); % Scaled sine function
y_cosine = h + scale * cos(x / scale); % Scaled cosine function

y = y_sine + 0.6 * y_cosine;

% Set the color of the superposition to black
color_above = [0, 0, 1]; % Blue color for above the line
color_below = [1, 0, 0]; % Red color for below the line

% Draw the superposition on the image
for i = 1:width
    for j = 1:height
        if j <= round(y(i))
            image(j, i, :) = color_below; % Set color below the line
        else
            image(j, i, :) = color_above; % Set color above the line
        end
    end
end

% Display the image
imshow(image);

To introduce randomness, you can tweak the following:

1. Number of sine and cosine function
2. Variable h in the above code to adjust the height from top and bottom.
3. The frequency of sine and cosine functions
4. Scaling factor

I hope this helps.