how can i find the biggest rectangle that fits inside a boundary in matlab

You can use the regionprops function to find the bounding box of the largest connected component in the image, which will give you the dimensions of the largest rectangle that fits inside the boundary.

Here's an example:

main.m
% Load the image
img = imread('path/to/image.png');

% Convert to binary image
bw = imbinarize(img);

% Find connected components
cc = bwconncomp(bw);

% Get region properties (bounding boxes)
props = regionprops(cc, 'BoundingBox');

% Find index of largest bounding box
boxes = cat(1, props.BoundingBox);
area = boxes(:,3) .* boxes(:,4);
[~, largestIdx] = max(area);

% Get dimensions of largest bounding box
largestBox = boxes(largestIdx, :);
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The largestBox variable contains the [x y width height] dimensions of the largest rectangle that fits inside the boundary.

Note that the boundary must be a closed curve in the image, otherwise you'll get an error when using bwconncomp. You may need to preprocess the image to ensure that the boundary is closed before running this code.