separate connected component in two or more regions based on certain criteria

I will start my question by presenting two images :

These are two different binarized images containing connected regions. I have marked red lines where I wish to separate the region.

my questions are

1. how can I separate the connected components into two or more isolated regions ? I want the method to be automated as I want to do this on many images.

I have some ideas on what the criterias should be for the separation to occur :

1. If the connected component contains more than a maximum amount of pixels, lets say 15 pixels, I want the region to be a canditate for splitting
2. if the region contains more than 15 pixels AND the minimum distance across the region is less than a given length then I want the region to be separated at that line defining this minimum width . I guess this is similar to saying that I want to split the region if its circularity is low, that is I do NOT want to split the largest blob in the center of both images.
3. If I cannot find this minimum width of the region I want to separate the region in two by requiring that the two resulting regions shall have the same amount of pixels.

I would be happy for advices on how to implement this into a working algorithm. Also other suggestions on splitting criteria is much appreciated.

Answer 1

[Matt J]

bwareaopen will accomplish item (1) straightforwardly. Other than that, since you haven't committed to a precise separation criteria, why not consider that in,

https://www.mathworks.com/company/newsletters/articles/the-watershed-transform-strategies-for-image-segmentation.html

Answer 2

[Image Analyst]

See Steve's blog

Watershed transform question from tech support » Watershed transform question from tech support

and

Marker-Controlled Watershed Segmentation - MATLAB & Simulink Example

The Watershed Transformation page

Do you know how to compute circularity? If not:

props = regionprops(mask, 'Area', 'Perimeter');
allAreas = [props.Area];
allPerimeters = [props.Perimeter];
circularities = allPerimeters ./ (4 * pi * allAreas);

[Image Analyst]

Also see bwferet() to get the distance across a blob at the farthest separation (widest point).