Detect and remove T/Y joints in a binary image

I have a binary image and I want to detect and remove all pixels with >2 pixels connected to them (e.g. Y and T joints). The image is produced by thinning of the image and all lines have a thickness of 1 pixel. Below is a sample image. My first guess was to check connectivity for all pixels but since I have hundreds of these objects in each image, this approach would be too expensive. Thanks,

[Walter Roberson]

Should the result be to break the Y/T into three line segments?

[Ramin Dastanpour]

Yes, exactly. But I need to get the index of the pixel on the joint as well. After breaking the joint I want to reconnect the disconnected objects which are in one direction (more).

Answer 1

[Walter Roberson]

NewImage = BWimage;
NewImage( (conv2(0+BWImage,[1 1 1;1 0 1;1 1 1],'same') .* BWimage) > 2 ) = 0;

[Walter Roberson]

With index:

NewImage = BWImage;
idxmask = (conv2(0+BWImage,[1 1 1;1 0 1;1 1 1],'same') .* BWimage) > 2;
NewImage(idxmask) = 0;
idx = find(idxmask);