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you could iterate over the white pixels only using findNonZero() , but this has the downside, that you have to check boundaries for each and every pixel, so imho, Brute Force does as well:

// let's collect "interesting points", 
// if there's only one neighbour, it's an endpoint, 
// if it has 3, it's a bifurcation(or T-junction), 
// 4 neighbours denote an X-like crossing.
vector<Point> one, three, four;

// let's use Mat_<T> for easy (y,x) access (also, [0..1] range): 
Mat_<uchar> bin = your_binary_img / 255;

// since we're checking 1 pixel neighbourhood, 
// we need to spare 1 pixel border on each side: 
for (int r=1; r<bin.rows-1; r++) {
    for (int c=1; c<bin.cols-1; c++) {
        uchar cen = bin(r,c);
        if (cen==0) continue; // background
        // now we just walk in a circle around the center pixel, 
        // and collect neighbours(starting top-left):    
        int neighbours = bin(r-1,c-1) + bin(r-1,c) + bin(r-1,c+1)
                       + bin(r,  c-1)              + bin(r,  c+1)
                       + bin(r+1,c-1) + bin(r+1,c) + bin(r+1,c+1);
        if (neighbours==1) one.push_back(Point(c,r));
        if (neighbours==3) three.push_back(Point(c,r));
        if (neighbours==4) four.push_back(Point(c,r));
    }
}