If regionprops is finding the objects correctly, then you can also ask it for the 'Eccentricity' property. It will be 0 for a perfect circle and 1 for a straight line. I'm getting a surprisingly high value of 0.69 for the left-most object in your example image, so it may take a little trial and error to set a threshold value that separates dots from lines.
Small objects may cause problems, so you might throw in some additional constraints. For example, perhaps the 'MajorAxisLength' has to be greater than a certain value for the object to be considered a line.
If your binary image came from thresholding grayscale values, you could also do your own center of mass analysis for each region, using the intensity of each pixel as the mass of a corresponding point particle. If the objects are on a quiet dark background, you could dilate each BW region a bit before using it to mask the grayscale image, to make sure you've covered the entire object.
