Restrict regionprops ellipse fitting algorithm to include only the binary objects

I have a binary image with complex object shapes. I am using regionprops to fit ellipses to the white zones (1s). I have attached the results of regionprops. However, regionprops is including a lot of the binary objects' background when fitting the ellipses. How do I restrict regionprops to only fit ellipses to the white parts of the image (1s) and not include any, or include as little as possible, parts of the blue region (0s)?