Unfortunately Infranview or paint.net won't be able to convert any bitmap to a vector. Although Bitmaps and vectors are "images" they are totally different from each other.
understanding the difference between bitmaps & vectors
Vector Magic Precision seems to do a pretty good job but it only allows you to do 2 free conversions and you have to sign up to download the results.
If you are looking for a program that converts bitmaps to vectors then you will proberly need a Vector based program like "Adobe illustrator", "CorelDraw" or "Serif DrawPlus" (trial versions are obtainable from the relative websites)