It seems like the OP isn't looking for something that uses a grayscale image as a displacement map on a highly subdivided plane (which any decent 3D software should be able to do), but take a 2-tone black and white image and use that to extrude a shape into 3D. And while the former method can be used to approximate the latter, the difference is that creating a high density lattice will use a ton of unnecessary polygons, and the end result will never be entirely smooth.
Probably the best method for this is to use photoshop to create a selection and convert it to a path. Here's a tutorial on exactly how that works:
http://www.photoshop-plus.co.uk/2011/05/24/converting-a-selection-into-a-path/Then import the paths into any 3D software. I use Lightwave, but I'm pretty sure any 3D app worth it's salt (including Blender, which is free), should be able to import illustrator paths as a curve or polygon, and then use the 3D software to extrude that flat shape along it's normal to give it height.