javax.jai.media.PlanarImage is a java.awt.image.RenderedImage - so you can get its Raster object, and from that you have access to its pixel data. So:
How can I determine whether the image is black-and-white ?
An image is B&W if all its pixels are either black or white, which means their individual R, G and B components all have values of 0, or all have values of 255.
How can I determine if the image is in TIFF format ?
TIFF is a file format, but a PlanarImage is an in-memory representation, so this question does not apply.
How can I convert an image to TIFF format if it is not ?
I generally use the javax.imageio.ImageIO class to load and store images. It doesn't support TIFF out of the box, but can be made to do so easily. Search for the
JAI-ImageIO package. I'm not sure where binary builds can be found, since the screwed-up move from java.net to the Kenai infrastructure lots of projects there are broken.
How can I convert an image to black-and-white if it is not ?
Devise an algorithm that reads all pixel values and -based on their R, G and B components- decides whether each pixel should be black or white.
You'll have to do some reading and learning about image processing before you're ready to tackle these, if you have never done any of this.
Also, in the long term, I advise to move away from JAI; it's been dead for years now.