I want to convert BMP image to JPEG image with different compression ratio. But I don't know the tool to compress image. I tried ImageMagick but it has no option for setting compression ratio.
Faststone image viewer (http://www.faststone.org) is a very intuitive application that does what you need and many other useful tasks. Not only you can choose the compression ratio you want but you have a real-time preview of both your image and the compressed image, side by side. You even can zoom the preview to see the artefcacts of the JPEG compression. It's freeware.
Actually, I want to compare my paper with this paper (http://www.sciencedirect.com/science/article/pii/S0920548909000580). I can compare by NC values under JPEG compression with different quality factors. However, I am not clear the relationship between quality factors and compression ratio. Is there any equation to describe this relationship??
To Ta: the way quality is related to compression ratio is known as the rate distorsion function. For a given compression algorithm, it has roughtly a "typical shape". But each image, due to its own content and complexity, has its own function that can be approximated by making some measurements. In the attached plot is the function for the Lena image compressed with JPEG.
Distorsion (or quality) is measured with PSNR while bit rate (=8 / compression_ratio for 8 bit images) is given in bit per pixel.