The mathematics behind image compression

As digital photos have become prolific and the quality and resolution of cell phone cameras dramatically increases, the mathematics behind image processing has become an exciting and important area of mathematical research.

Dr. Matt Demers works with students and collaborators to study fractal-based methods of image compression. The goal is to approximate a target image by using the fixed point of a fractal transform. This transform maps a parent block in an image into a smaller block, while grey-scale maps adjust the shading. Storing the fractal transform takes less space than to store the original images, so image compression is achieved!

While other methods have become more common in the field of image compression, interest and applicability of fractal imaging has continued. Dr. Demers and his students are interested in studying other applications of fractal imaging, such as reconstructing images that have been affected by missing information, the detection of visual edges of images, and the embedding of watermarks. ‘

These methods are directly applicable to many important everyday applications, including computer graphics, medical imaging, cryptography, and more. This work is ongoing and Dr. Demers is always looking for enthusiastic undergraduate students to help contribute to this field of work.

Stylistic view of camera lens

High school students interested in developing the mathematical and statistical skills to tackle a real world problem such as this should consider our Mathematical Science Major, with an Area of Emphasis in Signal Processing.

Prospective undergraduate students interested in working with Dr. Demers should visit his website, or read more about Graduate Studies at Guelph.