Each image pulls out different features of the original, which is the sum of the three. The images were provided by Ronald Coifman of Yale University . Indeed, mathematics is an essential element of imaging in these and many other settings. Medicine benefits from the techniques of tomography, including cutting-edge ideas like electrical impedance tomography that may greatly improve the detection of cancerous tumors, and MRI, where level set and marching methods can be used in the extraction of images of beating hearts.
Computer imaging depends on a whole range of mathematical tools.
Without proper illumination, the images created by computer graphics would appear flat and artificial rather than realistic and visually pleasing. Storing computer images is another challenge. Familiar references like Microsoft's Encarta encyclopedia and its 7000 color images fit on a single CD-ROM because of fractal image compression techniques. Image compression is also one of the essential tools of space exploration. Compression routinely increases the effective transmission rate of image data by a factor of 15 or 20.