Computational Imaging

Berthold.K. Horn

Slides (PDF, 2MB)

Turning computers into image forming devices is what "computational imaging" is about. In many fields, compute-intensive reconstruction methods produce images from raw data that exists in an encoded form. Since computing---unlike manufacture of precision physical apparatus--- is rapidly becoming faster and cheaper, it behooves us to consider systems where the emphasis is shifted towards more reliance on computing. Also, for some types of radiation, refractive and reflective elements simply are not available, so the usual optical systems methods cannot be employed. Examples of "computational imaging" systems include: 

(1) Coded Aperture Imaging. One view of coded aperture imaging is that multiple pin-holes produce an "image" convolved with a mask. The result can be de-convolved to obtain an image. But there is more---including some interesting mathematics. 

(2) Synthetic Aperture Microscopy. Optical properties of a target can be probed using finely textured illumination. Images taken with many different textures can provide enough information to reconstruct a high resolution image from many of lower resolution (in the limit, "images" obtained by a single photo cell).  

(3) Diaphanography or "Diffuse Optical Tomography". Discovering the distribution of absorption and/or scattering in a turbid medium is difficult because measurements of light transmitted from one place on the surface to another is affected not just by material along the line connecting the source and the detector, but by the diffusion of photon flux throughout the object.

(4) Exact Cone Beam Reconstruction. In the 1970's CT made the transition from parallel beam ray collection (one detector) to fan beams (linear array). New algorithms for reconstruction had to be found. Similarly, now we are in the process of going from fan beams to cone beams collected by area sensors. So far, even questions of what is the ideal "orbit" for the source remain unanswered.  


University of the Witwatersrand, B.Sc. (Eng.), Dec. 1965

MIT, S.M., June 1968

MIT, Ph.D., June 1970

See also

Significant Publications:

Winston, P.H. & B.K.P. Horn, “LISP”, Addison-Wesley, Reading, Massachusetts, 1981. Second edition 1984. Third edition 1989.

Horn, B.K.P. “Robot Vision”, MIT Press, Cambridge, Massachusetts & McGraw-Hill, New York, 1986.

Horn, B.K.P. & M.J. Brooks (eds.) “Shape from Shading”,
MIT Press, Cambridge Massachusetts, 1989.


* National Academy of Engineering - Member 2002
* American Association for Artificial Intelligence - Fellow 1990
* Rank Prize Fund - Rank Prize 1989