ESE 559 - Digital Image Processing II (Bayesian Image Processing)

Annotated Bibliography of Reference Books and Articles

Assorted math background topics, mostly related to linear algebra, will be reviewed. My favorite linear algebra book is the one by Strang [Stra80]. He has a later 3rd edition of this same book which has a nice appendix on SVD. Strang also wrote an excellent book on applied math [Stra86] that covers a variety of relevant topics. In general, Strang is great for insightful introductions to topics, but if one wants some great detail, then one must often resort to a more specialized book. One such book for linear algebra is the well known Matrix Computations by Golub and Van Loan [GoluV89].

Traditional image processing texts usually cover a wide variety of topics using a wide variety of mathematical models. In my opinion, some of the material in these books is pretty good despite the age of the books. The traditional field of image restoration, for example, is well covered, though the treatment of image analysis topics tends to be a bit moldy in these books. One famous book is the two-volume series by Rosenfeld and Kak [RoseK82a,RoseK82b], and another is the one by Pratt [Prat78]. (Pratt has a more recent edition though. Look it up.)

The book by Li [Li95], includes a collection of MRF formalisms and applied mathematical techniques used in various applications in computer vision. Much of it seems to focus on his own work, and other parts of it constitute a sort of encyclopaedic survey, but it may serve as a good reference in the MRF area.

The recent book by Ruanaidh and Fitzgerald [RuanF96] is really focussed on signal processing and not image processing, but the first four chapters are, in my opinion, a clear and accessible introduction to those aspects of Bayesian Inference, numerical methods, and MCMC, that are relevant to this course.

For a more detailed and formal mathematical treatment of MCMC topics with an Image Analysis flavor see the recent book by Winkler [Wink95]. The volume edited by Chellappa and Jain [ChelJ93], contains many MRF chapters of interest to us, including ones dealing with annealing methods, and medical imaging and other image processing application. (See especially the brilliant article by Rangarajan.)

1. [Stra80] G.~Strang, Linear Algebra and Its Applications, 2nd ed., Academic Press, New York, 1980.

2. [Stra86] G.~Strang, Introduction to Applied Mathematics, Wellesley-Cambridge Press, New York, 1986.

3. [GoluV89] G.~Golub and C.~Van Loan, Matrix Computations - 2nd Ed., Johns Hopkins University Press, Baltimore, 1986.

4. [RoseK82a] A.~Rosenfeld and A.~C. Kak, Digital Picture Processing, volume~1, Academic Press, New York, NY, 1982.

5. [RoseK82b] A.~Rosenfeld and A.~C. Kak, Digital Picture Processing, volume~2, Academic Press, New York, NY, 1982.

6. [Prat78] W.~Pratt, Digital Image Processing, John Wiley and Sons, New York, NY, 1978.

7. [Li95] S.~Z. Li, Markov Random Field Modeling in Computer Vision, Artificial Intelligence, Springer-Verlag, Tokyo, 1995.

8. [RuanF96] J.~Ruanaidh and W.~Fitzgerald, Numerical Bayesian Methods Applied to Signal Processing, Statistics and Computing, Springer, New York, 1996.

9. [Wink95] G.~Winkler, Image Analysis, Random Fields and Dynamic Monte Carlo Methods, Applications of Mathematics, Springer, Berlin, 1995.

10. [ChelJ93] R.~Chellapa and A.~Jain, Markov Random Fields: Theory and Application, Academic Press, Boston, 1993.

11. [LeeRG95a] S. J. Lee and A. Rangarajan and G. R. Gindi, Bayesian Image Reconstruction in SPECT Using Higher Order Mechanical Models as Priors, IEEE Transactions on Medical Imaging ,pp669--680,vol. 14, 1995.

12. [Chan95] M. T. Chan, Bayesian Image Reconstruction Using Image-Modeling Gibbs Priors, University of Pennsylvania, Philadelphia, PA,1995.

13. [Gool90] T. A. Gooley, Quantitative Comparisons of Statistical Methods in Image Reconstruction, University of Arizona,Tucson, AZ, 1990.

14. [ZhouL95] Z. Zhou and R. Leahy, Approximate Maximum Likelihood Parameter Estimation for Gibbs Priors, Signal and Image Processing Institute, University of Southern California, TR-285, June 1995.

15. [BlakZ87] A. Blake and A. Zisserman, Visual Reconstruction, MIT Press,Cambridge, MA, 1987.