S-114.4220 Research Seminar on Computational Science
The topic of the course in 2008 spring (period IV) is
Stochastic Models in Spatial and Image Analysis (3 p) L V
The topic will cover, e.g.,
- Connection between image analysis and spatial modeling (kriging)
- Connection between Gaussian processes, Wiener-filters,
Gaussian Markov Random fields, other Markov and non-Markov
hidden and non-hidden random fields, and wavelet analysis.
- Wiener filter and its connection to Gaussian process
regression and Kalman filters and RTS smoothers.
- FFT and FIR approximations to speed up Wiener filters and
- Image compression, e.g., wavelet-based compression in JPEG2000
- T. F. Chan, J. Shen (2005): Image Processing and Analysis:
Variational, PDE, Wavelet and Stochastic Methods
- B. Finkenstädt, L. Held, V. Isham (2006): Statistical Methods for
- M.A.R. Ferreire, H.K.H. Lee (2007): Multiscale Modeling - A
- Lim (1989): Two-Dimensional Signal and Image Processing
- Gonzalez and Woods (2002): Digital Image Processing
- Christakos (1992): Random Field Models in Earth Sciences
- H. L. Van Trees (1968): Detection, Estimation, and Modulation Theory Part I
- Dr.Tech. Simo Särkkä,
Docent, Dr.Tech. Aki Vehtari
Basics of Bayesian inference and matrix algebra. Basic knowledge
or ability to learn to use Matlab is needed for completing the
- Place and time
The seminars take place on Wednesdays at 14:15 in Innopoli 2, B317
(the seminar room of Laboratory of computational engineering, see
First lecture is 26.3. 14:15.
- Course Registration
- Please register for the course by sending email to
Remember to mention the student id. If you have an suggestion
for the topic of your presentation, you may mention it in the
English if at least one English speaking participant.
| Date || Talker || Subject
| 26.3. || Simo Särkkä
Overview of Image Analysis Methods and the Wiener Filter
| 2.4. || Aki Vehtari
Introduction to Gaussian Process Regression
| 9.4. ||
| 16.4. || Jouni Hartikainen
| 23.4. || Mats Sjöberg
Markov Random Fields
| 30.4. ||
| 7.5. || Janne Ojanen
| 14.5. || Aki Havulinna ||
Variational and PDE Methods
In every seminar talk, there is the author who writes a 2-4 page
summary paper about the subject and gives the talk, and an opponent,
whose task is to make questions and stimulate discussion after the
presentation. Every student is the author for (at least) one talk
and the opponent for another talk. The author should send the
summary paper to the opponent and to the teachers on the
monday preceding the presentation day. The slides should
be sent to the teacher latest on the day preceding the
presentation. The opponent prepares at least 2-3 questions about
the topic to stimulate discussion after the talk. Normal talk is
In the computer exercise, you should apply Wiener filter, median
filter and a freely chosen third method for removing different kinds
of noises and degradations from image and compare the results. The
exercise report should be returned in PDF format to the e-mail address
later than 16.6.2008.
You can choose any gray scale test image you want. One possible choice
is the use the classical Lena (Lenna) image, whose story can be found
Gray scale versions of the image can be found by typing "lenna image"
into the google. With the image, you should do the following:
- Generate a noisy image by adding additive Gaussian noise with
a given covariance function to the image and another image by adding
salt-and-pepper shot noise to the image.
- By investigating the covariance function of the original image,
choose couple of candidate covariance functions to be used in the
Wiener filter. Also compute the Fourier transforms of the covariance
functions that you have chosen.
- Design Wiener filters, which correspond to the choices of
covariance functions, and which can be used for removing the
noises from the images. Implement the filters in Matlab using FFT2
algorithm. Remember to take into account and eliminate the usual
border effects caused by the circular convolution of FFT
- Compare the results of the Wiener filters and median filter
(medfilt2 in Matlab)
with both types of noise in images.
- Compare the noise removal results to some freely chosen
alternative method. You can, for example, use a Wavelet based method,
variational method, stochastic relaxation or some other method that
you find appropriate.
- Construct a convolution filter, which approximates a simple motion
blur of the image. Using one of the covariance functions above,
a Wiener filter for removing the motion blur and noise from the image.
Test the performance of the filter in Matlab.
- How long does the filtering operation take and what is the
computational complexity of the Wiener filter with respect to the size
of the image? If the direct Gaussian process regression equations were
used in the computation, approximately how long would the computations
take and what would be the computational complexity in this case?
When sending email concerning the course, please add "S-114.4220" or
"1144220" to subject.
Dr.Tech. Simo Särkkä
Docent, Dr.Tech. Aki Vehtari
Test sivusta vastaa
Sivua on viimeksi päivitetty 14.5.2008