TMS016 / MSA301 Spatial statistics and image analysis Spring 26
This page contains the program of the course. Other information, such as learning outcomes, teachers, literature and examination, can be found in a separate course PM.
Program
Literature
We have the following books and acronyms:
- MvL: Theory of Spatial Statistics: A Concise Introduction, M.N.M. van Lieshout (found here)
- BC: Foundations of Computational Imaging: A Model-Based Approach, C. A. Bouman (found here)
- LN: Lecture notes Statistics of Imaging, M. Rudemo (found here)
Other relevant literature (which might be used in the course):
- HS: Handbook of spatial statistics, Gelfand, Diggle, Guttorp & Fuentes (found here)
- EL: The Elements of Statistical Learning, Hastie, Tibshirani & Friedman (found here)
- GH: Image Analysis for the Biological Sciences, Glasbey & Horgan (found here)
Note that all literature is freely available via the Chalmers library for registered students.
If you want to recap some basic probability and statistics notions, you may e.g. consult Section 2 and 3 of the book by Bouman (BC).
Some comments from the mid-meeting (27 April)
- The overall impression of the course seems good so far.
- The lectures would benefit from more visual exemplifications/illustrations.
- The discrepancy between the lectures (overview) and the exercise material (mathemtically technical) tends to be a bit large.
Concerning the image analysis conent of the course: it will appear towards the end of the course.
Examination and projects
The examination consists of two parts:
- A group-based project assignment. Grade: Pass/Fail.
- A written exam on June 3 2026, 14:00-18:00. Allowed exam aids: Chalmers approved calculator. Final grade (Chalmers: U-3-4-5; GU: U-G-VG): 3/G: 20 p, 4: 30 p , 5: 40 p, VG: 37.5 p, max: 50 p.
To pass the course, a student has to pass both the project part and the written exam. The final grade (Chalmers: U-3-4-5; GU: U-G-VG) on the course is based on the exam, which is individual.
The deadlines for the projects can be found at the end of this page under Course summary. All assignments should be uploaded under Canvas/Assignments.
The exact dates, times and places for the (re)exams can be found on the student portal.
Old exams can be found here. However, as the structure of the course has changed quite a bit with respect to last year, we have created a list of mock exam questions which should provide you with extra practice as well as an indication of the flavour of (parts of) the exam. The mock exam questions can be found here.
Project details:
The project work is done in groups of 1-3 students - please create a project group as early as possible (go to People and then to Project groups to find the groups). Once you have decided who to be in a group with, make sure that each group member goes to People and then to Project groups to register into the appropriate group slot. If you can not find anybody to be in a group with, please reach out to other people who you see have not yet been registered to a group or to people who are in a group which you see is not yet full - if you are unsuccessful in this endeavour, please reach out to Ottmar and Mathis as soon as possible so that they can help you to find a group to join.
The project involves that the group has to i) hand in a project report and ii) given an oral presentation of the project. The project has got a slightly new focus compared to previous years.
Each group selects any paper from the journal Spatial Statistics, which you can access via https://www.sciencedirect.com/journal/spatial-statistics (once you are logged in to the Chalmers library). Once you have reached the journal homepage, make searches based on different keywords which interest you (as a group), e.g. geostatistics, random field, point pattern, point process, Gibbs/Markov random field/state, disease mapping, image analysis, etc.
- The choice of paper has to be reported as a Canvas assignment (intended as a check from the course instructors). The deadline for this is deliberately set to after we have covered all the chapters 1-4 in van Lieshout's book.
- The group then reads the selected paper in detail and writes a summary/report on it, which needs to be handed in as a Canvas assignment towards the end of the course (the exact deadline will be found under the appropriate Canvas assignment). NOTE: The report should be minimum 5 and maximum 10 pages.
- Each group must also give an oral presentation of its selected paper summary/report; the oral presentation should be planned for 15 minutes. After the presentation, each group gets asked questions for approximately 5 minutes; the course instructors will direct individual questions to the group members.
In summary, the workflow for a student to pass this part of the course, i.e. the project, is that the student: 1) reads and understands the group’s paper, 2) takes part in writing the report, 3) has the group submit the report through Canvas, 4) takes part in putting together and preparing the group’s oral presentation, 5) carries out the oral presentation together with the group members, 6) answers questions directed to the student.
To book a time for your group's project presentation, go to https://choodle.portal.chalmers.se/zpM8xQzOZZMr96dj. Choose only one slot per group - if too many groups choose the same slot, we will have to move some groups to other days. Provide both the group number and the names of the group members, e.g. "Group 99 (Name 1, Name 2 & Namee 3)".
Deadline: 19 May, 15:00!!!
Presentation length:
- Groups with 1 member get 10 minutes to present + 5 minutes for questions.
- Groups with 2 members get 15 minutes to present + 5 minutes for questions.
- Groups with 3 members get 20 minutes to present + 5 minutes for questions.
Lectures and Exercises
The schedule of the course is in TimeEdit.
The course typically has two lectures and two computer exercises each week. Details for these are given in the schedule below, which will be updated during the course. For each lecture, the chapters covered in the books will be listed.
The lectures will be given in Euler.
Teachers of the course are Ottmar Cronie (lectures, examiner), ottmar@chalmers.se, and Mathis Rost (lectures, exercises/labs), mathisr@chalmers.se. Lecture notes of the lectures can be found in Files/Lecture notes.
The information below will be updated and extended on an ongoing basis.
| Date | Weekday | Time | Room | Teacher | Content | |
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| Week 13 |
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| March 23 | Monday | 8:00-9:45 | Euler | L1 | Ottmar |
Introduction MvL: Section 1, 2.1 Lecture notes: L1.pdf |
| Monday | 13:15-15:00 | MVF24 and MVF25 | E1 | Ottmar |
Exercise sheet 1: E1.pdf Matlab files: TMS016_Lab1B.zip
Exercise sheet solution: Lab1_solutions.pdf |
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| March 25 | Wednesday | 10:00-11:45 | Euler | L2 | Ottmar |
Gaussian random fields, different notions of stationarity and isotropy. MvL: Section 2.2, 2.3 LN: Section 5.1, 5.2 Lecture notes: L2.pdf |
| Wednesday | 13:15-15:00 | Online (MVF24 and MVF25) | E2 | Mathis |
Link for Zoom: Join from PC, Mac, Linux, iOS or Android: https://chalmers.zoom.us/j/63497363318
Exercise sheet solution: Lab1_solutions.pdf
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| Week 14 |
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| March 30 | Monday | 8:00-9:45 | Euler | L3 |
Ottmar |
Construction of covariance functions, intrinsic stationarity, and (semi) variograms and their modelling. MvL: Section 2.3, 2.4, 2.6 LN: Section 5.2, 5.3 Lecture notes: L3.pdf |
| Monday | 13:15-15:00 | MVF24 and MVF25 | E3 |
Cancelled due to illness |
Exercise sheet 2: E2.pdf |
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| April 1 | Wednesday | 10:00-11:45 | Euler | L4 |
Ottmar |
Kriging MvL: Section 2.7, 2.8, 2.9, 2.10, 2.11 LN: Section 5.4 Lecture notes: L4.pdf |
| Wednesday | 13:15-15:00 | MVF24 and MVF25 | E4 |
Mathis |
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| Week 15 |
Break |
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| Week 16 |
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| April 13 | Monday | 8:00-9:45 | Euler | L5 |
Ottmar |
Areal unit data, discrete random fields, neighbourhood relations, local characteristics, Ising model, Besag's theorem, conditional autoregrssion (CAR) models, conditional independence. MvL: Section 3.1, 3.2 LN: Section 4 Lecture notes: L5.pdf |
| Monday | 13:15-15:00 | MVF24 and MVF25 | E5 |
Mathis |
Exercise sheet 3: E3.pdf
Exercise sheet solution partA: Lab3_solution.pdf
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| April 15 | Wednesday | 10:00-11:45 | Euler | L6 |
Ottmar |
Gibbs states, (normalised) interaction potentials, partition functions, cliques, Markov random fields, Hammersely-Clifford theorem, Gaussian Markov random fields. MvL: Section 3.3, 3.4 LN: Section 4 BC: Section 4, 6.1, 6.2, 14.1-14.4 Lecture notes: L6.pdf |
| Wednesday | 13:15-15:00 | MVF24 and MVF25 | E6 |
Mathis |
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| Week 17 |
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| April 20 | Monday | 8:00-9:45 | Euler | L7 |
Ottmar |
Statistical inference for discrete random fields, (Monte-Carlo) maximum likelihood estimation, pseudolikelihood estimation, MCMC simulation (Gibbs sampling and Metropolis-Hastings sampling). MvL: Section 3.5, 3.6 BC: Section 14.5, 15 Lecture notes: L7.pdf |
| Monday | 13:15-15:00 | MVF24 and MVF25 | E7 |
Mathis |
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| April 22 | Wednesday | 10:00-11:45 |
Online lecture (via Zoom) so no class attendance! Zoom-link: https://chalmers.zoom.us/j/63704755201 Password: 359651
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L8 |
Ottmar |
Hierarchical modelling, disease mapping, image segmentation, posterior inference and MAP estimation. MvL: Section 3.7 We only mention what MvL says about MAP and segmentation here but more details can be found in Bouman's book (BC: Section 2.3, 5.1, 7, 16.1) Lecture notes: L7.pdf + Guest lecture: Adinia Iftimi, University of Valencia, Spain. Recording:
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| Wednesday | 13:15-15:00 | MVF24 and MVF25 | E8 |
Mathis |
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| Week 18 |
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| April 27 | Monday | 8:00-9:45 | Euler | L9 |
Ottmar |
Point processes and point patterns, intensity functions, sample and binomial point processes, Poisson processes. MvL: Section 4.1, 4.2, 4.3 Lecture notes: L8.pdf |
| Monday | 13:15-15:00 | MVF24 and MVF25 | E9 |
Mathis |
Exercise sheet 4:Lab4.pdf |
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| April 29 | Wednesday | 10:00-11:45 | Euler | L10 |
Ottmar |
Spatial interaction, product densities, (pair) correlation functions, Campbell's formula, (intensity reweighted) stationarity, isotropy, (kernel) intensity estimation, pair correlation function estimation, cumulative summary statistics. Lecture notes: L9.pdf MvL: Section 4.3, 4.4
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| Wednesday | 13:15-15:00 | MVF24 and MVF25 | E10 |
Mathis |
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| Week 19 |
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| May 4 | Monday | 8:00-9:45 | Euler | L11 |
Ottmar |
Finite point processes, Janossy densities, Gibbs processes andf their densities, Papangelou conditional intensities, Markov point processes. Lecture notes: L10.pdf MvL: Section 4.5, 4.6, 4.7 |
| Monday | 13:15-15:00 | MVF24 and MVF25 | E11 | Mathis |
This lab will be online |
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| May 6 | Wednesday | 10:00-11:45 | Euler | L12 | Ottmar |
Cox and cluster processes, maximum likelihood estimation, pseudolikelihood estimation, Monet Carlo maximum likelihood estimation, minimum contrast estimation, simulation envelopes and Monet Carlo goodness-of-fit testing Lecture notes: L11.pdf MvL: Section 4.8-4.12 |
| Wednesday | 13:15-15:00 | MVF24 and MVF25 | E12 | Mathis | There was a mistake in the in the Lab4.pdf It contained some theory which has not been introduced in the lecture. Here is the updated version: Lab4_v2.pdf |
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| Week 20 | ||||||
| May 11 | Monday | 8:00-9:45 | Euler | L13 | Ottmar |
Classical image analysis: Digital images, filters, segmentation (thresholding and k-means). LN: Section 1 GH: Section 1, 2, 3.1, 4.1 Lecture notes: L12.pdf |
| Monday | 13:15-15:00 | MVF24 and MVF25 | E13 | Mathis | Lab5: Lab5.pdf Lab5 notebook: Lab5_PartB_Coins_Image_Analysis.ipynb The notebook is part of the Lab. This time it will be in python. If you don't have it installed locally you may use some cloud based version like google colab. |
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| May 13 | Wednesday | 10:00-11:45 | Euler | L14 |
Ottmar |
Morphological operations, Computational imaging: hierarchical modelling and posterior inference, MAP and poetrior mean estimation, regularisation, linear observation model, prior choices LN: Section 1 GH: Section 5 BC: Section 5, 12, 16 Lecture notes: L13-14.pdf |
| Wednesday | 13:15-15:00 | MVF24 and MVF25 | E14 | Mathis | ||
| Week 21 | ||||||
| May 18 | Monday | 8:00-9:45 | Euler | L15 | Mathis |
Read at home: Gaussian mixture models, EM algorithm Lecture notes: L13-14.pdf Lecture today: Image classification |
| Monday | 13:15-15:00 | MVF24 and MVF25 | E15 | Mathis | ||
| May 20 | Wednesday | 10:00-11:45 | Euler |
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| Wednesday | 13:15-15:00 | MVH11 |
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| May 21 | Thursday | 10:00-11:45 | MVH11 |
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| Thursday | 13:15-15:00 | MVH11 |
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| May 22 | Friday | 10:00-11:45 | MVH11 |
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| Friday | 13:15-15:00 | MVH11 |
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Course summary:
| Date | Details | Due |
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