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Lund University

Mathematical Imaging Group


A PhD Course in Computer Vision was given in 1999. The course was given during two sessions of three and two days each. The first session during 5-7 May 1999 and the second during 19-20 August 1999. The course consists of 9 lectures (2x45 minutes each), 5 laboratory sessions, exercises/homework, and a small project. The course is sponsored by the project VISIT.

Projects in the Computer vision course.

There are four choices on projekts.
  1. Generation of VRML models from one image. In this project we are going to use results from the VISIT project View synthesis. Given one image of a piecewise planar scene. Find the intersection lines between the planes in the image. Use this to calculate a 3D reconstruction of the textured planes and encode this information in a VRML model. A suggestion on a project plan in swedishis available as well as Björn Johanssons article on the subject. The first part of the project is to acquire a good image to work with. It is advised that you show this image to Björn before you proceed. Contact him via e-mail at when you have acquired an image.
  2. Implementation of line detection in images. Automatic feature detectionin images is an important and difficult problem. In simplified situations, for example line detection with very distinct edges, the problem is possible to solve. The goal of the project is to develop matlab routine that use edge detection and line fitting to automatically extract and find edges. One idea is to use sub-pixel edge detection to find edges and their normal direction (estimate the gradient direction). Group edge points that have similar normal direction and lie on the same line. Fit a line to these edge points. Return the line parameter. Try the routine on different images. Try first with the plc-sequence.
  3. RANSAC matching from points in two images. The goal of the project is to develop a small system for automatic corner detection and matching in two images. Use Harris corner detector and then RANSAC (RANdom SAmpling Consensus) to find corresponding corners. Try the procedure on image pairs or on image sequences. A short image sequence is available here. Also are some reports from a student project that did tracking without RANSAC. A possible extension is to use correlation and corner detection to do a rough tracking of points in the sequence. From these tracks perform a random sampling (of say 8 tracks) and then solve for the fundamental matrix and check how many of the other tracks fulfill the fundamental matrix constraint well. Care must be taken in how well the fundamental constraint must be fulfilled for the remaining tracks.
  4. VRML-generation from the five images plc. The goal of the project is to construct a VRML model of the lines and the conics in the image sequence plc*.pgm used in the laboratory sessions. Extract image features and find the correspondences manually. Calculate first projective and then Euclidean structure and motion using the assumption of constant intrinsic parameters. Find out not only the motion of the camera, the structure of the points but also the structure of the scene lines and the conics. Encode the structure information in a VRML document and tell us by e-mail where the final reconstruction is located on the web.

First session 5-7 may 1999.

Wed 5/5: 10.15-12.00: Lecture 1. Room MH:333.
Wed 5/5: 13.15-15.00: Lecture 2. Room MH:333.
Wed 5/5: 15.15-17.00: Exercise/Lab session 1. Room MH:139.
Wed 5/5: Evening. Special arrangement.
Thu 6/5: 8.15-10.00: Lecture 3. Room MH:333.
Thu 6/5: 10.15-12.00: Exercise/Lab session 2. Room MH:140.
Thu 6/5: 13.15-15.00: Lecture 4. Room MH:333.
Thu 6/5: Evening. Get-to-gether-gathering (barbecue if wheather allows).
Fri 7/5: 8.15-10.00: Lecture 5. Room MH:333.
Fri 7/5: 10.15-12.00: Exercise/Lab session 3. Room MH:139.
Fri 7/5: 13.15-15.00: Lecture 6. Room MH:333.

Second session 19-20 august 1999.

Thu 19/8: 10.15-12.00: Lecture 7. Room MH:333.
Thu 19/8: 13.15-15.00: Exercise/Lab session 4. Room MH:139.
Thu 19/8: 15.15-17.00: Lecture 8. Room MH:333.
Thu 19/8: Evening arrangement?.
Fri 20/8: 8.15-10.00: Lecture 9. Room MH:333.
Fri 20/8: 10.15-12.00: Exercise/Lab session 5. Room MH:139.
Fri 20/8: 13.15-15.00: Evaluation, discussion, questions. Room MH:333.

Below you can find more information about the course.

Here is more information about the course:

Computer vision is a rapidly growing research cross-disciplinary area, which has far reaching applications within robotics, autonomous systems, virtual/augmented reality, medicine, etc. The basic problem is to calculate the three-dimensional structure of an unknown scene and the ego-motion of the camera from image measurements only. Tools like projective geometry, tensor analysis and advanced linear algebra have proved to be invaluable in understanding the geometry of vision. This course in computer vision will focus on the geometrical aspects of multiple projective transformation.

Course content

Imaging models. Projective geometry. Advanced linear algebra. Tensor analysis. Viewing geometry of points, lines, conics and other features. Absolute orientation. Review of low-level vision and feature extraction. Registration. Matching. Tracking. Multiple view geometry. Bundle adjustment. Self-calibration. Invariants. Recognition.

Laboratory groups.

Each group is responsible for the extraction of 15 points and 15 lines in one image. Coordinate the work among your self and then distribute the information to the other groups. For store the information in a text file

p1 = [ ...

10.1 123.4 567.8 ; ...

12.3 45.6 78.9; ...

1 1 1 ;...


l1 = [...

10.1 123.4 567.8 ; ...

12.3 45.6 78.9; ...

1 1 1 ;...


so that it will be easy to read the data to matlab. Use the variables p1 and l1 for the points and lines in image plc001. Use the variables p2 and l2 for the points and lines in image plc002. And similarly for plc003, plc004 and plc005. The groups are as follows:

  1. Group 1, (plc001)
  2. Group 2, (plc002)
  3. Group 3, (plc003)
  4. Group 4, (plc004)
  5. Group 5, (plc005)
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Kalle och Anders

Förslag på hotell:
Hotell Sparta (nära LTH) tfn 046-19 16 00
Hotell Ahlström (i centrum, ca 15 min gångväg från LTH) tfn 046-211 01 74

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Address: Mathematical Imaging Group, Centre for Mathematical Sciences, Lund university, Box 118 S-221 00 LUND, SWEDEN.
Phone:+46 46 222 85 37, Fax:+46 46 222 40 10
Publisher: Kalle Åström,
Last updated:990118