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- Trajectory estimation from reduced multidimensional data
In many applications, fitting multi-dimensional data is important.
Reduced data means data without the corresponding parameters given. E.g.
imagine the need to reconstruct the trajectory of a moving object based on
sampling points without associated times (i.e. the times when these sampling
points are reached by a moving object). Recent algorithms by Kozera et. al are
theoretically proved to have a given convergence order. Testing these
algorithms to check the sharpness of the trajectory estimates would be one
of the tasks of this project. Applications: medical image processing, computer
vision, physics and engineering.
- Curvature and torsion estimation from reduced 2-D and 3-D data
This topic, as above, tests the approximation orders by cumulative-chord
piecewise-quadratics and piecewise-cubics curvature and/or torsion
of the unknown curve given its sampling points (without knowing the
corresponding parameters). Other parameterizations than cumulative-chord
can be tested. Applications: image segmentation, engineering or medical
image processing.
- 3D shape reconstruction for multiple source photometric stereo
Given 3 images (with noise and with non-distant light sources) this
task is to recover the unknown shape that gives rise to the image. Since
images are noisy, the problem is converted into a non-linear optimization
technique which depends on large number of parameters. A special technique
(called Leap-Frog) based on overlapping iterative method can be applied
(it can be in fact apply to any optimization problem). This project will
implement this technique with possibly some acceleration schemes.
Other topics for Honours/MSc/PhD degree
may involve: shape reconstruction, computer graphics
or agreed student elected topic.
 Return to the list of 4th year projects
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