|
|
|
|
Home | CV | Research | Publications | Teaching | ISMM 2013 |
The construction of adaptive structuring elements that adjust their shape and size to the local structures in the image has recently been a popular topic in mathematical morphology. Despite that several methods for the construction of spatially adaptive structuring elements have been proposed, it is still an open problem, both from a theoretical and implementation point of view. We have proposed salience adaptive structuring elements that modify their shape and size according to the saliency of the edges in the image. We have examined topological properties of salience adaptive structuring elements and investigated their applicability to image filtering. We intend to further develop new methods for adaptive structuring elements as well as to extend the salience adaptive structuring elements toward multi-valued images and sparse image representations. Nonlocal morphological operators and adaptive morphological operators for both discrete and continuous framework are of interest in future studies.
Methods for measuring distances between sets can be useful for solving various image analysis
related problems, such as registration, image retrieval and segmentation evaluation. Depending on
how the distance measure is defined, it exhibits different properties, such as metricity,
monotonicity, continuity, sensitivity to noise, complexity and speed of computation. It is therefore
of interest to study and further develop different set distance measures, to be able to select
appropriate distances for the different applications.
An initial goal of this project is to evaluate existing and possibly develop new set distances which
are useful in image registration problems. We have proposed variations on Sum of Minimal Distances
as well as Complement set distances, and are currently exploring, and evaluating their
appropriateness for image registration. Of particular interest are properties of monotonicity and
continuity.
We intend to further extend this work within the framework of mathematical morphology towards more
general methods for shape description and analysis.
Previously, I was involved in the project of developing a mathematical model of efficient water flow management in water factory in the city of Zrenjanin, Serbia. We have developed a mathematical model for the pressure and a model for optimal pump scheduling for the particular water supply system.