WP1 Advanced reflectional symmetry

Responsible partner: UWB-CSE

Goal

To upgrade the existing own method for reflectional symmetry detection to handle highly non-uniform and noisy data, and to detect local symmetries besides the global ones.

Realisation

100%. UWB-CSE mostly. UM FERI (GeMMA) has developed an original method for detecting approximate global reflection symmetries. We have described it in a patent application smubmitted to the European Patent Office, which has already passed the first assessment of the patent examiner and we have returned it revised to the Office in February 2023.

 

WP2 Rotational, axial, centre symmetry, groups of symmetry

Responsible partner: UWB-CSE

Goal

To further process candidate planes of the global symmetry in order to provide more complex symmetries.

Realisation

100% (UWB-CSE). UM FERI did not participate in WP2.

 

WP3 More general types of symmetry

Responsible partner: UWB-CSE

Goal

Further generalization to handle rigid, affine, or even non-rigid symmetries.

Realisation

80% (UWB-CSE). UM FERI did not participate in WP3.

 

WP4 Symmetry of continuously described objects

Responsible partner: UWB-CSE

Goal

More sophisticated solution than the discretization of the continuously described object.

Realisation

The order of WP4 and WP5 has been reversed, so WP4 is still under implementation. UM FERI is not participating in WP4.

 

WP5 Approximate symmetry

Responsible partner: UWB-CSE

Goal

To investigate how to mutually relate the fitness evaluation of the symmetry planes and some degree of 'symmetry impreciseness' allowed, set by the user.

Realisation

100% (UWB-CSE). UM FERI participated indirectly through the development and use of the approximate symmetry functionality (local and global; reflection and rotational) in WP11 and WP12.

 

WP6 Equivalences of finite sets of points

Responsible partner: UWB-M

Goal

To formulate an efficient algorithm devoted to the detection of equivalences of finite point sets given as solutions of polynomial systems.

Realisation

100%. UWB-M mostly. UM FERI did not participate in WP6.

 

WP7 Exact projective (and other) equivalences between algebraic surfaces in 3-space

Responsible partner: UWB-M

Goal

Generalization of curve case solution for algebraic surfaces in 3D, at least for special classes.

Realisation

100%. UWB-M mostly. UM FERI did not participate in WP7.

 

WP8 Approximate projective equivalences of special algebraic varieties

Responsible partner: UWB-M

Goal

After previous study of exact equivalences between algebraic varieties we will consider possible extensions where one or both input objects are given by the implicit description with perturbed coefficients.

Realisation

100%. UWB-M mostly. UM FERI did not participate in WP8.

 

WP9 Approximate symmetries of perturbed surfaces

Responsible partner: UWB-M

Goal

To design efficient reconstruction algorithm for finding a suitable symmetric surface S’ sufficiently “close” to the given inexact surface S being a perturbation of some unknown algebraic surface S0. Exact symmetries of S’ represent the approximate symmetries of S.

Realisation

WP9 is ongoing. UM FERI is not participating in WP9.

 

WP10 Initial study of reflectional symmetry detection on EO data

Responsible partner: UM FERI

Goal

Establishing a framework of integration of existing and future symmetry detection algorithms (WP1-WP5) and for their practical validation in EO data fusion and applications.

Realisation

100%. UM FERI mostly. We have developed a Geographic Information System (GIS) based on the Gemma Fusion Suite (GFS) SDK, which supports the integration of various symmetry detection algorithms and the treatment of detected symmetries as additional features. We have also developed algorithms for global reflection symmetry detection with several accelerations, local reflection symmetry detection adapted to EO data, and local rotational symmetry detection also in EO data.

 

WP11 Symmetry-aware feature extraction in EO data fusion

Responsible partner: UM FERI

Goal

To extend an existing own EO feature extraction methodology with features provided by symmetry detection algorithms.

Realisation

100%. UM FERI mostly. We extracted target objects from the LIDAR point clouds and then used global symmetry detection for classification purposes. In this way, the water level of Lake Cerknica was predicted from Sentinel-2 multispectral imagery. We used our own region merging algorithm to assist the determination of the boundary of the intermittent lake.

 

WP12 Integration of symmetries into semantic segmentation and object recognition in EO data fusion

Responsible partner: UM FERI

Goal

Definition of new semantic classes and new object types, where symmetries are particularly expected to improve the segmentation and recognition abilities: differentiation between man-made and natural objects with similar topology and geometry, consideration of different types of buildings, some preliminary steps towards tree species classification.

Realisation

100%. UM FERI mostly. We have selected two pilot applications to be enhanced with symmetries: railway line detection and some preliminary steps towards tree species classification. For the second pilot, we have already prepared a rich test database of trees with different predefined canopy shapes and manually associated symmetry planes. We have also studied different criteria for optimising tree pruning and forest growth prediction, which will also be used for tree species differentiation.

 

WP13 Validation of symmetry utilization in EO data applications

Responsible partner: UM FERI

Goal

2-3 pilot applications already deployed on existing GIS platform shall be validated by using the extended symmetry-aware feature sets and data fusion methodology.

Realisation

WP13 is ongoing. Pilot application for railway track detection was implemented and tested, the paper is in preparation. Preliminary steps towards classification of tree species have been successfully validated, the paper is in preparation.