# cMinMax: A Fast Algorithm to Find the Corners of an N-dimensional Convex Polytope

### Dimitrios Chamzas, Dimitrios Chamzas, Constantinos Chamzas, Konstantinos Moustakas

#### Abstract

During the last years, the emerging field of Augmented & Virtual Reality (AR-VR) has seen tremendous growth. At the same time there is a trend to develop low cost high-quality AR systems where computing power is in demand. Feature points are extensively used in these real-time frame-rate and 3D applications, therefore efficient high-speed feature detectors are necessary. Corners are such special features and often are used as the first step in the marker alignment in Augmented Reality (AR). Corners are also used in image registration and recognition, tracking, SLAM, robot path finding and 2D or 3D object detection and retrieval. Therefore there is a large number of corner detection algorithms but most of them are too computationally intensive for use in real-time applications of any complexity. Many times the border of the image is a convex polygon. For this special, but quite common case, we have developed a specific algorithm, cMinMax. The proposed algorithm is faster, approximately by a factor of 5 compared to the widely used Harris Corner Detection algorithm. In addition is highly parallelizable. The algorithm is suitable for the fast registration of markers in augmented reality systems and in applications where a computationally efficient real time feature detector is necessary. The algorithm can also be extended to N-dimensional polyhedrons.

Download#### Paper Citation

#### in Harvard Style

Chamzas D., Chamzas C. and Moustakas K. (2021). **cMinMax: A Fast Algorithm to Find the Corners of an N-dimensional Convex Polytope**.In *Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,* ISBN 978-989-758-488-6, pages 229-236. DOI: 10.5220/0010259002290236

#### in Bibtex Style

@conference{grapp21,

author={Dimitrios Chamzas and Constantinos Chamzas and Konstantinos Moustakas},

title={cMinMax: A Fast Algorithm to Find the Corners of an N-dimensional Convex Polytope},

booktitle={Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,},

year={2021},

pages={229-236},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010259002290236},

isbn={978-989-758-488-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,

TI - cMinMax: A Fast Algorithm to Find the Corners of an N-dimensional Convex Polytope

SN - 978-989-758-488-6

AU - Chamzas D.

AU - Chamzas C.

AU - Moustakas K.

PY - 2021

SP - 229

EP - 236

DO - 10.5220/0010259002290236