James F. Peters, B.Sc.(Math), M.Sc.(Math), Ph.D., emph{Constructive Specification of Communicating Systems}, Postdoctoral Fellow, Syracuse University, New York (1991), Asst. Prof., University of Arkansas, 1991-1994, and Researcher, Jet Propulsion Laboratory/Caltech, Pasadena, California (1991-1994), Full Professor, ECE Department, University of Manitoba, 1995-present, Visiting Professor, Mathematics Department, Adiyaman University, Adiyaman, Turkey, 2014-present, Visiting Researcher, Universit` a degli Studi di Salerno, Department of Mathematics DIPMAT

Fisciano, Italy, 2014-present. He is the author of Topology of Digital Images. Visual Pattern Discovery in Proximity Spaces, Springer, 2014, (with S.A. Naimpally) Topology with Applications. Topological Spaces Near and Far, World Scientific, 2013, as well as over 350 published articles. He introduced near set theory in 2007, followed by the introduction of tolerance near sets in 2009, descriptive proximity spaces in 2013, strongly near Wallman proximity in 2014, proximal Vorono" i and Delaunay tessellations in 2015. His main research interests are computational proximity, digital topology and geometry, near sets, and visual pattern recognition in various applications areas such as digital images.

M.Sc. 1: Approximately close fixed point sets with applications.

M.Sc. 2: Quaternionic holes and their triangulation in discovering visual scene shapes.

M.Sc. 3: Shape detection in connected voxels in video frames.

M.Sc. 4: Barcodes in pictographic representation of video frames.

M.Sc. 5: Perception of time and rate-of-change in near set theory.

Ph.D. 1: Shape absorption: Spatial & Descriptive approaches to shape absorption with applications in video analysis.

Ph.D. 2: Free group presentation of video frame vortexes with applications.

Ph.D. 3: Shape fixed point sets with applications.

Ph.D. 4: Descriptive proximities of shapes in visual scenes.

Ph.D. 5: Self-maps that lead to fixed points with engineering applications.

Postdoc 1: Amiable fixed point sets and their homotopic presentation.

Postdoc 2: Shapes and their Approximate Descriptive Proximities.

My research focuses on the computational geometry, topology and physics of digital images, especially in video frames. Computation geometry is a geometry equipped with a hefty set of step-by-step methods that lifts classical forms of geometry to a level that is practical in extracting useful information from physical shapes tiled with polygons on visual scenes. Computational geometry provides a handy toolbox for topologists who are interested in exploring the connectedness of structures that appear in the spaces that we work in. Since we want to consider what photographic records of visual scenes tell us about the physical world, it makes sense to combine what we know about geometry and topology with physics. The handmaiden of computational geometry is an algorithmic form topology. Computational topology combines step-by-step methods (algorithms) useful in establishing the nearness or apartness of nonempty sets of cell complexes. In the plane, a cell complex is a collection of vertices and edges attached to each other. What we call a triangle is a natural outcome of edges attached to each other. The topology part of this study focuses on a planar view of the nearness of cell complexes, which are sets of path-connected vertices. The whole idea is to find ways to attach edges to vertices in such a way that they form simple closed curves that cover and overlap the boundaries of surface shapes. Computational physics is an algorithmic approach to physics. The basic approach is to extract the inherent structures of image shapes that would otherwise be hidden or, at least, escape our attention in a casual visual scan of digital images. This form of physics enters into the picture in considering methods of determining the wavelengths of picture elements (pixels) in the visible portion of the electromagnetic spectrum, particle characteristics of pixels such as energy and hue angles, saturation and value, which lurk in sequences of video frames. The physics that we have in mind can be found traditional approaches to electromagnetic systems. The study of electromagnetism focuses on the electromagnetic field and its interaction with matter. An electromagnetic field is a physical field produced by electrically charged objects. geometry, topology and physics have long and illustrious histories that give evidence of the importance of considering the geometry and topology of the interplay between physical structures illuminated by crowds of photons with different wavelengths bombarding physical surfaces and overlapping surface-covering cell complexes.

Researchgate ( https://www.researchgate.net/profile/James_Peters ) provides a detailed overview of the research streams represented by my research group and includes downloadable publications that reflect current research in computational proximity and related research areas.

Wikipedia ( https://en.wikipedia.org/wiki/Near_sets ) provides a good overview of a broad spectrum of research directions in the study of proximities and near sets.

1. Peters, J.F., Computational Geometry, Topology and Physics of Digital Images with Applications. Shape Vortexes, Optical Vortex Nerves and Proximities. Intelligent Systems Library volume 162, Springer Nature Switzerland, 2020, https://doi.org/10.1007/978-3-030-22192-8

2. Peters, J.F., Foundations of Computer Vision. Computational Geometry, Visual Image Structures and Object Shape Recognition. Intelligent Systems Library volume 124, Springer Nature Switzerland, 2017, https://doi.org/10.1007/978-3-319-52843-2

3. Peters, J.F., Naimpally, S.A., Applications of near sets, Notices of the American Math. Society 59 (4), 2012, 536-542.

4. James F Peters, C. Guadagni, Strong proximities on smooth manifolds and Voronoi diagrams. 4, Advances in Math.: Sci. Journal, no. 2, 08/2015, 91-107.

5. Peters, J.F., Local near sets. Pattern discovery in proximity spaces, Mathematics in Computer Science, Mathematics in Computer Science 04/2013; 7:87-106. DOI:10.1007/s11786-013-0143-z

6. Naimpally, S.A., Peters, J.F., Topology with Applications. Topological Spaces Via Near and Far, World Scientific, Singapore, 2013, ISBN: 13 978-981-4407-65-6.

7. Peters, J.F., Topology of Digital Images. Visual Pattern Discovery in Proximity Spaces. 1 edited by Janusz Kacprzyk, Lakhmi C. Jain, 01/2014; Springer., ISBN: ISBN 978-3-642-53844-5 and ISBN 978-3-642-53845-2 (eBook).

8. Randima Hettiarachchi, James F. Peters: Multi-Manifold LLE Learning in Pattern Recognition. Pattern Recognition 09/2015; 48(9):2947-2960. DOI:10.1016/j.patcog.2015.04.003

9. James F Peters, S. Ramanna: Proximal three-way decisions: Theory and applications in social networks. Knowledge-Based Systems 01/2015; DOI:10.1016/j.knosys.2015.07.021

10. James F Peters: Image and scene analysis. Taylor and Francis Encyclopedia of Image Processing, 2016.