Computer-aided inverse panorama on a conical projection surface

Abstract The aim of this study is to develop a practical method of direct mapping of an inverse conical panorama with computer aid. The panoramic image is a central projection onto a conical surface from the centres dispersed on a circular or straight path located outside the projection surface. The proposed method is a nonlinear projection in which the resulting image is treated as a sequence of stitched pictures of zero width taken from a moving view point. Geometric data and relations between the projected points are utilised to formulate algorithms for drawing of inverse panoramic images of straight lines, which further enables drawing of wire frame models of represented forms. Images are drawn as plots of a function in the Mathcad software. However, in order to make drawing more efficient and convenient, as well as for the practical applications of them, the algorithms can be implemented in any graphical package.

[1]  Drawing with Divergent Perspective, Ancient and Modern , 2011, Perception.

[2]  Jong-Gil Han,et al.  Cultural Heritage Sites Visualization System based on Outdoor Augmented Reality , 2013 .

[3]  T. Gibbons Cubism and 'The Fourth Dimension' in the Context of the Late Nineteenth-Century and Early Twentieth-Century Revival of Occult Idealism , 1981, Journal of the Warburg and Courtauld Institutes.

[4]  J. Snyder Flattening the Earth: Two Thousand Years of Map Projections , 1994 .

[5]  D. M. Parker,et al.  The Perception of Spatial Structure with Oblique Viewing: An Explanation for Byzantine Perspective? , 1994, Perception.

[6]  Jolanta Dzwierzynska,et al.  Computer-Aided Panoramic Images Enriched by Shadow Construction on a Prism and Pyramid Polyhedral Surface , 2017, Symmetry.

[7]  Qian Zhang,et al.  Object panorama creation based on a general photographing environment , 2011, ICUIMC '11.

[8]  R. Arnheim Inverted Perspective in Art: Display and Expression , 1972 .

[9]  Margarita N. Favorskaya,et al.  Panorama Construction from Multi-view Cameras in Outdoor Scenes , 2015 .

[10]  David Salomon,et al.  Transformations and projections in computer graphics , 2006 .

[11]  Shahriar Negahdaripour,et al.  A conical panoramic stereo imaging system for 3-D scene reconstruction , 2003, Oceans 2003. Celebrating the Past ... Teaming Toward the Future (IEEE Cat. No.03CH37492).

[12]  Johannes Wallner,et al.  Architectural geometry , 2007, Comput. Graph..

[13]  Michael Felsberg,et al.  Image Alignment for Panorama Stitching in Sparsely Structured Environments , 2015, SCIA.

[14]  F. Jaureguizar,et al.  Stabilization of Inverse Perspective Mapping Images based on Robust Vanishing Point Estimation , 2007, 2007 IEEE Intelligent Vehicles Symposium.

[16]  Steve Kopp,et al.  Understanding Map Projections , 2001 .

[17]  Jinyong Jeong,et al.  Adaptive Inverse Perspective Mapping for lane map generation with SLAM , 2016, 2016 13th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI).

[18]  David J. Fleet,et al.  Stable estimation of image orientation , 1994, Proceedings of 1st International Conference on Image Processing.

[20]  Mario Garavaglia,et al.  Application of the structured illumination method to study the topography of the sole of the foot during a walk , 2003 .

[21]  Clemena Antonova On the Problem of Reverse Perspective: Definitions East and West , 2010, Leonardo.

[22]  O. Goncharov,et al.  Interrelation Between Perspective Constructions and Constancy of Magnitude Perception , 2012 .

[23]  Massimo Bertozzi,et al.  Stereo inverse perspective mapping: theory and applications , 1998, Image Vis. Comput..