Local Moebius transformations applied to omnidirectional images
TL;DR: This work presents a new method to transform omnidirectional images based on a combination of Moebius transformations in the complex plane and weighting functions that restrict the action of these mappings to regions of interest.
About: This article is published in Computers & Graphics.The article was published on 2017-11-01. It has received 8 citations till now. The article focuses on the topics: Weighting & Zoom.
Citations
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23 Mar 2019
TL;DR: A novel method to explore large displacement optical flow algorithms to obtain point correspondences, and use cross-checking and geometric constraints to detect and remove bad matches and produces a dense depth map registered to a reference view so that depth-image-based-rendering techniques can be explored for providing three-degrees-of-freedom plus immersive experiences to virtual reality users.
Abstract: We propose a novel method for estimating the 3D geometry of indoor scenes based on multiple spherical images. Our technique produces a dense depth map registered to a reference view so that depth-image-based-rendering (DIBR) techniques can be explored for providing three-degrees-of-freedom plus immersive experiences to virtual reality users. The core of our method is to explore large displacement optical flow algorithms to obtain point correspondences, and use cross-checking and geometric constraints to detect and remove bad matches. We show that selecting a subset of the best dense matches leads to better pose estimates than traditional approaches based on sparse feature matching, and explore a weighting scheme to obtain the depth maps. Finally, we adapt a fast image-guided filter to the spherical domain for enforcing local spatial consistency, improving the 3D estimates. Experimental results indicate that our method quantitatively outperforms competitive approaches on computer-generated images and synthetic data under noisy correspondences and camera poses. Also, we show that the estimated depth maps obtained from only a few real spherical captures of the scene are capable of producing coherent synthesized binocular stereoscopic views by using traditional DIBR methods.
21 citations
Cites background from "Local Moebius transformations appli..."
...The poles are over-sampled in the equirectangular domain (the top and bottom rows correspond to a small region on the sphere) [39], enhancing the distortions....
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...The equirectangular projection highly distorts the information depending on its location on the scene, being particularly high near the poles of the sphere [39], as illustrated in Figures 2(a)-(b)....
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TL;DR: In this paper, fast and accurate superpixel algorithms tailored to the spherical domain were proposed for 360-degree images, which are evaluated under common figures of merit, and a benchmark annotated dataset is introduced.
3 citations
24 Oct 2022
TL;DR: Omnidirectional media are becoming widespread with the increasing popularization of devices for capture and visualization as discussed by the authors , and applications exploring immersive augmented, mixed, and virtual reality experiences can strongly benefit from omnidirectal vision.
Abstract: Omnidirectional media are becoming widespread with the increasing popularization of devices for capture and visualization. Unlike traditional pinhole-based images, omnidirectional images are defined on the surface of a sphere, present a full field of view, and store light intensities from a whole scene. In particular, applications exploring immersive augmented, mixed, and virtual reality experiences can strongly benefit from omnidirectional vision. Though omnidirectional images are defined on the spherical domain, they are commonly mapped to one or multiple planes. Those sphere-to-plane mappings generate distorted images, and, if directly applied, most traditional visual computing algorithms tend to present some quality degradation. This tutorial paper revises the spherical imaging model, common capture device types, and prominent representation formats. It also discusses the significant challenges of spherical visual computing and showcases the advances in three selected applications.
1 citations
TL;DR: A new method to correct distortions in equirectangular images, i.e., images that use the longitude/latitude representation to describe the full spherical field of view around a given viewpoint, which shows that Mobius transformations are the correct mathematical tool to deal with the conflicting distortions.
1 citations
24 Oct 2022
TL;DR: Omnidirectional media are becoming widespread with the increasing popularization of devices for capture and visualization as discussed by the authors , and applications exploring immersive augmented, mixed, and virtual reality experiences can strongly benefit from omnidirectal vision.
Abstract: Omnidirectional media are becoming widespread with the increasing popularization of devices for capture and visualization. Unlike traditional pinhole-based images, omnidirectional images are defined on the surface of a sphere, present a full field of view, and store light intensities from a whole scene. In particular, applications exploring immersive augmented, mixed, and virtual reality experiences can strongly benefit from omnidirectional vision. Though omnidirectional images are defined on the spherical domain, they are commonly mapped to one or multiple planes. Those sphere-to-plane mappings generate distorted images, and, if directly applied, most traditional visual computing algorithms tend to present some quality degradation. This tutorial paper revises the spherical imaging model, common capture device types, and prominent representation formats. It also discusses the significant challenges of spherical visual computing and showcases the advances in three selected applications.
1 citations
References
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TL;DR: This work forms stitching as a multi-image matching problem, and uses invariant local features to find matches between all of the images, and is insensitive to the ordering, orientation, scale and illumination of the input images.
Abstract: This paper concerns the problem of fully automated panoramic image stitching. Though the 1D problem (single axis of rotation) is well studied, 2D or multi-row stitching is more difficult. Previous approaches have used human input or restrictions on the image sequence in order to establish matching images. In this work, we formulate stitching as a multi-image matching problem, and use invariant local features to find matches between all of the images. Because of this our method is insensitive to the ordering, orientation, scale and illumination of the input images. It is also insensitive to noise images that are not part of a panorama, and can recognise multiple panoramas in an unordered image dataset. In addition to providing more detail, this paper extends our previous work in the area (Brown and Lowe, 2003) by introducing gain compensation and automatic straightening steps.
2,550 citations
Book•
31 Oct 2012
TL;DR: The approach to map projections in which maps are made (using geometric principles from a sphere Snyder JP (1987) Map projections: a working manual.
Abstract: If projection is not specified here it uses proj='aeqd' (azimuthal equidistant). Returns: grid: grid object (R39), Snyder, J. P. Map Projections–A Working Manual. This web page relates to the PROJ.4 Cartographic Projections library OF90-284.pdf (2.7MB): The main users manual for PROJ, however, this VerticalDatums working notes on the project to support vertical datums in Map projections: An introduction to cartography emphasizing map projections: their properties. Abstract The approach to map projections in which maps (using geometric principles) from a sphere Snyder JP (1987) Map projections: a working manual.
1,145 citations
"Local Moebius transformations appli..." refers background in this paper
...the stereographic projection that identifies the sphere with the 96 extended complex plane (also known as Riemann sphere) [12] 97 and the Mercator projection from cartography books [13] are 98 well known to preserve shapes but they bend straight lines....
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03 Aug 1997
TL;DR: This paper presents a novel approach to creating full view panoramic mosaics from image sequences that does not require any controlled motions or constraints on how the images are taken (as long as there is no strong motion parallax).
Abstract: This paper presents a novel approach to creating full view panoramic mosaics from image sequences. Unlike current panoramic stitching methods, which usually require pure horizontal camera panning, our system does not require any controlled motions or constraints on how the images are taken (as long as there is no strong motion parallax). For example, images taken from a hand-held digital camera can be stitched seamlessly into panoramic mosaics. Because we represent our image mosaics using a set of transforms, there are no singularity problems such as those existing at the top and bottom of cylindrical or spherical maps. Our algorithm is fast and robust because it directly recovers 3D rotations instead of general 8 parameter planar perspective transforms. Methods to recover camera focal length are also presented. We also present an algorithm for efficiently extracting environment maps from our image mosaics. By mapping the mosaic onto an artibrary texture-mapped polyhedron surrounding the origin, we can explore the virtual environment using standard 3D graphics viewers and hardware without requiring special-purpose players. CR
999 citations
"Local Moebius transformations appli..." refers background in this paper
...Due to the development of robust computational photog83 raphy techniques [6, 7] and the Internet, panoramic omnidi84...
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Book•
27 Mar 1997
TL;DR: This chapter discusses Geometry and Complex Arithmetic, non-Euclidean Geometry*, Winding Numbers and Topology, and Vector Fields and Complex Integration.
Abstract: 1: Geometry and Complex Arithmetic. 2: Complex functions as Transformations. 3: Mobius Transformations and Inversion. 4: Differentiation: The Amplitwist Concept. 5: Further Geometry of Differentiation. 6: Non-Euclidean Geometry*. 7: Winding Numbers and Topology. 8: Complex Integration: Cauchy's Theorem. 9: Cauchy's Formula and Its Applications. 10: Vector Fields: Physics and Topology. 11: Vector Fields and Complex Integration. 12: Flows and Harmonic Functions
668 citations
"Local Moebius transformations appli..." refers background in this paper
...where a, b, c, d are given complex numbers (for more details on 165 these transformations we refer to [12, 19]) and z ∈ C∪{∞}....
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...the stereographic projection that identifies the sphere with the 96 extended complex plane (also known as Riemann sphere) [12] 97 and the Mercator projection from cartography books [13] are 98 well known to preserve shapes but they bend straight lines....
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TL;DR: A uniform framework for representing and using world projections is proposed and it is argued that the best general-purpose representation is the is projection onto a cube.
Abstract: Various techniques have been developed that employ projections of the world as seen from a particular viewpoint. Blinn and Newell introduced reflection mapping for simulating mirror reflections on curved surfaces. Miller and Hoffman have presented a general illumination model based on environment mapping. World projections have also been used to model distant objects and to produce pictures with the fish-eye distortion required for Omnimax frames. This article proposes a uniform framework for representing and using world projections and argues that the best general-purpose representation is the is projection onto a cube. Surface shading and texture filtering are discussed in the context of environment mapping, and methods are presented for obtaining diffuse and specular surface illumination from prefiltered environment maps. Comparisons are made with ray tracing, noting that two problems with ray tracing?obtaining diffuse reflection and antialiasing specular reflection?can be handled effectively by environment mapping.
590 citations
"Local Moebius transformations appli..." refers methods in this paper
...method works well as long as the orientation discontinuities in110 troduced by the multiple projection planes are well hidden by 111 the scene, which is also a limitation for cube maps [14, 15]....
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