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Cubic Spline Interpolation in Real-Time Applications using Three Control Points
Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, Faculty of Science & Engineering.
2019 (English)In: Proceedings of International Conference in Central Europe on Computer Graphics, Visualization and ComputerVision’2019 / [ed] Vaclav Skala, World Society for Computer Graphics , 2019, Vol. 2901, p. 1-10Conference paper, Published paper (Refereed)
Abstract [en]

Spline interpolation is widely used in many different applications like computer graphics, animations and robotics. Many of these applications are run in real-time with constraints on computational complexity, thus fueling the need for computational inexpensive, real-time, continuous and loop-free data interpolation techniques. Often Catmull- Rom splines are used, which use four control-points: the two points between which to interpolate as well as the point directly before and the one directly after. If interpolating over time, this last point will ly in the future. However, in real-time applications future values may not be known in advance, meaning that Catmull-Rom splines are not applicable. In this paper we introduce another family of interpolation splines (dubbed Three-Point-Splines) which show the same characteristics as Catmull-Rom, but which use only three control-points, omitting the one “in the future”. Therefore they can generate smooth interpolation curves even in applications which do not have knowledge of future points, without the need for more computational complex methods. The generated curves are more rigid than Catmull-Rom, and because of that the Three-Point-Splines will not generate self-intersections within an interpolated curve segment, a property that has to be introduced to Catmull-Rom by careful parameterization. Thus, the Three-Point-Splines allow for greater freedom in parameterization, and can therefore be adapted to the application at hand, e.g. to a requested curvature or limitations on acceleration/deceleration. We will also show a method that allows to change the control-points during an ongoing interpolation, both with Thee-Point-Splines as well as with Catmull-Rom splines.

Place, publisher, year, edition, pages
World Society for Computer Graphics , 2019. Vol. 2901, p. 1-10
Series
Computer Science Research Notes, ISSN 2464-4617, E-ISSN 2464-4625 ; 2901
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-162119ISBN: 978-80-86943-37-4 (print)OAI: oai:DiVA.org:liu-162119DiVA, id: diva2:1371363
Conference
27. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision WSCG 2019, Plzen, Czech Republic, May 27 – 30, 2019
Available from: 2019-11-19 Created: 2019-11-19 Last updated: 2019-11-19
In thesis
1. Interpolation Techniques with Applications in Video Coding
Open this publication in new window or tab >>Interpolation Techniques with Applications in Video Coding
2019 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Recent years have seen the advent of RGB+D video (color+depth video), which enables new applications like free-viewpoint video, 3D and virtual reality. This is however achieved by adding additional data, thus increasing the bitrate. On the other hand, the added geometrical data can be used for more accurate frame prediction, thus decreasing bitrate. Modern encoders use previously decoded frames to predict other ones, meaning they only need to encode the difference. When geometrical data is available, previous frames can instead be projected to the frame that is currently predicted, thus reaching a higher accuracy and a higher compression.

In this thesis, different techniques are described and evaluated enabling such a prediction scheme based on projecting from depth-images, so called depth-image based rendering (DIBR). A DIBR method is found that maximizes image quality, in terms of minimizing the differences of the projected frame to the groundtruth of the frame it was projected to, i.e. the frame that is to be predicted. This was achieved by evaluating combinations of both state-of-the-art methods for DIBR as well as own extensions, meant to solve artifacts that were discovered during this work. Furthermore, a real-time version of this DIBR method is derived and, since the deph-maps will be compressed as well, the impact of depth-map compression on the achieved projection quality is evaluated, for different compression methods including novel extensions of existing methods. Finally, spline methods are derived for both geometrical and color interpolation.

Although all this was done with a focus on video compression, many of the presented methods are useful for other applications as well, like free-viewpoint video or animation.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2019. p. 38
Series
Linköping Studies in Science and Technology. Licentiate Thesis, ISSN 0280-7971 ; 1858
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
urn:nbn:se:liu:diva-162116 (URN)9789179299514 (ISBN)
Presentation
2019-12-09, Ada Lovelace, Campus Valla, Linköping, 13:15 (English)
Opponent
Supervisors
Available from: 2019-11-19 Created: 2019-11-19 Last updated: 2019-12-10Bibliographically approved

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Ogniewski, Jens

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