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.

Color interpolation is still the most used method for image upsampling, since it offers the simplest and therefore fastest algorithms. However, in recent years research concentrated on other techniques to counter the shortcomings of interpolation techniques (like color artifacts or the fact that interpolation does not take statistics into account), while interpolation itself has ceased to be an active research topic. Still, current interpolation techniques can be improved. Especially it should be possible to avoid color artifacts by carefully choosing the correct interpolation schemes. In this paper we derive mathematical constraints which need to be fulfilled to reach an artifact-free interpolation, and use these to develop an interpolation method which is basically a self-configuring cubic spline.

More and more devices have depth sensors, making RGB+D video (colour+depth video) increasingly common. RGB+D video allows the use of depth image based rendering (DIBR) to render a given scene from different viewpoints, thus making it a useful asset in view prediction for 3D and free-viewpoint video coding. In this paper we evaluate a multitude of algorithms for scattered data interpolation, in order to optimize the performance of DIBR for video coding. This also includes novel contributions like a Kriging refinement step, an edge suppression step to suppress artifacts, and a scale-adaptive kernel. Our evaluation uses the depth extension of the Sintel datasets. Using ground-truth sequences is crucial for such an optimization, as it ensures that all errors and artifacts are caused by the prediction itself rather than noisy or erroneous data. We also present a comparison with the commonly used mesh-based projection.

With depth sensors becoming more and more common, and applications with varying viewpoints (like e.g. virtual reality) becoming more and more popular, there is a growing demand for real-time depth-image-based-rendering algorithms that reach a high quality. Starting from a quality-wise top performing depth-image-based-renderer, we develop a real-time version. Despite reaching a high quality as well, the new OpenGL-based renderer decreases runtime by (at least) 2 magnitudes. This was made possible by discovering similarities between forward-based and mesh-based rendering, which enable us to remove the common parallelization bottleneck of competing memory access, and facilitated by the implementation of accurate yet fast algorithms for the different parts of the rendering pipeline. We evaluated the proposed renderer using a publicly available dataset with ground-truth depth and camera data, that contains both rapid camera movements and rotations as well as complex scenes and is therefore challenging to project accurately.

Many of the latest smart phones and tablets come with integrated depth sensors, that make depth-maps freely available, thus enabling new forms of applications like rendering from different view points. However, efficient compression exploiting the characteristics of depth-maps as well as the requirements of these new applications is still an open issue. In this paper, we evaluate different depth-map compression algorithms, with a focus on tree-based methods and view projection as application.

The contributions of this paper are the following: 1. extensions of existing geometric compression trees, 2. a comparison of a number of different trees, 3. a comparison of them to a state-of-the-art video coder, 4. an evaluation using ground-truth data that considers both depth-maps and predicted frames with arbitrary camera translation and rotation.

Despite our best efforts, and contrary to earlier results, current video depth-map compression outperforms tree-based methods in most cases. The reason for this is likely that previous evaluations focused on low-quality, low-resolution depth maps, while high-resolution depth (as needed in the DIBR setting) has been ignored up until now. We also demonstrate that PSNR on depth-maps is not always a good measure of their utility.