Plenoptic image watermarking to preserve copyright

Common camera loses a huge amount of information obtainable from scene as it does not record the value of individual rays passing a point and it merely keeps the summation of intensities of all the rays passing a point. Plenoptic images can be exploited to provide a 3D representation of the scene and watermarking such images can be helpful to protect the ownership of these images. In this paper we propose a method for watermarking the plenoptic images to achieve this aim. The performance of the proposed method is validated by experimental results and a compromise is held between imperceptibility and robustness

Coherent multi-dimensional segmentation of multiview images using a variational framework and applications to image based rendering

Image Based Rendering (IBR) and in particular light field rendering has attracted a lot of attention for interpolating new viewpoints from a set of multiview images. New images of a scene are interpolated directly from nearby available ones, thus enabling a photorealistic rendering. Sampling theory for light fields has shown that exact geometric information in the scene is often unnecessary for rendering new views. Indeed, the band of the function is approximately limited and new views can be rendered using classical interpolation methods. However, IBR using undersampled light fields suffers from aliasing effects and is difficult particularly when the scene has large depth variations and occlusions. In order to deal with these cases, we study two approaches: New sampling schemes have recently emerged that are able to perfectly reconstruct certain classes of parametric signals that are not bandlimited but characterized by a finite number of parameters. In this context, we derive novel sampling schemes for piecewise sinusoidal and polynomial signals. In particular, we show that a piecewise sinusoidal signal with arbitrarily high frequencies can be exactly recovered given certain conditions. These results are applied to parametric multiview data that are not bandlimited. We also focus on the problem of extracting regions (or layers) in multiview images that can be individually rendered free of aliasing. The problem is posed in a multidimensional variational framework using region competition. In extension to previous methods, layers are considered as multi-dimensional hypervolumes. Therefore the segmentation is done jointly over all the images and coherence is imposed throughout the data. However, instead of propagating active hypersurfaces, we derive a semi-parametric methodology that takes into account the constraints imposed by the camera setup and the occlusion ordering. The resulting framework is a global multi-dimensional region competition that is consistent in all the images and efficiently handles occlusions. We show the validity of the approach with captured light fields. Other special effects such as augmented reality and disocclusion of hidden objects are also demonstrated

Shape from bandwidth: the 2-D orthogonal projection case

Could bandwidth—one of the most classic concepts in signal processing—have a new purpose? In this paper, we investigate the feasibility of using bandwidth to infer shape from a single image. As a first analysis, we limit our attention to orthographic projection and assume a 2-D world. We show that, under certain conditions, a single image of a surface, painted with a bandlimited texture, is enough to deduce the surface up to an equivalence class. This equivalence class is unavoidable, since it stems from surface transformations that are invisible to orthographic projections. A proof of concept algorithm is presented and tested with both a simulation and a simple practical experiment

Head Related Transfer Functions Interpolation Considering Acoustics

We are proposing an interpolation technique for head related transfer functions (HRTFs). For deriving the algorithm we study the dual problem where sound is emitted from the listener’s ear and the generated sound field is recorded along a circular array of microphones around the listener. The proposed interpolation algorithm is based on the observation that spatial bandwidth of the measured sound along the circular array is limited (for all practical purposes). Further, we observe that this spatial bandwidth increases linearly with the frequency of the emitted sound. The result of the analysis leads to the conclusion that the necessary angle between HRTFs is about 5 degrees in order to be able to reconstruct all HRTFs up to 44.1 kHz in the horizontal plane

The plenacoustic function and its applications

This thesis is a study of the spatial evolution of the sound field. We first present an analysis of the sound field along different geometries. In the case of the sound field studied along a line in a room, we describe a two-dimensional function characterizing the sound field along space and time. Calculating the Fourier transform of this function leads to a spectrum having a butterfly shape. The spectrum is shown to be almost bandlimited along the spatial frequency dimension, which allows the interpolation of the sound field at any position along the line when a sufficient number of microphones is present. Using this Fourier representation of the sound field, we develop a spatial sampling theorem trading off quality of reconstruction with spatial sampling frequency. The study is generalized for planes of microphones and microphones located in three dimensions. The presented theory is compared to simulations and real measurements of room impulse responses. We describe a similar theory for circular arrays of microphones or loudspeakers. Application of this theory is presented for the study of the angular sampling of head-related transfer functions (HRTFs). As a result, we show that to reconstruct HRTFs at any possible angle in the horizontal plane, an angular spacing of 5 degrees is necessary for HRTFs sampled at 44.1 kHz. Because recording that many HRTFs is not easy, we develop interpolation techniques to achieve acceptable results for databases containing two or four times fewer HRTFs. The technique is based on the decomposition of the HRTFs in their carrier and complex envelopes. With the Fourier representation of the sound field, it is then shown how one can correctly obtain all room impulse responses measured along a trajectory when using a moving loudspeaker or microphone. The presented method permits the reconstruction of the room impulse responses at any position along the trajectory, provided that the speed satisfies a given relation. The maximal speed is shown to be dependent on the maximal frequency emitted and the radius of the circle. This method takes into account the Doppler effect present when one element is moving in the scenario. It is then shown that the measurement of HRTFs in the horizontal plane can be achieved in less than one second. In the last part, we model spatio-temporal channel impulse responses between a fixed source and a moving receiver. The trajectory followed by the moving element is modeled as a continuous autoregressive process. The presented model is simple and versatile. It allows the generation of random trajectories with a controlled smoothness. Application of this study can be found in the modeling of acoustic channels for acoustic echo cancellation or of time-varying multipath electromagnetic channels used in mobile wireless communications

Recording, compression and representation of dense light fields

The concept of light fields allows image based capture of scenes, providing, on a recorded dataset, many of the features available in computer graphics, like simulation of different viewpoints, or change of core camera parameters, including depth of field. Due to the increase in the recorded dimension from two for a regular image to four for a light field recording, previous works mainly concentrate on small or undersampled light field recordings. This thesis is concerned with the recording of a dense light field dataset, including the estimation of suitable sampling parameters, as well as the implementation of the required capture, storage and processing methods. Towards this goal, the influence of an optical system on the, possibly bandunlimited, light field signal is examined, deriving the required sampling rates from the bandlimiting effects of the camera and optics. To increase storage capacity and bandwidth a very fast image compression methods is introduced, providing an order of magnitude faster compression than previous methods, reducing the I/O bottleneck for light field processing. A fiducial marker system is provided for the calibration of the recorded dataset, which provides a higher number of reference points than previous methods, improving camera pose estimation. In conclusion this work demonstrates the feasibility of dense sampling of a large light field, and provides a dataset which may be used for evaluation or as a reference for light field processing tasks like interpolation, rendering and sampling.Das Konzept des Lichtfelds erlaubt eine bildbasierte Erfassung von Szenen und ermöglicht es, auf den erfassten Daten viele Effekte aus der Computergrafik zu berechnen, wie das Simulieren alternativer Kamerapositionen oder die Veränderung zentraler Parameter, wie zum Beispiel der Tiefenschärfe. Aufgrund der enorm vergrößerte Datenmenge die für eine Aufzeichnung benötigt wird, da Lichtfelder im Vergleich zu den zwei Dimensionen herkömmlicher Kameras über vier Dimensionen verfügen, haben frühere Arbeiten sich vor allem mit kleinen oder unterabgetasteten Lichtfeldaufnahmen beschäftigt. Diese Arbeit hat das Ziel eine dichte Aufnahme eines Lichtfeldes vorzunehmen. Dies beinhaltet die Berechnung adäquater Abtastparameter, sowie die Implementierung der benötigten Aufnahme-, Verarbeitungs- und Speicherprozesse. In diesem Zusammenhang werden die bandlimitierenden Effekte des optischen Aufnahmesystems auf das möglicherweise nicht bandlimiterte Signal des Lichtfeldes untersucht und die benötigten Abtastraten davon abgeleitet. Um die Bandbreite und Kapazität des Speichersystems zu erhöhen wird ein neues, extrem schnelles Verfahren der Bildkompression eingeführt, welches um eine Größenordnung schneller operiert als bisherige Methoden. Für die Kalibrierung der Kamerapositionen des aufgenommenen Datensatzes wird ein neues System von sich selbst identifizierenden Passmarken vorgestellt, welches im Vergleich zu früheren Methoden mehr Referenzpunkte auf gleichem Raum zu Verfügung stellen kann und so die Kamerakalibrierung verbessert. Kurz zusammengefasst demonstriert diese Arbeit die Durchführbarkeit der Aufnahme eines großen und dichten Lichtfeldes, und stellt einen entsprechenden Datensatz zu Verfügung. Der Datensatz ist geeignet als Referenz für die Untersuchung von Methoden zur Verarbeitung von Lichtfeldern, sowie für die Evaluation von Methoden zur Interpolation, zur Abtastung und zum Rendern

Super-resolution from unregistered aliased images

Aliasing in images is often considered as a nuisance. Artificial low frequency patterns and jagged edges appear when an image is sampled at a too low frequency. However, aliasing also conveys useful information about the high frequency content of the image, which is exploited in super-resolution applications. We use a set of input images of the same scene to extract such high frequency information and create a higher resolution aliasing-free image. Typically, there is a small shift or more complex motion between the different images, such that they contain slightly different information about the scene. Super-resolution image reconstruction can be formulated as a multichannel sampling problem with unknown offsets. This results in a set of equations that are linear in the unknown signal coefficients but nonlinear in the offsets. This thesis concentrates on the computation of these offsets, as they are an essential prerequisite for an accurate high resolution reconstruction. If a part of the image spectra is free of aliasing, the planar shift and rotation parameters can be computed using only this low frequency information. In such a case, the images can be registered pairwise to a reference image. Such a method is not applicable if the images are undersampled by a factor of two or larger. A higher number of images needs to be registered jointly. Two subspace methods are discussed for such highly aliased images. The first approach is based on a Fourier description of the aliased signals as a sum of overlapping parts of the spectrum. It uses a rank condition to find the correct offsets. The second one uses a more general expansion in an arbitrary Hilbert space to compute the signal offsets. The sampled signal is represented as a linear combination of sampled basis functions. The offsets are computed by projecting the signal onto varying subspaces. Under certain conditions, in particular for bandlimited signals, the nonlinear super-resolution equations can be written as a set of polynomial equations. Using Buchberger's algorithm, the solution can then be computed as a Gröbner basis for the corresponding polynomial ideal. After a description of a standard algorithm, adaptations are made for the use with noisy measurements. The techniques presented in this thesis are tested in simulations and practical experiments. The experiments are performed on sets of real images taken with a digital camera. The results show the validity of the algorithms: registration parameters are computed with subpixel precision, and aliasing is accurately removed from the resulting high resolution image. This thesis is produced according to the concepts of reproducible research. All the results and examples used in this thesis are reproducible using the code and data available online

On the bandlimitedness of the plenoptic function

Image based-rendering (IBR) can be seen as the sampling and reconstruction of the plenoptic function. The question of the minimum sampling rate in IBR can be addressed via spectral analysis of the plenoptic function. We study a model of the scene where bandlimited images are “painted” on surfaces (e.g. of objects or walls). We show that, in general, the plenoptic function is not bandlimited unless the surfaces are flat. We then characterize the spectral decay of the plenoptic function for this model. The value of the plenoptic function p(t, u, v, w) is the light intensity of the intersection of the light ray specified by (t, u, v, w) with the nearest object surface from the camera plane. u camera plane w image plane object surfac