Asynchrony Increases Efficiency: Time Encoding of Videos and Low-Rank Signals

In event-based sensing, many sensors independently and asynchronously emit events when there is a change in their input. Event-based sensing can present significant improvements in power efficiency when compared to traditional sampling, because (1) the output is a stream of events where the important information lies in the timing of the events, and (2) the sensor can easily be controlled to output information only when interesting activity occurs at the input. Moreover, event-based sampling can often provide better resolution than standard uniform sampling. Not only does this occur because individual event-based sensors have higher temporal resolution (Rebecq et al., 2021) it also occurs because the asynchrony of events within a sensor and therefore across sensors allows for less redundant and more informative encoding. We would like to explain how such curious results come about. To do so, we use ideal time encoding machines as a proxy for event-based sensors. We explore time encoding of signals with low rank structure, and apply the resulting theory to video. We then see how the asynchronous firing across time encoding machines can couple spatial sampling density with temporal resolution, leading to better reconstruction, whereas, in frame-based video, temporal resolution depends solely on the frame-rate and spatial resolution solely on the pixel grid used.

How Asynchronous Events Encode Video

Karen Adam, Adam James Scholefield, Martin Vetterli

As event-based sensing gains in popularity, theoretical understanding is needed to harness this technology’s potential. Instead of recording video by capturing frames, event-based cameras have sensors that emit events when their inputs change, thus encoding information in the timing of events. This creates new challenges in establishing reconstruction guarantees and algorithms, but also provides advantages over frame-based video. We use time encoding machines to model event-based sensors: TEMs also encode their inputs by emitting events characterized by their timing and reconstruction from time encodings is well understood. We consider the case of time encoding bandlimited video and demonstrate a dependence between spatial sensor density and overall spatial and temporal resolution. Such a dependence does not occur in frame-based video, where temporal resolution depends solely on the frame rate of the video and spatial resolution depends solely on the pixel grid. However, this dependence arises naturally in event-based video and allows oversampling in space to provide better time resolution. As such, event-based vision encourages using more sensors that emit fewer events over time.

IEEE2021

Super-resolution from unregistered aliased images

Patrick Vandewalle

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.

EPFL2006

Audio-Visual Fusion

Anna Llagostera Casanovas

The perception that we have about the world is influenced by elements of diverse nature. Indeed humans tend to integrate information coming from different sensory modalities to better understand their environment. Following this observation, scientists have been trying to combine different research domains. In particular, in joint audio-visual signal processing the information recorded with one or more video-cameras and one or more microphones is combined in order to extract more knowledge about a given scene than when analyzing each modality separately. In this thesis we attempt the fusion of audio and video modalities when considering one video-camera and one microphone. This is the most common configuration in electronic devices such as laptops and cellphones, and it does not require controlled environments such as previously prepared meeting rooms. Even though numerous approaches have been proposed in the last decade, the fusion of audio and video modalities is still an open problem. All the methods in this domain are based on an assumption of synchrony between related events in audio and video channels, i.e. the appearance of a sound is approximately synchronous with the movement of the image structure that has generated it. However, most approaches do not exploit the spatio-temporal consistency that characterizes video signals and, as a result, they assess the synchrony between single pixels and the soundtrack. The results that they obtain are thus sensitive to noise and the coherence between neighboring pixels is not ensured. This thesis presents two novel audio-visual fusion methods which follow completely different strategies to evaluate the synchrony between moving image structures and sounds. Each fusion method is successfully demonstrated on a different application in this domain. Our first audio-visual fusion approach is focused on the modeling of audio and video signals. We propose to decompose each modality into a small set of functions representing the structures that are inherent in the signals. The audio signal is decomposed into a set of atoms representing concentrations of energy in the spectrogram (sounds) and the video signal is concisely represented by a set of image structures evolving through time, i.e. changing their location, size or orientation. As a result, meaningful features can be easily defined for each modality, as the presence of a sound and the movement of a salient image structure. Finally, the fusion step simply evaluates the co-occurrence of these relevant events. This approach is applied to the blind detection and separation of the audio-visual sources that are present in a scene. In contrast, the second method that we propose uses basic features and it is more focused on the fusion strategy that combines them. This approach is based on a nonlinear diffusion procedure that progressively erodes a video sequence and converts it into an audio-visual video sequence, where only the information that is required in applications in the joint audio-visual domain is kept. For this purpose we define a diffusion coefficient that depends on the synchrony between video motion and audio energy and preserves regions moving coherently with the presence of sounds. Thus, the regions that are least diffused are likely to be part of the video modality of the audio-visual source, and the application of this fusion method to the unsupervised extraction of audio-visual objects is straightforward. Unlike many methods in this domain which are specific to speakers, the fusion methods that we present in this thesis are completely general and they can be applied to all kind of audio-visual sources. Furthermore, our analysis is not limited to one source at a time, i.e. all applications can deal with multiple simultaneous sources. Finally, this thesis tackles the audio-visual fusion problem from a novel perspective, by proposing creative fusion methods and techniques borrowed from other domains such as the blind source separation, nonlinear diffusion based on partial differential equations (PDE) and graph cut segmentation.