This talk reviews differential equations on manifolds of matrices or tensors of low rank. They serve to approximate, in a low-rank format, large time-dependent matrices and tensors that are either given explicitly via their increments or are unknown solutions of differential equations. Furthermore, low-rank differential equations are used in novel algorithms for eigenvalue optimisation, for instance in robust-stability problems.
Organizers: Philipp Hennig
Glasses, lacking the order of crystals, are in many ways still regarded as poorly understood. Yet glasses, lacking the complications of different crystallographic symmetries, also show some remarkable correlations of diverse properties.
This talk shows how embedded optimization - i.e. autonomous optimization algorithms receiving data, solving problems, and sending answers continuously - are able to address challenging control problems. When nonlinear differential equation models are used to predict and optimize future system behaviour, one speaks of Nonlinear Model Predictive Control (NMPC).The talk presents experimental applications of NMPC to time and energy optimal control of mechatronic systems and discusses some of the algorithmic tricks that make NMPC optimization rates up to 1 MHz possible. Finally, we present on particular challenging application, tethered flight for airborne wind energy systems.
Organizers: Sebastian Trimpe
The goal of lifelong visual learning is to develop techniques that continuously and autonomously learn from visual data, potentially for years or decades. During this time the system should build an ever-improving base of generic visual information, and use it as background knowledge and context for solving specific computer vision tasks. In my talk, I will highlight two recent results from our group on the road towards lifelong visual scene understanding: the derivation of theoretical guarantees for lifelong learning systems and the development of practical methods for object categorization based on semantic attributes.
Organizers: Gerard Pons-Moll
Point-light walkers and stick figures rendered orthographically and without self-occlusion do not contain any information as to their depth. For instance, a frontoparallel projection could depict a walker from the front or from the back. Nevertheless, observers show a strong bias towards seeing the walker as facing the viewer. A related stimulus, the silhouette of a human figure, does not seem to show such a bias. We develop these observations into a tool to study the cause of the facing the viewer bias observed for biological motion displays.
I will give a short overview about existing theories with respect to the facing-the-viewer bias, and about a number of findings that seem hard to explain with any single one of them. I will then present the results of our studies on both stick figures and silhouettes which gave rise to a new theory about the facing the viewer bias, and I will eventually present an experiment that tests a hypothesis resulting from it. The studies are discussed in the context of one of the most general problems the visual system has to solve: How do we disambiguate an initially ambiguous sensory world and eventually arrive at the perception of a stable, predictable "reality"?
Compared to static image segmentation, video segmentation is still in its infancy. Various research groups have different tasks in mind when they talk of video segmentation. For some it is motion segmentation, some think of an over-segmentation with thousands of regions per video, and others understand video segmentation as contour tracking. I will go through what I think are reasonable video segmentation subtasks and will touch the issue of benchmarking. I will also discuss the difference between image and video segmentation. Due to the availability of motion and the redundancy of successive frames, video segmentation should actually be easier than image segmentation. However, recent evidence indicates the opposite: at least at the level of superpixel segmentation, image segmentation methodology is more advanced than what can be found in the video segmentation literature.
Organizers: Gerard Pons-Moll
In the first part of our talk, we present an approach for large displacement optical flow. Optical flow computation is a key component in many computer vision systems designed for tasks such as action
detection or activity recognition. Inspired by the large displacement optical flow of Brox and Malik, our approach DeepFlow combines a novel matching algorithm with a variational approach . Our matching algorithm builds upon a multi-stage architecture interleaving convolutions and max-pooling. DeepFlow efficiently handles large displacements occurring in realistic videos, and shows competitive performance on optical flow benchmarks.
In the second part of our talk, we present a state-of-the-art approach for action recognition based on motion stabilized trajectory descriptors and a Fisher vector representation. We briefly review the recent trajectory-based video features and, then, introduce their motion stabilized version, combining human detection and dominant motion estimation. Fisher vectors summarize the information of a video efficiently. Results on several of the recent action datasets as well as the TrecVid MED dataset show that our approach outperforms the state-of-the-art
Computer vision problems often involve optimization of two quantities, one of which is time. Such problems can be formulated as time-constrained optimization or performance-constrained search for the fastest algorithm. We show that it is possible to obtain quasi-optimal time-constrained solutions to some vision problems by applying Wald's theory of sequential decision-making. Wald assumes independence of observation, which is rarely true in computer vision. We address the problem by combining Wald's sequential probability ratio test and AdaBoost. The solution, called the WaldBoost, can be viewed as a principled way to build a close-to-optimal “cascade of classifiers” of the Viola-Jones type. The approach will be demonstrated on four tasks: (i) face detection, (ii) establishing reliable correspondences between image, (iii) real-time detection of interest points and (iv) model search and outlier detection using RANSAC. In the face detection problem, the objective is learning the fastest detector satisfying constraints on false positive and false negative rates. The correspondence pruning addresses the problem of fast selection with a predefined false negative rated. In interest point problem we show how a fast implementation of known detectors can obtained by Waldboost. The “mimicked” detectors provide a training set of positive and negative examples of interest ponts and WaldBoost learns a detector, (significantly) faster than the providers of the training set, formed as a linear combination of efficiently computable feature. In RANSAC, we show how to exploit Wald's test in a randomised model verification procedure to obtain an algorithm significantly faster than deterministic verification yet with equivalent probabilistic guarantees of correctness.
Organizers: Gerard Pons-Moll
Stereo matching -- establishing correspondences between images taken from nearby viewpoints -- is one of the oldest problems in computer vision. While impressive progress has been made over the last two decades, most current stereo methods do not scale to the high-resolution images taken by today's cameras since they require searching the full space of all possible disparity hypotheses over all pixels.
In this talk I will describe a new scalable stereo method that only evaluates a small portion of the search space. The method first generates plane hypotheses from matched sparse features, which are then refined into surface hypotheses using local slanted plane sweeps over a narrow disparity range. Finally, each pixel is assigned to one of the local surface hypotheses. The technique achieves significant speedups over previous algorithms and achieves state-of-the-art accuracy on high-resolution stereo pairs of up to 19 megapixels.
I will also present a new dataset of high-resolution stereo pairs with subpixel-accurate ground truth, and provide a brief outlook on the upcoming new version of the Middlebury stereo benchmark.
Gaussian process regression is a non-parametric Bayesian machine learning paradigm, where instead of estimating parameters of fixed-form functions, we model the whole unknown functions as Gaussian processes. Gaussian processes are also commonly used for representing uncertainties in models of dynamic systems in many applications such as tracking, navigation, and automatic control systems. The latter models are often formulated as state-space models, where the use of non-linear Kalman filter type of methods is common. The aim of this talk is to discuss connections of Kalman filtering methods and Gaussian process regression. In particular, I discuss representations of Gaussian processes as state-space models, which enable the use of computationally efficient Kalman-filter-based (or more general Bayesian-filter-based) solutions to Gaussian process regression problems. This also allows for computationally efficient inference in latent force models (LFM), which are models combining first-principles mechanical models with non-parametric Gaussian process regression models.
Organizers: Philipp Hennig