arXiv subjects

Guillermo Gallego

Publications and source records attributed to Guillermo Gallego.

At least 73 records · Page 4Linked to original sources

arXiv2021

The Refined Assortment Optimization Problem

We introduce the refined assortment optimization problem where a firm may decide to make some of its products harder to get instead of making them unavailable as in the traditional assortment optimization problem. Airlines, for example, offer fares with severe restrictions rather than making them unavailable. This is a more subtle way of handling the trade-off between demand induction and demand cannibalization. For the latent class MNL model, a firm that engages in refined assortment optimization can make up to $\min(n,m)$ times more than one that insists on traditional assortment optimization, where $n$ is the number of products and $m$ the number of customer types. Surprisingly, the revenue-ordered assortment heuristic has the same performance guarantees relative to {\em personalized} refined assortment optimization as it does to traditional assortment optimization. Based on this finding, we construct refinements of the revenue-order heuristic and measure their improved performance relative to the revenue-ordered assortment and the optimal traditional assortment optimization problem. We also provide tight bounds on the ratio of the expected revenues for the refined versus the traditional assortment optimization for some well known discrete choice models.

econ.TH↗

arXiv2020

Event-based Vision: A Survey

Event cameras are bio-inspired sensors that differ from conventional frame cameras: Instead of capturing images at a fixed rate, they asynchronously measure per-pixel brightness changes, and output a stream of events that encode the time, location and sign of the brightness changes. Event cameras offer attractive properties compared to traditional cameras: high temporal resolution (in the order of microseconds), very high dynamic range (140 dB vs. 60 dB), low power consumption, and high pixel bandwidth (on the order of kHz) resulting in reduced motion blur. Hence, event cameras have a large potential for robotics and computer vision in challenging scenarios for traditional cameras, such as low-latency, high speed, and high dynamic range. However, novel methods are required to process the unconventional output of these sensors in order to unlock their potential. This paper provides a comprehensive overview of the emerging field of event-based vision, with a focus on the applications and the algorithms developed to unlock the outstanding properties of event cameras. We present event cameras from their working principle, the actual sensors that are available and the tasks that they have been used for, from low-level vision (feature detection and tracking, optic flow, etc.) to high-level vision (reconstruction, segmentation, recognition). We also discuss the techniques developed to process events, including learning-based techniques, as well as specialized processors for these novel sensors, such as spiking neural networks. Additionally, we highlight the challenges that remain to be tackled and the opportunities that lie ahead in the search for a more efficient, bio-inspired way for machines to perceive and interact with the world.

cs.CV↗

arXiv2020

Sensor Artificial Intelligence and its Application to Space Systems -- A White Paper

Information and communication technologies have accompanied our everyday life for years. A steadily increasing number of computers, cameras, mobile devices, etc. generate more and more data, but at the same time we realize that the data can only partially be analyzed with classical approaches. The research and development of methods based on artificial intelligence (AI) made enormous progress in the area of interpretability of data in recent years. With growing experience, both, the potential and limitations of these new technologies are increasingly better understood. Typically, AI approaches start with the data from which information and directions for action are derived. However, the circumstances under which such data are collected and how they change over time are rarely considered. A closer look at the sensors and their physical properties within AI approaches will lead to more robust and widely applicable algorithms. This holistic approach which considers entire signal chains from the origin to a data product, "Sensor AI", is a highly relevant topic with great potential. It will play a decisive role in autonomous driving as well as in areas of automated production, predictive maintenance or space research. The goal of this white paper is to establish "Sensor AI" as a dedicated research topic. We want to exchange knowledge on the current state-of-the-art on Sensor AI, to identify synergies among research groups and thus boost the collaboration in this key technology for science and industry.

cs.CY↗

arXiv2020

Nonparametric Pricing Analytics with Customer Covariates

Personalized pricing analytics is becoming an essential tool in retailing. Upon observing the personalized information of each arriving customer, the firm needs to set a price accordingly based on the covariates such as income, education background, past purchasing history to extract more revenue. For new entrants of the business, the lack of historical data may severely limit the power and profitability of personalized pricing. We propose a nonparametric pricing policy to simultaneously learn the preference of customers based on the covariates and maximize the expected revenue over a finite horizon. The policy does not depend on any prior assumptions on how the personalized information affects consumers' preferences (such as linear models). It is adaptively splits the covariate space into smaller bins (hyper-rectangles) and clusters customers based on their covariates and preferences, offering similar prices for customers who belong to the same cluster trading off granularity and accuracy. We show that the algorithm achieves a regret of order $O(\log(T)^2 T^{(2+d)/(4+d)})$, where $T$ is the length of the horizon and $d$ is the dimension of the covariate. It improves the current regret in the literature \citep{slivkins2014contextual}, under mild technical conditions in the pricing context (smoothness and local concavity). We also prove that no policy can achieve a regret less than $O(T^{(2+d)/(4+d)})$ for a particular instance and thus demonstrate the near optimality of the proposed policy.

cs.LG↗

arXiv2019

Event-Based Motion Segmentation by Motion Compensation

In contrast to traditional cameras, whose pixels have a common exposure time, event-based cameras are novel bio-inspired sensors whose pixels work independently and asynchronously output intensity changes (called "events"), with microsecond resolution. Since events are caused by the apparent motion of objects, event-based cameras sample visual information based on the scene dynamics and are, therefore, a more natural fit than traditional cameras to acquire motion, especially at high speeds, where traditional cameras suffer from motion blur. However, distinguishing between events caused by different moving objects and by the camera's ego-motion is a challenging task. We present the first per-event segmentation method for splitting a scene into independently moving objects. Our method jointly estimates the event-object associations (i.e., segmentation) and the motion parameters of the objects (or the background) by maximization of an objective function, which builds upon recent results on event-based motion-compensation. We provide a thorough evaluation of our method on a public dataset, outperforming the state-of-the-art by as much as 10%. We also show the first quantitative evaluation of a segmentation algorithm for event cameras, yielding around 90% accuracy at 4 pixels relative displacement.

cs.CV↗

arXiv2019

Focus Is All You Need: Loss Functions For Event-based Vision

Event cameras are novel vision sensors that output pixel-level brightness changes ("events") instead of traditional video frames. These asynchronous sensors offer several advantages over traditional cameras, such as, high temporal resolution, very high dynamic range, and no motion blur. To unlock the potential of such sensors, motion compensation methods have been recently proposed. We present a collection and taxonomy of twenty two objective functions to analyze event alignment in motion compensation approaches (Fig. 1). We call them Focus Loss Functions since they have strong connections with functions used in traditional shape-from-focus applications. The proposed loss functions allow bringing mature computer vision tools to the realm of event cameras. We compare the accuracy and runtime performance of all loss functions on a publicly available dataset, and conclude that the variance, the gradient and the Laplacian magnitudes are among the best loss functions. The applicability of the loss functions is shown on multiple tasks: rotational motion, depth and optical flow estimation. The proposed focus loss functions allow to unlock the outstanding properties of event cameras.

cs.CV↗

arXiv2018

Asynchronous, Photometric Feature Tracking using Events and Frames

We present a method that leverages the complementarity of event cameras and standard cameras to track visual features with low-latency. Event cameras are novel sensors that output pixel-level brightness changes, called "events". They offer significant advantages over standard cameras, namely a very high dynamic range, no motion blur, and a latency in the order of microseconds. However, because the same scene pattern can produce different events depending on the motion direction, establishing event correspondences across time is challenging. By contrast, standard cameras provide intensity measurements (frames) that do not depend on motion direction. Our method extracts features on frames and subsequently tracks them asynchronously using events, thereby exploiting the best of both types of data: the frames provide a photometric representation that does not depend on motion direction and the events provide low-latency updates. In contrast to previous works, which are based on heuristics, this is the first principled method that uses raw intensity measurements directly, based on a generative event model within a maximum-likelihood framework. As a result, our method produces feature tracks that are both more accurate (subpixel accuracy) and longer than the state of the art, across a wide variety of scenes.

cs.CV↗

arXiv2018

Semi-Dense 3D Reconstruction with a Stereo Event Camera

Event cameras are bio-inspired sensors that offer several advantages, such as low latency, high-speed and high dynamic range, to tackle challenging scenarios in computer vision. This paper presents a solution to the problem of 3D reconstruction from data captured by a stereo event-camera rig moving in a static scene, such as in the context of stereo Simultaneous Localization and Mapping. The proposed method consists of the optimization of an energy function designed to exploit small-baseline spatio-temporal consistency of events triggered across both stereo image planes. To improve the density of the reconstruction and to reduce the uncertainty of the estimation, a probabilistic depth-fusion strategy is also developed. The resulting method has no special requirements on either the motion of the stereo event-camera rig or on prior knowledge about the scene. Experiments demonstrate our method can deal with both texture-rich scenes as well as sparse scenes, outperforming state-of-the-art stereo methods based on event data image representations.

cs.CV↗

arXiv2018

Continuous-Time Visual-Inertial Odometry for Event Cameras

Event cameras are bio-inspired vision sensors that output pixel-level brightness changes instead of standard intensity frames. They offer significant advantages over standard cameras, namely a very high dynamic range, no motion blur, and a latency in the order of microseconds. However, due to the fundamentally different structure of the sensor's output, new algorithms that exploit the high temporal resolution and the asynchronous nature of the sensor are required. Recent work has shown that a continuous-time representation of the event camera pose can deal with the high temporal resolution and asynchronous nature of this sensor in a principled way. In this paper, we leverage such a continuous-time representation to perform visual-inertial odometry with an event camera. This representation allows direct integration of the asynchronous events with micro-second accuracy and the inertial measurements at high frequency. The event camera trajectory is approximated by a smooth curve in the space of rigid-body motions using cubic splines. This formulation significantly reduces the number of variables in trajectory estimation problems. We evaluate our method on real data from several scenes and compare the results against ground truth from a motion-capture system. We show that our method provides improved accuracy over the result of a state-of-the-art visual odometry method for event cameras. We also show that both the map orientation and scale can be recovered accurately by fusing events and inertial data. To the best of our knowledge, this is the first work on visual-inertial fusion with event cameras using a continuous-time framework.

cs.RO↗

arXiv2018

A Unifying Contrast Maximization Framework for Event Cameras, with Applications to Motion, Depth, and Optical Flow Estimation

We present a unifying framework to solve several computer vision problems with event cameras: motion, depth and optical flow estimation. The main idea of our framework is to find the point trajectories on the image plane that are best aligned with the event data by maximizing an objective function: the contrast of an image of warped events. Our method implicitly handles data association between the events, and therefore, does not rely on additional appearance information about the scene. In addition to accurately recovering the motion parameters of the problem, our framework produces motion-corrected edge-like images with high dynamic range that can be used for further scene analysis. The proposed method is not only simple, but more importantly, it is, to the best of our knowledge, the first method that can be successfully applied to such a diverse set of important vision tasks with event cameras.

cs.CV↗

arXiv2018

Event-based Vision meets Deep Learning on Steering Prediction for Self-driving Cars

Event cameras are bio-inspired vision sensors that naturally capture the dynamics of a scene, filtering out redundant information. This paper presents a deep neural network approach that unlocks the potential of event cameras on a challenging motion-estimation task: prediction of a vehicle's steering angle. To make the best out of this sensor-algorithm combination, we adapt state-of-the-art convolutional architectures to the output of event sensors and extensively evaluate the performance of our approach on a publicly available large scale event-camera dataset (~1000 km). We present qualitative and quantitative explanations of why event cameras allow robust steering prediction even in cases where traditional cameras fail, e.g. challenging illumination conditions and fast motion. Finally, we demonstrate the advantages of leveraging transfer learning from traditional to event-based vision, and show that our approach outperforms state-of-the-art algorithms based on standard cameras.

cs.CV↗

arXiv2017

Translation of "Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung" by Erwin Kruppa (1913)

Erwin Kruppa's 1913 paper, Erwin Kruppa, "Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung", Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Kaiserlichen Akademie der Wissenschaften, Vol. 122 (1913), pp. 1939-1948, which may be translated as "To determine a 3D object from two perspective views with known inner orientation", is a landmark paper in Computer Vision because it provides the first five-point algorithm for relative pose estimation. Kruppa showed that (a finite number of solutions for) the relative pose between two calibrated images of a rigid object can be computed from five point matches between the images. Kruppa's work also gained attention in the topic of camera self-calibration, as presented in (Maybank and Faugeras, 1992). Since the paper is still relevant today (more than a hundred citations within the last ten years) and the paper is not available online, we ordered a copy from the German National Library in Frankfurt and provide an English translation along with the German original. We also adapt the terminology to a modern jargon and provide some clarifications (highlighted in sans-serif font). For a historical review of geometric computer vision, the reader is referred to the recent survey paper (Sturm, 2011).

cs.CV↗

arXiv2017

The Event-Camera Dataset and Simulator: Event-based Data for Pose Estimation, Visual Odometry, and SLAM

New vision sensors, such as the Dynamic and Active-pixel Vision sensor (DAVIS), incorporate a conventional global-shutter camera and an event-based sensor in the same pixel array. These sensors have great potential for high-speed robotics and computer vision because they allow us to combine the benefits of conventional cameras with those of event-based sensors: low latency, high temporal resolution, and very high dynamic range. However, new algorithms are required to exploit the sensor characteristics and cope with its unconventional output, which consists of a stream of asynchronous brightness changes (called "events") and synchronous grayscale frames. For this purpose, we present and release a collection of datasets captured with a DAVIS in a variety of synthetic and real environments, which we hope will motivate research on new algorithms for high-speed and high-dynamic-range robotics and computer-vision applications. In addition to global-shutter intensity images and asynchronous events, we provide inertial measurements and ground-truth camera poses from a motion-capture system. The latter allows comparing the pose accuracy of ego-motion estimation algorithms quantitatively. All the data are released both as standard text files and binary files (i.e., rosbag). This paper provides an overview of the available data and describes a simulator that we release open-source to create synthetic event-camera data.

cs.RO↗

arXiv2017

Event-based, 6-DOF Camera Tracking from Photometric Depth Maps

Event cameras are bio-inspired vision sensors that output pixel-level brightness changes instead of standard intensity frames. These cameras do not suffer from motion blur and have a very high dynamic range, which enables them to provide reliable visual information during high-speed motions or in scenes characterized by high dynamic range. These features, along with a very low power consumption, make event cameras an ideal complement to standard cameras for VR/AR and video game applications. With these applications in mind, this paper tackles the problem of accurate, low-latency tracking of an event camera from an existing photometric depth map (i.e., intensity plus depth information) built via classic dense reconstruction pipelines. Our approach tracks the 6-DOF pose of the event camera upon the arrival of each event, thus virtually eliminating latency. We successfully evaluate the method in both indoor and outdoor scenes and show that---because of the technological advantages of the event camera---our pipeline works in scenes characterized by high-speed motion, which are still unaccessible to standard cameras.

cs.CV↗

arXiv2015

Online Resource Allocation with Customer Choice

We introduce a general model of resource allocation with customer choice. In this model, there are multiple resources that are available over a finite horizon. The resources are non-replenishable and perishable. Each unit of a resource can be instantly made into one of several products. There are multiple customer types arriving randomly over time. An assortment of products must be offered to each arriving customer, depending on the type of the customer, the time of arrival, and the remaining inventory. From this assortment, the customer selects a product according to a general choice model. The selection generates a product-dependent and customer-type-dependent reward. The objective of the system is to maximize the total expected reward earned over the horizon. The above problem has a number of applications, including personalized assortment optimization, revenue management of parallel flights, and web- and mobile-based appointment scheduling. We derive online algorithms that are asymptotically optimal and achieve the best constant relative performance guarantees for this class of problems.

math.OC↗

arXiv2015

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

math.OC↗

arXiv2015

Event-based Camera Pose Tracking using a Generative Event Model

Event-based vision sensors mimic the operation of biological retina and they represent a major paradigm shift from traditional cameras. Instead of providing frames of intensity measurements synchronously, at artificially chosen rates, event-based cameras provide information on brightness changes asynchronously, when they occur. Such non-redundant pieces of information are called "events". These sensors overcome some of the limitations of traditional cameras (response time, bandwidth and dynamic range) but require new methods to deal with the data they output. We tackle the problem of event-based camera localization in a known environment, without additional sensing, using a probabilistic generative event model in a Bayesian filtering framework. Our main contribution is the design of the likelihood function used in the filter to process the observed events. Based on the physical characteristics of the sensor and on empirical evidence of the Gaussian-like distribution of spiked events with respect to the brightness change, we propose to use the contrast residual as a measure of how well the estimated pose of the event-based camera and the environment explain the observed events. The filter allows for localization in the general case of six degrees-of-freedom motions.

cs.CV↗

arXiv2014

A compact formula for the derivative of a 3-D rotation in exponential coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

cs.CV↗