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2019


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Decoding subcategories of human bodies from both body- and face-responsive cortical regions

Foster, C., Zhao, M., Romero, J., Black, M. J., Mohler, B. J., Bartels, A., Bülthoff, I.

NeuroImage, 202(15):116085, November 2019 (article)

Abstract
Our visual system can easily categorize objects (e.g. faces vs. bodies) and further differentiate them into subcategories (e.g. male vs. female). This ability is particularly important for objects of social significance, such as human faces and bodies. While many studies have demonstrated category selectivity to faces and bodies in the brain, how subcategories of faces and bodies are represented remains unclear. Here, we investigated how the brain encodes two prominent subcategories shared by both faces and bodies, sex and weight, and whether neural responses to these subcategories rely on low-level visual, high-level visual or semantic similarity. We recorded brain activity with fMRI while participants viewed faces and bodies that varied in sex, weight, and image size. The results showed that the sex of bodies can be decoded from both body- and face-responsive brain areas, with the former exhibiting more consistent size-invariant decoding than the latter. Body weight could also be decoded in face-responsive areas and in distributed body-responsive areas, and this decoding was also invariant to image size. The weight of faces could be decoded from the fusiform body area (FBA), and weight could be decoded across face and body stimuli in the extrastriate body area (EBA) and a distributed body-responsive area. The sex of well-controlled faces (e.g. excluding hairstyles) could not be decoded from face- or body-responsive regions. These results demonstrate that both face- and body-responsive brain regions encode information that can distinguish the sex and weight of bodies. Moreover, the neural patterns corresponding to sex and weight were invariant to image size and could sometimes generalize across face and body stimuli, suggesting that such subcategorical information is encoded with a high-level visual or semantic code.

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paper pdf DOI [BibTex]

2019


paper pdf DOI [BibTex]


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Active Perception based Formation Control for Multiple Aerial Vehicles

Tallamraju, R., Price, E., Ludwig, R., Karlapalem, K., Bülthoff, H. H., Black, M. J., Ahmad, A.

IEEE Robotics and Automation Letters, Robotics and Automation Letters, IEEE, August 2019 (article) Accepted

Abstract
We present a novel robotic front-end for autonomous aerial motion-capture (mocap) in outdoor environments. In previous work, we presented an approach for cooperative detection and tracking (CDT) of a subject using multiple micro-aerial vehicles (MAVs). However, it did not ensure optimal view-point configurations of the MAVs to minimize the uncertainty in the person's cooperatively tracked 3D position estimate. In this article, we introduce an active approach for CDT. In contrast to cooperatively tracking only the 3D positions of the person, the MAVs can actively compute optimal local motion plans, resulting in optimal view-point configurations, which minimize the uncertainty in the tracked estimate. We achieve this by decoupling the goal of active tracking into a quadratic objective and non-convex constraints corresponding to angular configurations of the MAVs w.r.t. the person. We derive this decoupling using Gaussian observation model assumptions within the CDT algorithm. We preserve convexity in optimization by embedding all the non-convex constraints, including those for dynamic obstacle avoidance, as external control inputs in the MPC dynamics. Multiple real robot experiments and comparisons involving 3 MAVs in several challenging scenarios are presented.

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pdf Project Page [BibTex]

pdf Project Page [BibTex]


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Learning and Tracking the 3D Body Shape of Freely Moving Infants from RGB-D sequences

Hesse, N., Pujades, S., Black, M., Arens, M., Hofmann, U., Schroeder, S.

Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2019 (article)

Abstract
Statistical models of the human body surface are generally learned from thousands of high-quality 3D scans in predefined poses to cover the wide variety of human body shapes and articulations. Acquisition of such data requires expensive equipment, calibration procedures, and is limited to cooperative subjects who can understand and follow instructions, such as adults. We present a method for learning a statistical 3D Skinned Multi-Infant Linear body model (SMIL) from incomplete, low-quality RGB-D sequences of freely moving infants. Quantitative experiments show that SMIL faithfully represents the RGB-D data and properly factorizes the shape and pose of the infants. To demonstrate the applicability of SMIL, we fit the model to RGB-D sequences of freely moving infants and show, with a case study, that our method captures enough motion detail for General Movements Assessment (GMA), a method used in clinical practice for early detection of neurodevelopmental disorders in infants. SMIL provides a new tool for analyzing infant shape and movement and is a step towards an automated system for GMA.

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pdf Journal DOI [BibTex]

pdf Journal DOI [BibTex]


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Perceptual Effects of Inconsistency in Human Animations

Kenny, S., Mahmood, N., Honda, C., Black, M. J., Troje, N. F.

ACM Trans. Appl. Percept., 16(1):2:1-2:18, Febuary 2019 (article)

Abstract
The individual shape of the human body, including the geometry of its articulated structure and the distribution of weight over that structure, influences the kinematics of a person’s movements. How sensitive is the visual system to inconsistencies between shape and motion introduced by retargeting motion from one person onto the shape of another? We used optical motion capture to record five pairs of male performers with large differences in body weight, while they pushed, lifted, and threw objects. From these data, we estimated both the kinematics of the actions as well as the performer’s individual body shape. To obtain consistent and inconsistent stimuli, we created animated avatars by combining the shape and motion estimates from either a single performer or from different performers. Using these stimuli we conducted three experiments in an immersive virtual reality environment. First, a group of participants detected which of two stimuli was inconsistent. Performance was very low, and results were only marginally significant. Next, a second group of participants rated perceived attractiveness, eeriness, and humanness of consistent and inconsistent stimuli, but these judgements of animation characteristics were not affected by consistency of the stimuli. Finally, a third group of participants rated properties of the objects rather than of the performers. Here, we found strong influences of shape-motion inconsistency on perceived weight and thrown distance of objects. This suggests that the visual system relies on its knowledge of shape and motion and that these components are assimilated into an altered perception of the action outcome. We propose that the visual system attempts to resist inconsistent interpretations of human animations. Actions involving object manipulations present an opportunity for the visual system to reinterpret the introduced inconsistencies as a change in the dynamics of an object rather than as an unexpected combination of body shape and body motion.

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publisher pdf DOI [BibTex]

publisher pdf DOI [BibTex]


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Spatial Continuity Effect vs. Spatial Contiguity Failure. Revising the Effects of Spatial Proximity Between Related and Unrelated Representations

Beege, M., Wirzberger, M., Nebel, S., Schneider, S., Schmidt, N., Rey, G. D.

Frontiers in Education, 4:86, 2019 (article)

Abstract
The split-attention effect refers to learning with related representations in multimedia. Spatial proximity and integration of these representations are crucial for learning processes. The influence of varying amounts of proximity between related and unrelated information has not yet been specified. In two experiments (N1 = 98; N2 = 85), spatial proximity between a pictorial presentation and text labels was manipulated (high vs. medium vs. low). Additionally, in experiment 1, a control group with separated picture and text presentation was implemented. The results revealed a significant effect of spatial proximity on learning performance. In contrast to previous studies, the medium condition leads to the highest transfer, and in experiment 2, the highest retention score. These results are interpreted considering cognitive load and instructional efficiency. Findings indicate that transfer efficiency is optimal at a medium distance between representations in experiment 1. Implications regarding the spatial contiguity principle and the spatial contiguity failure are discussed.

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link (url) DOI [BibTex]


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The Virtual Caliper: Rapid Creation of Metrically Accurate Avatars from 3D Measurements

Pujades, S., Mohler, B., Thaler, A., Tesch, J., Mahmood, N., Hesse, N., Bülthoff, H. H., Black, M. J.

IEEE Transactions on Visualization and Computer Graphics, 25, pages: 1887,1897, IEEE, 2019 (article)

Abstract
Creating metrically accurate avatars is important for many applications such as virtual clothing try-on, ergonomics, medicine, immersive social media, telepresence, and gaming. Creating avatars that precisely represent a particular individual is challenging however, due to the need for expensive 3D scanners, privacy issues with photographs or videos, and difficulty in making accurate tailoring measurements. We overcome these challenges by creating “The Virtual Caliper”, which uses VR game controllers to make simple measurements. First, we establish what body measurements users can reliably make on their own body. We find several distance measurements to be good candidates and then verify that these are linearly related to 3D body shape as represented by the SMPL body model. The Virtual Caliper enables novice users to accurately measure themselves and create an avatar with their own body shape. We evaluate the metric accuracy relative to ground truth 3D body scan data, compare the method quantitatively to other avatar creation tools, and perform extensive perceptual studies. We also provide a software application to the community that enables novices to rapidly create avatars in fewer than five minutes. Not only is our approach more rapid than existing methods, it exports a metrically accurate 3D avatar model that is rigged and skinned.

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Project Page IEEE Open Access IEEE Open Access PDF DOI [BibTex]

Project Page IEEE Open Access IEEE Open Access PDF DOI [BibTex]


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Doing more with less: Meta-reasoning and meta-learning in humans and machines

Griffiths, T., Callaway, F., Chang, M., Grant, E., Krueger, P. M., Lieder, F.

Current Opinion in Behavioral Sciences, 2019 (article)

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DOI [BibTex]

DOI [BibTex]


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Cognitive Prostheses for Goal Achievement

Lieder, F., Chen, O. X., Krueger, P. M., Griffiths, T.

Nature Human Behavior, 2019 (article)

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DOI [BibTex]

DOI [BibTex]


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Effects of system response delays on elderly humans’ cognitive performance in a virtual training scenario

Wirzberger, M., Schmidt, R., Georgi, M., Hardt, W., Brunnett, G., Rey, G. D.

Scientific Reports, 9:8291, 2019 (article)

Abstract
Observed influences of system response delay in spoken human-machine dialogues are rather ambiguous and mainly focus on perceived system quality. Studies that systematically inspect effects on cognitive performance are still lacking, and effects of individual characteristics are also often neglected. Building on benefits of cognitive training for decelerating cognitive decline, this Wizard-of-Oz study addresses both issues by testing 62 elderly participants in a dialogue-based memory training with a virtual agent. Participants acquired the method of loci with fading instructional guidance and applied it afterward to memorizing and recalling lists of German nouns. System response delays were randomly assigned, and training performance was included as potential mediator. Participants’ age, gender, and subscales of affinity for technology (enthusiasm, competence, positive and negative perception of technology) were inspected as potential moderators. The results indicated positive effects on recall performance with higher training performance, female gender, and less negative perception of technology. Additionally, memory retention and facets of affinity for technology moderated increasing system response delays. Participants also provided higher ratings in perceived system quality with higher enthusiasm for technology but reported increasing frustration with a more positive perception of technology. Potential explanations and implications for the design of spoken dialogue systems are discussed.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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A meta-analysis of the segmenting effect

Rey, G. D., Beege, M., Nebel, S., Wirzberger, M., Schmitt, T., Schneider, S.

Educational Psychology Review, 2019 (article)

Abstract
The segmenting effect states that people learn better when multimedia instructions are presented in (meaningful and coherent) learner-paced segments, rather than as continuous units. This meta-analysis contains 56 investigations including 88 pairwise comparisons and reveals a significant segmenting effect with small to medium effects for retention and transfer performance. Segmentation also reduces the overall cognitive load and increases learning time. These four effects are confirmed for a system-paced segmentation. The meta-analysis tests different explanations for the segmenting effect that concern facilitating chunking and structuring due to segmenting the multimedia instruction by the instructional designer, providing more time for processing the instruction and allowing the learners to adapt the presentation pace to their individual needs. Moderation analyses indicate that learners with high prior knowledge benefitted more from segmenting instructional material than learners with no or low prior knowledge in terms of retention performance.

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DOI [BibTex]

DOI [BibTex]


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A rational reinterpretation of dual process theories

Milli, S., Lieder, F., Griffiths, T.

2019 (article)

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DOI [BibTex]

DOI [BibTex]


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Probabilistic Linear Solvers: A Unifying View

Bartels, S., Cockayne, J., Ipsen, I. C. F., Hennig, P.

Statistics and Computing, 2019 (article) Accepted

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link (url) [BibTex]

link (url) [BibTex]

2018


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Deep Inertial Poser: Learning to Reconstruct Human Pose from Sparse Inertial Measurements in Real Time

Huang, Y., Kaufmann, M., Aksan, E., Black, M. J., Hilliges, O., Pons-Moll, G.

ACM Transactions on Graphics, (Proc. SIGGRAPH Asia), 37, pages: 185:1-185:15, ACM, November 2018, Two first authors contributed equally (article)

Abstract
We demonstrate a novel deep neural network capable of reconstructing human full body pose in real-time from 6 Inertial Measurement Units (IMUs) worn on the user's body. In doing so, we address several difficult challenges. First, the problem is severely under-constrained as multiple pose parameters produce the same IMU orientations. Second, capturing IMU data in conjunction with ground-truth poses is expensive and difficult to do in many target application scenarios (e.g., outdoors). Third, modeling temporal dependencies through non-linear optimization has proven effective in prior work but makes real-time prediction infeasible. To address this important limitation, we learn the temporal pose priors using deep learning. To learn from sufficient data, we synthesize IMU data from motion capture datasets. A bi-directional RNN architecture leverages past and future information that is available at training time. At test time, we deploy the network in a sliding window fashion, retaining real time capabilities. To evaluate our method, we recorded DIP-IMU, a dataset consisting of 10 subjects wearing 17 IMUs for validation in 64 sequences with 330,000 time instants; this constitutes the largest IMU dataset publicly available. We quantitatively evaluate our approach on multiple datasets and show results from a real-time implementation. DIP-IMU and the code are available for research purposes.

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data code pdf preprint video DOI Project Page [BibTex]

2018


data code pdf preprint video DOI Project Page [BibTex]


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Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

Tronarp, F., Kersting, H., Särkkä, S., Hennig, P.

ArXiv preprint 2018, arXiv:1810.03440 [stat.ME], October 2018 (article)

Abstract
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consists of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP---which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a Bayesian state estimation problem and all widely-used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers, which were formulated in terms of generating synthetic measurements of the vector field, come out as specific approximations. We derive novel solvers, both Gaussian and non-Gaussian, from the Bayesian state estimation problem posed in this paper and compare them with other probabilistic solvers in illustrative experiments.

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link (url) Project Page [BibTex]


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Deep Neural Network-based Cooperative Visual Tracking through Multiple Micro Aerial Vehicles

Price, E., Lawless, G., Ludwig, R., Martinovic, I., Buelthoff, H. H., Black, M. J., Ahmad, A.

IEEE Robotics and Automation Letters, Robotics and Automation Letters, 3(4):3193-3200, IEEE, October 2018, Also accepted and presented in the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). (article)

Abstract
Multi-camera tracking of humans and animals in outdoor environments is a relevant and challenging problem. Our approach to it involves a team of cooperating micro aerial vehicles (MAVs) with on-board cameras only. DNNs often fail at objects with small scale or far away from the camera, which are typical characteristics of a scenario with aerial robots. Thus, the core problem addressed in this paper is how to achieve on-board, online, continuous and accurate vision-based detections using DNNs for visual person tracking through MAVs. Our solution leverages cooperation among multiple MAVs and active selection of most informative regions of image. We demonstrate the efficiency of our approach through simulations with up to 16 robots and real robot experiments involving two aerial robots tracking a person, while maintaining an active perception-driven formation. ROS-based source code is provided for the benefit of the community.

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Published Version link (url) DOI [BibTex]

Published Version link (url) DOI [BibTex]


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First Impressions of Personality Traits From Body Shapes

Hu, Y., Parde, C. J., Hill, M. Q., Mahmood, N., O’Toole, A. J.

Psychological Science, 29(12):1969-–1983, October 2018 (article)

Abstract
People infer the personalities of others from their facial appearance. Whether they do so from body shapes is less studied. We explored personality inferences made from body shapes. Participants rated personality traits for male and female bodies generated with a three-dimensional body model. Multivariate spaces created from these ratings indicated that people evaluate bodies on valence and agency in ways that directly contrast positive and negative traits from the Big Five domains. Body-trait stereotypes based on the trait ratings revealed a myriad of diverse body shapes that typify individual traits. Personality-trait profiles were predicted reliably from a subset of the body-shape features used to specify the three-dimensional bodies. Body features related to extraversion and conscientiousness were predicted with the highest consensus, followed by openness traits. This study provides the first comprehensive look at the range, diversity, and reliability of personality inferences that people make from body shapes.

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publisher site pdf DOI [BibTex]

publisher site pdf DOI [BibTex]


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Visual Perception and Evaluation of Photo-Realistic Self-Avatars From 3D Body Scans in Males and Females

Thaler, A., Piryankova, I., Stefanucci, J. K., Pujades, S., de la Rosa, S., Streuber, S., Romero, J., Black, M. J., Mohler, B. J.

Frontiers in ICT, 5, pages: 1-14, September 2018 (article)

Abstract
The creation or streaming of photo-realistic self-avatars is important for virtual reality applications that aim for perception and action to replicate real world experience. The appearance and recognition of a digital self-avatar may be especially important for applications related to telepresence, embodied virtual reality, or immersive games. We investigated gender differences in the use of visual cues (shape, texture) of a self-avatar for estimating body weight and evaluating avatar appearance. A full-body scanner was used to capture each participant's body geometry and color information and a set of 3D virtual avatars with realistic weight variations was created based on a statistical body model. Additionally, a second set of avatars was created with an average underlying body shape matched to each participant’s height and weight. In four sets of psychophysical experiments, the influence of visual cues on the accuracy of body weight estimation and the sensitivity to weight changes was assessed by manipulating body shape (own, average) and texture (own photo-realistic, checkerboard). The avatars were presented on a large-screen display, and participants responded to whether the avatar's weight corresponded to their own weight. Participants also adjusted the avatar's weight to their desired weight and evaluated the avatar's appearance with regard to similarity to their own body, uncanniness, and their willingness to accept it as a digital representation of the self. The results of the psychophysical experiments revealed no gender difference in the accuracy of estimating body weight in avatars. However, males accepted a larger weight range of the avatars as corresponding to their own. In terms of the ideal body weight, females but not males desired a thinner body. With regard to the evaluation of avatar appearance, the questionnaire responses suggest that own photo-realistic texture was more important to males for higher similarity ratings, while own body shape seemed to be more important to females. These results argue for gender-specific considerations when creating self-avatars.

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pdf DOI [BibTex]

pdf DOI [BibTex]


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Robust Physics-based Motion Retargeting with Realistic Body Shapes

Borno, M. A., Righetti, L., Black, M. J., Delp, S. L., Fiume, E., Romero, J.

Computer Graphics Forum, 37, pages: 6:1-12, July 2018 (article)

Abstract
Motion capture is often retargeted to new, and sometimes drastically different, characters. When the characters take on realistic human shapes, however, we become more sensitive to the motion looking right. This means adapting it to be consistent with the physical constraints imposed by different body shapes. We show how to take realistic 3D human shapes, approximate them using a simplified representation, and animate them so that they move realistically using physically-based retargeting. We develop a novel spacetime optimization approach that learns and robustly adapts physical controllers to new bodies and constraints. The approach automatically adapts the motion of the mocap subject to the body shape of a target subject. This motion respects the physical properties of the new body and every body shape results in a different and appropriate movement. This makes it easy to create a varied set of motions from a single mocap sequence by simply varying the characters. In an interactive environment, successful retargeting requires adapting the motion to unexpected external forces. We achieve robustness to such forces using a novel LQR-tree formulation. We show that the simulated motions look appropriate to each character’s anatomy and their actions are robust to perturbations.

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pdf video Project Page Project Page [BibTex]

pdf video Project Page Project Page [BibTex]


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Convergence Rates of Gaussian ODE Filters

Kersting, H., Sullivan, T. J., Hennig, P.

arXiv preprint 2018, arXiv:1807.09737 [math.NA], July 2018 (article)

Abstract
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives a priori as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. We prove worst-case local convergence rates of order $h^{q+1}$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $h^q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyse how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we present explicit formulas for the steady states and show that the posterior confidence intervals are well calibrated in all considered cases that exhibit global convergence---in the sense that they globally contract at the same rate as the truncation error.

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Learning 3D Shape Completion under Weak Supervision

Stutz, D., Geiger, A.

Arxiv, May 2018 (article)

Abstract
We address the problem of 3D shape completion from sparse and noisy point clouds, a fundamental problem in computer vision and robotics. Recent approaches are either data-driven or learning-based: Data-driven approaches rely on a shape model whose parameters are optimized to fit the observations; Learning-based approaches, in contrast, avoid the expensive optimization step by learning to directly predict complete shapes from incomplete observations in a fully-supervised setting. However, full supervision is often not available in practice. In this work, we propose a weakly-supervised learning-based approach to 3D shape completion which neither requires slow optimization nor direct supervision. While we also learn a shape prior on synthetic data, we amortize, i.e., learn, maximum likelihood fitting using deep neural networks resulting in efficient shape completion without sacrificing accuracy. On synthetic benchmarks based on ShapeNet and ModelNet as well as on real robotics data from KITTI and Kinect, we demonstrate that the proposed amortized maximum likelihood approach is able to compete with fully supervised baselines and outperforms data-driven approaches, while requiring less supervision and being significantly faster.

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PDF Project Page Project Page [BibTex]


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Assessing body image in anorexia nervosa using biometric self-avatars in virtual reality: Attitudinal components rather than visual body size estimation are distorted

Mölbert, S. C., Thaler, A., Mohler, B. J., Streuber, S., Romero, J., Black, M. J., Zipfel, S., Karnath, H., Giel, K. E.

Psychological Medicine, 48(4):642-653, March 2018 (article)

Abstract
Background: Body image disturbance (BID) is a core symptom of anorexia nervosa (AN), but as yet distinctive features of BID are unknown. The present study aimed at disentangling perceptual and attitudinal components of BID in AN. Methods: We investigated n=24 women with AN and n=24 controls. Based on a 3D body scan, we created realistic virtual 3D bodies (avatars) for each participant that were varied through a range of ±20% of the participants' weights. Avatars were presented in a virtual reality mirror scenario. Using different psychophysical tasks, participants identified and adjusted their actual and their desired body weight. To test for general perceptual biases in estimating body weight, a second experiment investigated perception of weight and shape matched avatars with another identity. Results: Women with AN and controls underestimated their weight, with a trend that women with AN underestimated more. The average desired body of controls had normal weight while the average desired weight of women with AN corresponded to extreme AN (DSM-5). Correlation analyses revealed that desired body weight, but not accuracy of weight estimation, was associated with eating disorder symptoms. In the second experiment, both groups estimated accurately while the most attractive body was similar to Experiment 1. Conclusions: Our results contradict the widespread assumption that patients with AN overestimate their body weight due to visual distortions. Rather, they illustrate that BID might be driven by distorted attitudes with regard to the desired body. Clinical interventions should aim at helping patients with AN to change their desired weight.

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doi pdf DOI Project Page [BibTex]


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Body size estimation of self and others in females varying in BMI

Thaler, A., Geuss, M. N., Mölbert, S. C., Giel, K. E., Streuber, S., Romero, J., Black, M. J., Mohler, B. J.

PLoS ONE, 13(2), Febuary 2018 (article)

Abstract
Previous literature suggests that a disturbed ability to accurately identify own body size may contribute to overweight. Here, we investigated the influence of personal body size, indexed by body mass index (BMI), on body size estimation in a non-clinical population of females varying in BMI. We attempted to disentangle general biases in body size estimates and attitudinal influences by manipulating whether participants believed the body stimuli (personalized avatars with realistic weight variations) represented their own body or that of another person. Our results show that the accuracy of own body size estimation is predicted by personal BMI, such that participants with lower BMI underestimated their body size and participants with higher BMI overestimated their body size. Further, participants with higher BMI were less likely to notice the same percentage of weight gain than participants with lower BMI. Importantly, these results were only apparent when participants were judging a virtual body that was their own identity (Experiment 1), but not when they estimated the size of a body with another identity and the same underlying body shape (Experiment 2a). The different influences of BMI on accuracy of body size estimation and sensitivity to weight change for self and other identity suggests that effects of BMI on visual body size estimation are self-specific and not generalizable to other bodies.

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pdf DOI Project Page [BibTex]


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Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

Kanagawa, M., Hennig, P., Sejdinovic, D., Sriperumbudur, B. K.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

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arXiv [BibTex]

arXiv [BibTex]


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Schema-related cognitive load influences performance, speech, and physiology in a dual-task setting: A continuous multi-measure approach

Wirzberger, M., Herms, R., Esmaeili Bijarsari, S., Eibl, M., Rey, G. D.

Cognitive Research: Principles and Implications, 3:46, Springer Nature, 2018 (article)

Abstract
Schema acquisition processes comprise an essential source of cognitive demands in learning situations. To shed light on related mechanisms and influencing factors, this study applied a continuous multi-measure approach for cognitive load assessment. In a dual-task setting, a sample of 123 student participants learned visually presented symbol combinations with one of two levels of complexity while memorizing auditorily presented number sequences. Learners’ cognitive load during the learning task was addressed by secondary task performance, prosodic speech parameters (pauses, articulation rate), and physiological markers (heart rate, skin conductance response). While results revealed increasing primary and secondary task performance over the trials, decreases in speech and physiological parameters indicated a reduction in the overall level of cognitive load with task progression. In addition, the robustness of the acquired schemata was confirmed by a transfer task that required participants to apply the obtained symbol combinations. Taken together, the observed pattern of evidence supports the idea of a logarithmically decreasing progression of cognitive load with increasing schema acquisition, and further hints on robust and stable transfer performance, even under enhanced transfer demands. Finally, theoretical and practical consequences consider evidence on desirable difficulties in learning as well as the potential of multimodal cognitive load detection in learning applications.

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DOI [BibTex]

DOI [BibTex]


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Numerical Quadrature for Probabilistic Policy Search

Vinogradska, J., Bischoff, B., Achterhold, J., Koller, T., Peters, J.

IEEE Transactions on Pattern Analysis and Machine Intelligence, pages: 1-1, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Augmented Reality Meets Computer Vision: Efficient Data Generation for Urban Driving Scenes

Alhaija, H., Mustikovela, S., Mescheder, L., Geiger, A., Rother, C.

International Journal of Computer Vision (IJCV), 2018, 2018 (article)

Abstract
The success of deep learning in computer vision is based on the availability of large annotated datasets. To lower the need for hand labeled images, virtually rendered 3D worlds have recently gained popularity. Unfortunately, creating realistic 3D content is challenging on its own and requires significant human effort. In this work, we propose an alternative paradigm which combines real and synthetic data for learning semantic instance segmentation and object detection models. Exploiting the fact that not all aspects of the scene are equally important for this task, we propose to augment real-world imagery with virtual objects of the target category. Capturing real-world images at large scale is easy and cheap, and directly provides real background appearances without the need for creating complex 3D models of the environment. We present an efficient procedure to augment these images with virtual objects. In contrast to modeling complete 3D environments, our data augmentation approach requires only a few user interactions in combination with 3D models of the target object category. Leveraging our approach, we introduce a novel dataset of augmented urban driving scenes with 360 degree images that are used as environment maps to create realistic lighting and reflections on rendered objects. We analyze the significance of realistic object placement by comparing manual placement by humans to automatic methods based on semantic scene analysis. This allows us to create composite images which exhibit both realistic background appearance as well as a large number of complex object arrangements. Through an extensive set of experiments, we conclude the right set of parameters to produce augmented data which can maximally enhance the performance of instance segmentation models. Further, we demonstrate the utility of the proposed approach on training standard deep models for semantic instance segmentation and object detection of cars in outdoor driving scenarios. We test the models trained on our augmented data on the KITTI 2015 dataset, which we have annotated with pixel-accurate ground truth, and on the Cityscapes dataset. Our experiments demonstrate that the models trained on augmented imagery generalize better than those trained on fully synthetic data or models trained on limited amounts of annotated real data.

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pdf Project Page [BibTex]

pdf Project Page [BibTex]


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Omnidirectional DSO: Direct Sparse Odometry with Fisheye Cameras

Matsuki, H., von Stumberg, L., Usenko, V., Stueckler, J., Cremers, D.

IEEE Robotics and Automation Letters (RA-L) & Int. Conference on Intelligent Robots and Systems (IROS), Robotics and Automation Letters (RA-L), IEEE, 2018 (article)

ev

[BibTex]

[BibTex]


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Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper introduces a novel Hilbert space representation of a counterfactual distribution---called counterfactual mean embedding (CME)---with applications in nonparametric causal inference. Counterfactual prediction has become an ubiquitous tool in machine learning applications, such as online advertisement, recommendation systems, and medical diagnosis, whose performance relies on certain interventions. To infer the outcomes of such interventions, we propose to embed the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel. Under appropriate assumptions, the CME allows us to perform causal inference over the entire landscape of the counterfactual distribution. The CME can be estimated consistently from observational data without requiring any parametric assumption about the underlying distributions. We also derive a rate of convergence which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Our framework can deal with not only real-valued outcome, but potentially also more complex and structured outcomes such as images, sequences, and graphs. Lastly, our experimental results on off-policy evaluation tasks demonstrate the advantages of the proposed estimator.

ei pn

arXiv [BibTex]

arXiv [BibTex]


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Model-based Kernel Sum Rule: Kernel Bayesian Inference with Probabilistic Models

Nishiyama, Y., Kanagawa, M., Gretton, A., Fukumizu, K.

Arxiv e-prints, arXiv:1409.5178v2 [stat.ML], 2018 (article)

Abstract
Kernel Bayesian inference is a powerful nonparametric approach to performing Bayesian inference in reproducing kernel Hilbert spaces or feature spaces. In this approach, kernel means are estimated instead of probability distributions, and these estimates can be used for subsequent probabilistic operations (as for inference in graphical models) or in computing the expectations of smooth functions, for instance. Various algorithms for kernel Bayesian inference have been obtained by combining basic rules such as the kernel sum rule (KSR), kernel chain rule, kernel product rule and kernel Bayes' rule. However, the current framework only deals with fully nonparametric inference (i.e., all conditional relations are learned nonparametrically), and it does not allow for flexible combinations of nonparametric and parametric inference, which are practically important. Our contribution is in providing a novel technique to realize such combinations. We introduce a new KSR referred to as the model-based KSR (Mb-KSR), which employs the sum rule in feature spaces under a parametric setting. Incorporating the Mb-KSR into existing kernel Bayesian framework provides a richer framework for hybrid (nonparametric and parametric) kernel Bayesian inference. As a practical application, we propose a novel filtering algorithm for state space models based on the Mb-KSR, which combines the nonparametric learning of an observation process using kernel mean embedding and the additive Gaussian noise model for a state transition process. While we focus on additive Gaussian noise models in this study, the idea can be extended to other noise models, such as the Cauchy and alpha-stable noise models.

pn

arXiv [BibTex]

arXiv [BibTex]


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Attention please! Enhanced attention control abilities compensate for instructional impairments in multimedia learning

Wirzberger, M., Rey, G. D.

Journal of Computers in Education, 5(2):243-257, Springer Nature, 2018 (article)

Abstract
Learners exposed to multimedia learning contexts have to deal with a variety of visual stimuli, demanding a conducive design of learning material to maintain limitations in attentional resources. Within the current study, effects and constraints arising from two selected impairing features are investigated in more detail within a computer-based learning task on factor analysis. A sample of 53 students received a combination of textual and pictorial elements that explained the topic, while impaired attention was systematically induced in a 2 × 2 factorial between-subjects design by interrupting system-notifications (with vs. without) and seductive text passages (with vs. without). Learners’ ability for controlled attention was assessed with a standardized psychological attention inventory. Approaching the results, learners receiving seductive text passages spent significantly more time on the learning material. In addition, a moderation effect of attention control abilities on the relationship between interruptions and retention performance resulted. Explanations for the obtained findings are discussed referring to mechanisms of compensation, load, and activation.

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DOI [BibTex]

DOI [BibTex]


Thumb xl hp teaser
A probabilistic model for the numerical solution of initial value problems

Schober, M., Särkkä, S., Philipp Hennig,

Statistics and Computing, Springer US, 2018 (article)

Abstract
We study connections between ordinary differential equation (ODE) solvers and probabilistic regression methods in statistics. We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics. Adding to this picture, we show that several multistep methods of Nordsieck form can be recast as Kalman filtering on q-times integrated Wiener processes. Doing so provides a family of IVP solvers that return a Gaussian posterior measure, rather than a point estimate. We show that some such methods have low computational overhead, nontrivial convergence order, and that the posterior has a calibrated concentration rate. Additionally, we suggest a step size adaptation algorithm which completes the proposed method to a practically useful implementation, which we experimentally evaluate using a representative set of standard codes in the DETEST benchmark set.

pn

PDF Code DOI Project Page [BibTex]


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Temporal Human Action Segmentation via Dynamic Clustering

Zhang, Y., Sun, H., Tang, S., Neumann, H.

arXiv preprint arXiv:1803.05790, 2018 (article)

Abstract
We present an effective dynamic clustering algorithm for the task of temporal human action segmentation, which has comprehensive applications such as robotics, motion analysis, and patient monitoring. Our proposed algorithm is unsupervised, fast, generic to process various types of features, and applica- ble in both the online and offline settings. We perform extensive experiments of processing data streams, and show that our algorithm achieves the state-of- the-art results for both online and offline settings.

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link (url) [BibTex]

link (url) [BibTex]


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The Computational Challenges of Pursuing Multiple Goals: Network Structure of Goal Systems Predicts Human Performance

Reichman, D., Lieder, F., Bourgin, D. D., Talmon, N., Griffiths, T. L.

PsyArXiv, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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The moderating role of arousal on the seductive detail effect in a multimedia learning setting

Schneider, S., Wirzberger, M., Rey, G. D.

Applied Cognitive Psychology, Wiley, 2018 (article)

Abstract
Arousal has been found to increase learners' attentional resources. In contrast, seductive details (interesting but learning‐irrelevant information) are considered to distract attention away from relevant information and, thus, hinder learning. However, a possibly moderating role of arousal on the seductive detail effect has not been examined yet. In this study, arousal variations were induced via audio files of false heartbeats. In consequence, 100 participants were randomly assigned to a 2 (with or without seductive details) × 2 (lower vs. higher false heart rates) between‐subjects design. Data on learning performance, cognitive load, motivation, heartbeat frequency, and electro‐dermal activity were collected. Results show learning‐inhibiting effects for seductive details and learning‐enhancing effects for higher false heart rates. Cognitive processes mediate both effects. However, the detrimental effect of seductive details was not present when heart rate was higher. Results indicate that the seductive detail effect is moderated by a learner's state of arousal.

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DOI [BibTex]

DOI [BibTex]


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Motion Segmentation & Multiple Object Tracking by Correlation Co-Clustering

Keuper, M., Tang, S., Andres, B., Brox, T., Schiele, B.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2018 (article)

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pdf DOI Project Page [BibTex]

pdf DOI Project Page [BibTex]


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Learning 3D Shape Completion under Weak Supervision

Stutz, D., Geiger, A.

International Journal of Computer Vision (IJCV), 2018, 2018 (article)

Abstract
We address the problem of 3D shape completion from sparse and noisy point clouds, a fundamental problem in computer vision and robotics. Recent approaches are either data-driven or learning-based: Data-driven approaches rely on a shape model whose parameters are optimized to fit the observations; Learning-based approaches, in contrast, avoid the expensive optimization step by learning to directly predict complete shapes from incomplete observations in a fully-supervised setting. However, full supervision is often not available in practice. In this work, we propose a weakly-supervised learning-based approach to 3D shape completion which neither requires slow optimization nor direct supervision. While we also learn a shape prior on synthetic data, we amortize, i.e., learn, maximum likelihood fitting using deep neural networks resulting in efficient shape completion without sacrificing accuracy. On synthetic benchmarks based on ShapeNet and ModelNet as well as on real robotics data from KITTI and Kinect, we demonstrate that the proposed amortized maximum likelihood approach is able to compete with a fully supervised baseline and outperforms the data-driven approach of Engelmann et al., while requiring less supervision and being significantly faster.

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pdf Project Page [BibTex]

pdf Project Page [BibTex]


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Object Scene Flow

Menze, M., Heipke, C., Geiger, A.

ISPRS Journal of Photogrammetry and Remote Sensing, 2018 (article)

Abstract
This work investigates the estimation of dense three-dimensional motion fields, commonly referred to as scene flow. While great progress has been made in recent years, large displacements and adverse imaging conditions as observed in natural outdoor environments are still very challenging for current approaches to reconstruction and motion estimation. In this paper, we propose a unified random field model which reasons jointly about 3D scene flow as well as the location, shape and motion of vehicles in the observed scene. We formulate the problem as the task of decomposing the scene into a small number of rigidly moving objects sharing the same motion parameters. Thus, our formulation effectively introduces long-range spatial dependencies which commonly employed local rigidity priors are lacking. Our inference algorithm then estimates the association of image segments and object hypotheses together with their three-dimensional shape and motion. We demonstrate the potential of the proposed approach by introducing a novel challenging scene flow benchmark which allows for a thorough comparison of the proposed scene flow approach with respect to various baseline models. In contrast to previous benchmarks, our evaluation is the first to provide stereo and optical flow ground truth for dynamic real-world urban scenes at large scale. Our experiments reveal that rigid motion segmentation can be utilized as an effective regularizer for the scene flow problem, improving upon existing two-frame scene flow methods. At the same time, our method yields plausible object segmentations without requiring an explicitly trained recognition model for a specific object class.

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Project Page [BibTex]

Project Page [BibTex]


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Rational metareasoning and the plasticity of cognitive control

Lieder, F., Shenhav, A., Musslick, S., Griffiths, T. L.

{PLoS Computational Biology}, 14(4):e1006043, Public Library of Science, 2018 (article)

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Project Page [BibTex]

Project Page [BibTex]


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Over-representation of extreme events in decision making reflects rational use of cognitive resources

Lieder, F., Griffiths, T. L., Hsu, M.

Psychological Review, 125(1):1-32, 2018 (article)

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[BibTex]

[BibTex]

2017


Thumb xl probls sketch n3 0 ei0
Probabilistic Line Searches for Stochastic Optimization

Mahsereci, M., Hennig, P.

Journal of Machine Learning Research, 18(119):1-59, November 2017 (article)

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link (url) Project Page [BibTex]

2017


link (url) Project Page [BibTex]


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Learning a model of facial shape and expression from 4D scans

Li, T., Bolkart, T., Black, M. J., Li, H., Romero, J.

ACM Transactions on Graphics, 36(6):194:1-194:17, November 2017, Two first authors contributed equally (article)

Abstract
The field of 3D face modeling has a large gap between high-end and low-end methods. At the high end, the best facial animation is indistinguishable from real humans, but this comes at the cost of extensive manual labor. At the low end, face capture from consumer depth sensors relies on 3D face models that are not expressive enough to capture the variability in natural facial shape and expression. We seek a middle ground by learning a facial model from thousands of accurately aligned 3D scans. Our FLAME model (Faces Learned with an Articulated Model and Expressions) is designed to work with existing graphics software and be easy to fit to data. FLAME uses a linear shape space trained from 3800 scans of human heads. FLAME combines this linear shape space with an articulated jaw, neck, and eyeballs, pose-dependent corrective blendshapes, and additional global expression from 4D face sequences in the D3DFACS dataset along with additional 4D sequences.We accurately register a template mesh to the scan sequences and make the D3DFACS registrations available for research purposes. In total the model is trained from over 33, 000 scans. FLAME is low-dimensional but more expressive than the FaceWarehouse model and the Basel Face Model. We compare FLAME to these models by fitting them to static 3D scans and 4D sequences using the same optimization method. FLAME is significantly more accurate and is available for research purposes (http://flame.is.tue.mpg.de).

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data/model video code chumpy code tensorflow paper supplemental Project Page [BibTex]

data/model video code chumpy code tensorflow paper supplemental Project Page [BibTex]


Thumb xl molbert
Investigating Body Image Disturbance in Anorexia Nervosa Using Novel Biometric Figure Rating Scales: A Pilot Study

Mölbert, S. C., Thaler, A., Streuber, S., Black, M. J., Karnath, H., Zipfel, S., Mohler, B., Giel, K. E.

European Eating Disorders Review, 25(6):607-612, November 2017 (article)

Abstract
This study uses novel biometric figure rating scales (FRS) spanning body mass index (BMI) 13.8 to 32.2 kg/m2 and BMI 18 to 42 kg/m2. The aims of the study were (i) to compare FRS body weight dissatisfaction and perceptual distortion of women with anorexia nervosa (AN) to a community sample; (ii) how FRS parameters are associated with questionnaire body dissatisfaction, eating disorder symptoms and appearance comparison habits; and (iii) whether the weight spectrum of the FRS matters. Women with AN (n = 24) and a community sample of women (n = 104) selected their current and ideal body on the FRS and completed additional questionnaires. Women with AN accurately picked the body that aligned best with their actual weight in both FRS. Controls underestimated their BMI in the FRS 14–32 and were accurate in the FRS 18–42. In both FRS, women with AN desired a body close to their actual BMI and controls desired a thinner body. Our observations suggest that body image disturbance in AN is unlikely to be characterized by a visual perceptual disturbance, but rather by an idealization of underweight in conjunction with high body dissatisfaction. The weight spectrum of FRS can influence the accuracy of BMI estimation.

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publisher DOI Project Page [BibTex]


Thumb xl manoteaser
Embodied Hands: Modeling and Capturing Hands and Bodies Together

Romero, J., Tzionas, D., Black, M. J.

ACM Transactions on Graphics, (Proc. SIGGRAPH Asia), 36(6):245:1-245:17, 245:1–245:17, ACM, November 2017 (article)

Abstract
Humans move their hands and bodies together to communicate and solve tasks. Capturing and replicating such coordinated activity is critical for virtual characters that behave realistically. Surprisingly, most methods treat the 3D modeling and tracking of bodies and hands separately. Here we formulate a model of hands and bodies interacting together and fit it to full-body 4D sequences. When scanning or capturing the full body in 3D, hands are small and often partially occluded, making their shape and pose hard to recover. To cope with low-resolution, occlusion, and noise, we develop a new model called MANO (hand Model with Articulated and Non-rigid defOrmations). MANO is learned from around 1000 high-resolution 3D scans of hands of 31 subjects in a wide variety of hand poses. The model is realistic, low-dimensional, captures non-rigid shape changes with pose, is compatible with standard graphics packages, and can fit any human hand. MANO provides a compact mapping from hand poses to pose blend shape corrections and a linear manifold of pose synergies. We attach MANO to a standard parameterized 3D body shape model (SMPL), resulting in a fully articulated body and hand model (SMPL+H). We illustrate SMPL+H by fitting complex, natural, activities of subjects captured with a 4D scanner. The fitting is fully automatic and results in full body models that move naturally with detailed hand motions and a realism not seen before in full body performance capture. The models and data are freely available for research purposes at http://mano.is.tue.mpg.de.

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website youtube paper suppl video link (url) DOI Project Page [BibTex]

website youtube paper suppl video link (url) DOI Project Page [BibTex]


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An Online Scalable Approach to Unified Multirobot Cooperative Localization and Object Tracking

Ahmad, A., Lawless, G., Lima, P.

IEEE Transactions on Robotics (T-RO), 33, pages: 1184 - 1199, October 2017 (article)

Abstract
In this article we present a unified approach for multi-robot cooperative simultaneous localization and object tracking based on particle filters. Our approach is scalable with respect to the number of robots in the team. We introduce a method that reduces, from an exponential to a linear growth, the space and computation time requirements with respect to the number of robots in order to maintain a given level of accuracy in the full state estimation. Our method requires no increase in the number of particles with respect to the number of robots. However, in our method each particle represents a full state hypothesis, leading to the linear dependency on the number of robots of both space and time complexity. The derivation of the algorithm implementing our approach from a standard particle filter algorithm and its complexity analysis are presented. Through an extensive set of simulation experiments on a large number of randomized datasets, we demonstrate the correctness and efficacy of our approach. Through real robot experiments on a standardized open dataset of a team of four soccer playing robots tracking a ball, we evaluate our method's estimation accuracy with respect to the ground truth values. Through comparisons with other methods based on i) nonlinear least squares minimization and ii) joint extended Kalman filter, we further highlight our method's advantages. Finally, we also present a robustness test for our approach by evaluating it under scenarios of communication and vision failure in teammate robots.

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Published Version link (url) DOI [BibTex]

Published Version link (url) DOI [BibTex]


Thumb xl early stopping teaser
Early Stopping Without a Validation Set

Mahsereci, M., Balles, L., Lassner, C., Hennig, P.

arXiv preprint arXiv:1703.09580, 2017 (article)

Abstract
Early stopping is a widely used technique to prevent poor generalization performance when training an over-expressive model by means of gradient-based optimization. To find a good point to halt the optimizer, a common practice is to split the dataset into a training and a smaller validation set to obtain an ongoing estimate of the generalization performance. In this paper we propose a novel early stopping criterion which is based on fast-to-compute, local statistics of the computed gradients and entirely removes the need for a held-out validation set. Our experiments show that this is a viable approach in the setting of least-squares and logistic regression as well as neural networks.

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link (url) Project Page Project Page [BibTex]


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Krylov Subspace Recycling for Fast Iterative Least-Squares in Machine Learning

Roos, F. D., Hennig, P.

arXiv preprint arXiv:1706.00241, 2017 (article)

Abstract
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time approximations, such as spectral and inducing-point methods, have been suggested and are now in wide use. These are low-rank approximations that choose the low-rank space a priori and do not refine it over time. While this allows linear cost in the data-set size, it also causes a finite, uncorrected approximation error. Authors from numerical linear algebra have explored ways to iteratively refine such low-rank approximations, at a cost of a small number of matrix-vector multiplications. This idea is particularly interesting in the many situations in machine learning where one has to solve a sequence of related symmetric positive definite linear problems. From the machine learning perspective, such deflation methods can be interpreted as transfer learning of a low-rank approximation across a time-series of numerical tasks. We study the use of such methods for our field. Our empirical results show that, on regression and classification problems of intermediate size, this approach can interpolate between low computational cost and numerical precision.

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link (url) Project Page [BibTex]


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Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings

Kanagawa, M., Sriperumbudur, B. K., Fukumizu, K.

Arxiv e-prints, arXiv:1709.00147v1 [math.NA], 2017 (article)

Abstract
This paper presents convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We provide convergence guarantees based on two different assumptions on a quadrature rule: one on quadrature weights, and the other on design points. More precisely, we show that convergence rates can be derived (i) if the sum of absolute weights remains constant (or does not increase quickly), or (ii) if the minimum distance between distance design points does not decrease very quickly. As a consequence of the latter result, we derive a rate of convergence for Bayesian quadrature in misspecified settings. We reveal a condition on design points to make Bayesian quadrature robust to misspecification, and show that, under this condition, it may adaptively achieve the optimal rate of convergence in the Sobolev space of a lesser order (i.e., of the unknown smoothness of a test integrand), under a slightly stronger regularity condition on the integrand.

pn

arXiv [BibTex]

arXiv [BibTex]


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Fast Bayesian hyperparameter optimization on large datasets

Klein, A., Falkner, S., Bartels, S., Hennig, P., Hutter, F.

Electronic Journal of Statistics, 11, 2017 (article)

pn

[BibTex]

[BibTex]