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Li Fei-Fei

Li Fei-Fei appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Computer VisionMachine LearningArtificial IntelligenceRoboticsHuman-Computer InteractionComputation and Languageeess.IVNeural and Evolutionary ComputingNeurons and Cognitioncs.CYeess.ASInformation RetrievalSound

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Published work

50 published item(s)

preprint2026arXiv

ESI-Bench: Towards Embodied Spatial Intelligence that Closes the Perception-Action Loop

Spatial intelligence unfolds through a perception-action loop: agents act to acquire observations, and reason about how observations vary as a function of action. Rather than passively processing what is seen, they actively uncover what is unseen - occluded structure, dynamics, containment, and functionality that cannot be resolved from passive sensing alone. We move beyond prior formulations of spatial intelligence that assume oracle observations by recasting the observer as an actor. We introduce ESI-BENCH, a comprehensive benchmark for embodied spatial intelligence spanning 10 task categories and 29 subcategories built on OmniGibson, grounded in Spelke's core knowledge systems. Agents must decide what abilities to deploy - perception, locomotion, and manipulation - and how to sequence them to actively accumulate task-relevant evidence. We conduct extensive experiments on state-of-the-art MLLMs and find that active exploration substantially outperforms passive counterparts, with agents spontaneously discovering emergent spatial strategies without explicit instructions, while random multi-view often adds noise rather than signal despite consuming far more images. Most failures stem not from weak perception but from action blindness: poor action choices lead to poor observations, which in turn drive cascading errors. While explicit 3D grounding stabilizes reasoning on depth-sensitive tasks, imperfect 3D representation proves more harmful than 2D baselines by distorting spatial relations. Human studies further reveal that unlike humans who seek falsifying viewpoints and revise beliefs under contradiction, models commit prematurely with high confidence regardless of evidence quality, exposing a metacognitive gap that neither better perception nor more embodied interaction alone can close.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

PointWorld: Scaling 3D World Models for In-The-Wild Robotic Manipulation

Humans anticipate, from a glance and a contemplated action of their bodies, how the 3D world will respond, a capability that is equally vital for robotic manipulation. We introduce PointWorld, a large pre-trained 3D world model that unifies state and action in a shared 3D space as 3D point flows: given one or few RGB-D images and a sequence of low-level robot action commands, PointWorld forecasts per-pixel displacements in 3D that respond to the given actions. By representing actions as 3D point flows instead of embodiment-specific action spaces (e.g., joint positions), this formulation directly conditions on physical geometries of robots while seamlessly integrating learning across embodiments. To train our 3D world model, we curate a large-scale dataset spanning real and simulated robotic manipulation in open-world environments, enabled by recent advances in 3D vision and simulated environments, totaling about 2M trajectories and 500 hours across a single-arm Franka and a bimanual humanoid. Through rigorous, large-scale empirical studies of backbones, action representations, learning objectives, partial observability, data mixtures, domain transfers, and scaling, we distill design principles for large-scale 3D world modeling. With a real-time (0.1s) inference speed, PointWorld can be efficiently integrated in the model-predictive control (MPC) framework for manipulation. We demonstrate that a single pre-trained checkpoint enables a real-world Franka robot to perform rigid-body pushing, deformable and articulated object manipulation, and tool use, without requiring any demonstrations or post-training and all from a single image captured in-the-wild. Project website at https://point-world.github.io/.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

StereoPolicy: Improving Robotic Manipulation Policies via Stereo Perception

Recent advances in robot imitation learning have yielded powerful visuomotor policies capable of manipulating a wide variety of objects directly from monocular visual inputs. However, monocular observations inherently lack reliable depth cues and spatial awareness, which are critical for precise manipulation in cluttered or geometrically complex scenes. To address this limitation, we introduce StereoPolicy, a new visuomotor policy learning framework that directly leverages synchronized stereo image pairs to strengthen geometric reasoning, without requiring explicit 3D reconstruction or camera calibration. StereoPolicy employs pretrained 2D vision encoders to process each image independently and fuses the resulting representations through a Stereo Transformer. This design implicitly captures spatial correspondence and disparity cues. The framework integrates seamlessly with diffusion-based and pretrained vision-language-action (VLA) policies, delivering consistent improvements over RGB, RGB-D, point cloud, and multi-view baselines across three simulation benchmarks: RoboMimic, RoboCasa, and OmniGibson. We further validate StereoPolicy on real-robot experiments spanning both tabletop and bimanual mobile manipulation settings. Our results underscore stereo vision as a scalable and robust modality that bridges 2D pretrained representations with 3D geometric understanding for robotic manipulation.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

VideoWeave: A Data-Centric Approach for Efficient Video Understanding

Training video-language models is often prohibitively expensive due to the high cost of processing long frame sequences and the limited availability of annotated long videos. We present VideoWeave, a simple yet effective approach to improve data efficiency by constructing synthetic long-context training samples that splice together short, captioned videos from existing datasets. Rather than modifying model architectures or optimization objectives, VideoWeave reorganizes available video-text pairs to expand temporal diversity within fixed compute. We systematically study how different data composition strategies like random versus visually clustered splicing and caption enrichment affect downstream performance on downstream video question answering. Under identical compute constraints, models trained with VideoWeave achieve higher accuracy than conventional video finetuning. Our results highlight that reorganizing training data, rather than altering architectures, may offer a simple and scalable path for training video-language models. We link our code for all experiments here.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

Dream2Flow: Bridging Video Generation and Open-World Manipulation with 3D Object Flow

Generative video modeling has emerged as a compelling tool to zero-shot reason about plausible physical interactions for open-world manipulation. Yet, it remains a challenge to translate such human-led motions into the low-level actions demanded by robotic systems. We observe that given an initial image and task instruction, these models excel at synthesizing sensible object motions. Thus, we introduce Dream2Flow, a framework that bridges video generation and robotic control through 3D object flow as an intermediate representation. Our method reconstructs 3D object motions from generated videos and formulates manipulation as object trajectory tracking. By separating the state changes from the actuators that realize those changes, Dream2Flow overcomes the embodiment gap and enables zero-shot guidance from pre-trained video models to manipulate objects of diverse categories-including rigid, articulated, deformable, and granular. Through trajectory optimization or reinforcement learning, Dream2Flow converts reconstructed 3D object flow into executable low-level commands without task-specific demonstrations. Simulation and real-world experiments highlight 3D object flow as a general and scalable interface for adapting video generation models to open-world robotic manipulation. Videos and visualizations are available at https://dream2flow.github.io/.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Study of Face Obfuscation in ImageNet

Face obfuscation (blurring, mosaicing, etc.) has been shown to be effective for privacy protection; nevertheless, object recognition research typically assumes access to complete, unobfuscated images. In this paper, we explore the effects of face obfuscation on the popular ImageNet challenge visual recognition benchmark. Most categories in the ImageNet challenge are not people categories; however, many incidental people appear in the images, and their privacy is a concern. We first annotate faces in the dataset. Then we demonstrate that face obfuscation has minimal impact on the accuracy of recognition models. Concretely, we benchmark multiple deep neural networks on obfuscated images and observe that the overall recognition accuracy drops only slightly (<= 1.0%). Further, we experiment with transfer learning to 4 downstream tasks (object recognition, scene recognition, face attribute classification, and object detection) and show that features learned on obfuscated images are equally transferable. Our work demonstrates the feasibility of privacy-aware visual recognition, improves the highly-used ImageNet challenge benchmark, and suggests an important path for future visual datasets. Data and code are available at https://github.com/princetonvisualai/imagenet-face-obfuscation.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

GaitForeMer: Self-Supervised Pre-Training of Transformers via Human Motion Forecasting for Few-Shot Gait Impairment Severity Estimation

Parkinson's disease (PD) is a neurological disorder that has a variety of observable motor-related symptoms such as slow movement, tremor, muscular rigidity, and impaired posture. PD is typically diagnosed by evaluating the severity of motor impairments according to scoring systems such as the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS). Automated severity prediction using video recordings of individuals provides a promising route for non-intrusive monitoring of motor impairments. However, the limited size of PD gait data hinders model ability and clinical potential. Because of this clinical data scarcity and inspired by the recent advances in self-supervised large-scale language models like GPT-3, we use human motion forecasting as an effective self-supervised pre-training task for the estimation of motor impairment severity. We introduce GaitForeMer, Gait Forecasting and impairment estimation transforMer, which is first pre-trained on public datasets to forecast gait movements and then applied to clinical data to predict MDS-UPDRS gait impairment severity. Our method outperforms previous approaches that rely solely on clinical data by a large margin, achieving an F1 score of 0.76, precision of 0.79, and recall of 0.75. Using GaitForeMer, we show how public human movement data repositories can assist clinical use cases through learning universal motion representations. The code is available at https://github.com/markendo/GaitForeMer .

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Generalizable Task Planning through Representation Pretraining

The ability to plan for multi-step manipulation tasks in unseen situations is crucial for future home robots. But collecting sufficient experience data for end-to-end learning is often infeasible in the real world, as deploying robots in many environments can be prohibitively expensive. On the other hand, large-scale scene understanding datasets contain diverse and rich semantic and geometric information. But how to leverage such information for manipulation remains an open problem. In this paper, we propose a learning-to-plan method that can generalize to new object instances by leveraging object-level representations extracted from a synthetic scene understanding dataset. We evaluate our method with a suite of challenging multi-step manipulation tasks inspired by household activities and show that our model achieves measurably better success rate than state-of-the-art end-to-end approaches. Additional information can be found at https://sites.google.com/view/gentp

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

MaskViT: Masked Visual Pre-Training for Video Prediction

The ability to predict future visual observations conditioned on past observations and motor commands can enable embodied agents to plan solutions to a variety of tasks in complex environments. This work shows that we can create good video prediction models by pre-training transformers via masked visual modeling. Our approach, named MaskViT, is based on two simple design decisions. First, for memory and training efficiency, we use two types of window attention: spatial and spatiotemporal. Second, during training, we mask a variable percentage of tokens instead of a fixed mask ratio. For inference, MaskViT generates all tokens via iterative refinement where we incrementally decrease the masking ratio following a mask scheduling function. On several datasets we demonstrate that MaskViT outperforms prior works in video prediction, is parameter efficient, and can generate high-resolution videos (256x256). Further, we demonstrate the benefits of inference speedup (up to 512x) due to iterative decoding by using MaskViT for planning on a real robot. Our work suggests that we can endow embodied agents with powerful predictive models by leveraging the general framework of masked visual modeling with minimal domain knowledge.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

ObjectFolder 2.0: A Multisensory Object Dataset for Sim2Real Transfer

Objects play a crucial role in our everyday activities. Though multisensory object-centric learning has shown great potential lately, the modeling of objects in prior work is rather unrealistic. ObjectFolder 1.0 is a recent dataset that introduces 100 virtualized objects with visual, acoustic, and tactile sensory data. However, the dataset is small in scale and the multisensory data is of limited quality, hampering generalization to real-world scenarios. We present ObjectFolder 2.0, a large-scale, multisensory dataset of common household objects in the form of implicit neural representations that significantly enhances ObjectFolder 1.0 in three aspects. First, our dataset is 10 times larger in the amount of objects and orders of magnitude faster in rendering time. Second, we significantly improve the multisensory rendering quality for all three modalities. Third, we show that models learned from virtual objects in our dataset successfully transfer to their real-world counterparts in three challenging tasks: object scale estimation, contact localization, and shape reconstruction. ObjectFolder 2.0 offers a new path and testbed for multisensory learning in computer vision and robotics. The dataset is available at https://github.com/rhgao/ObjectFolder.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On the Opportunities and Risks of Foundation Models

AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Physion: Evaluating Physical Prediction from Vision in Humans and Machines

While current vision algorithms excel at many challenging tasks, it is unclear how well they understand the physical dynamics of real-world environments. Here we introduce Physion, a dataset and benchmark for rigorously evaluating the ability to predict how physical scenarios will evolve over time. Our dataset features realistic simulations of a wide range of physical phenomena, including rigid and soft-body collisions, stable multi-object configurations, rolling, sliding, and projectile motion, thus providing a more comprehensive challenge than previous benchmarks. We used Physion to benchmark a suite of models varying in their architecture, learning objective, input-output structure, and training data. In parallel, we obtained precise measurements of human prediction behavior on the same set of scenarios, allowing us to directly evaluate how well any model could approximate human behavior. We found that vision algorithms that learn object-centric representations generally outperform those that do not, yet still fall far short of human performance. On the other hand, graph neural networks with direct access to physical state information both perform substantially better and make predictions that are more similar to those made by humans. These results suggest that extracting physical representations of scenes is the main bottleneck to achieving human-level and human-like physical understanding in vision algorithms. We have publicly released all data and code to facilitate the use of Physion to benchmark additional models in a fully reproducible manner, enabling systematic evaluation of progress towards vision algorithms that understand physical environments as robustly as people do.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Rethinking Architecture Design for Tackling Data Heterogeneity in Federated Learning

Federated learning is an emerging research paradigm enabling collaborative training of machine learning models among different organizations while keeping data private at each institution. Despite recent progress, there remain fundamental challenges such as the lack of convergence and the potential for catastrophic forgetting across real-world heterogeneous devices. In this paper, we demonstrate that self-attention-based architectures (e.g., Transformers) are more robust to distribution shifts and hence improve federated learning over heterogeneous data. Concretely, we conduct the first rigorous empirical investigation of different neural architectures across a range of federated algorithms, real-world benchmarks, and heterogeneous data splits. Our experiments show that simply replacing convolutional networks with Transformers can greatly reduce catastrophic forgetting of previous devices, accelerate convergence, and reach a better global model, especially when dealing with heterogeneous data. We release our code and pretrained models at https://github.com/Liangqiong/ViT-FL-main to encourage future exploration in robust architectures as an alternative to current research efforts on the optimization front.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Revisiting the "Video" in Video-Language Understanding

What makes a video task uniquely suited for videos, beyond what can be understood from a single image? Building on recent progress in self-supervised image-language models, we revisit this question in the context of video and language tasks. We propose the atemporal probe (ATP), a new model for video-language analysis which provides a stronger bound on the baseline accuracy of multimodal models constrained by image-level understanding. By applying this model to standard discriminative video and language tasks, such as video question answering and text-to-video retrieval, we characterize the limitations and potential of current video-language benchmarks. We find that understanding of event temporality is often not necessary to achieve strong or state-of-the-art performance, even compared with recent large-scale video-language models and in contexts intended to benchmark deeper video-level understanding. We also demonstrate how ATP can improve both video-language dataset and model design. We describe a technique for leveraging ATP to better disentangle dataset subsets with a higher concentration of temporally challenging data, improving benchmarking efficacy for causal and temporal understanding. Further, we show that effectively integrating ATP into full video-level temporal models can improve efficiency and state-of-the-art accuracy.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Conceptual Metaphors Impact Perceptions of Human-AI Collaboration

With the emergence of conversational artificial intelligence (AI) agents, it is important to understand the mechanisms that influence users' experiences of these agents. We study a common tool in the designer's toolkit: conceptual metaphors. Metaphors can present an agent as akin to a wry teenager, a toddler, or an experienced butler. How might a choice of metaphor influence our experience of the AI agent? Sampling metaphors along the dimensions of warmth and competence---defined by psychological theories as the primary axes of variation for human social perception---we perform a study (N=260) where we manipulate the metaphor, but not the behavior, of a Wizard-of-Oz conversational agent. Following the experience, participants are surveyed about their intention to use the agent, their desire to cooperate with the agent, and the agent's usability. Contrary to the current tendency of designers to use high competence metaphors to describe AI products, we find that metaphors that signal low competence lead to better evaluations of the agent than metaphors that signal high competence. This effect persists despite both high and low competence agents featuring human-level performance and the wizards being blind to condition. A second study confirms that intention to adopt decreases rapidly as competence projected by the metaphor increases. In a third study, we assess effects of metaphor choices on potential users' desire to try out the system and find that users are drawn to systems that project higher competence and warmth. These results suggest that projecting competence may help attract new users, but those users may discard the agent unless it can quickly correct with a lower competence metaphor. We close with a retrospective analysis that finds similar patterns between metaphors and user attitudes towards past conversational agents such as Xiaoice, Replika, Woebot, Mitsuku, and Tay.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

DualSMC: Tunneling Differentiable Filtering and Planning under Continuous POMDPs

A major difficulty of solving continuous POMDPs is to infer the multi-modal distribution of the unobserved true states and to make the planning algorithm dependent on the perceived uncertainty. We cast POMDP filtering and planning problems as two closely related Sequential Monte Carlo (SMC) processes, one over the real states and the other over the future optimal trajectories, and combine the merits of these two parts in a new model named the DualSMC network. In particular, we first introduce an adversarial particle filter that leverages the adversarial relationship between its internal components. Based on the filtering results, we then propose a planning algorithm that extends the previous SMC planning approach [Piche et al., 2018] to continuous POMDPs with an uncertainty-dependent policy. Crucially, not only can DualSMC handle complex observations such as image input but also it remains highly interpretable. It is shown to be effective in three continuous POMDP domains: the floor positioning domain, the 3D light-dark navigation domain, and a modified Reacher domain.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Dynamics Learning with Cascaded Variational Inference for Multi-Step Manipulation

The fundamental challenge of planning for multi-step manipulation is to find effective and plausible action sequences that lead to the task goal. We present Cascaded Variational Inference (CAVIN) Planner, a model-based method that hierarchically generates plans by sampling from latent spaces. To facilitate planning over long time horizons, our method learns latent representations that decouple the prediction of high-level effects from the generation of low-level motions through cascaded variational inference. This enables us to model dynamics at two different levels of temporal resolutions for hierarchical planning. We evaluate our approach in three multi-step robotic manipulation tasks in cluttered tabletop environments given high-dimensional observations. Empirical results demonstrate that the proposed method outperforms state-of-the-art model-based methods by strategically interacting with multiple objects.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

IRIS: Implicit Reinforcement without Interaction at Scale for Learning Control from Offline Robot Manipulation Data

Learning from offline task demonstrations is a problem of great interest in robotics. For simple short-horizon manipulation tasks with modest variation in task instances, offline learning from a small set of demonstrations can produce controllers that successfully solve the task. However, leveraging a fixed batch of data can be problematic for larger datasets and longer-horizon tasks with greater variations. The data can exhibit substantial diversity and consist of suboptimal solution approaches. In this paper, we propose Implicit Reinforcement without Interaction at Scale (IRIS), a novel framework for learning from large-scale demonstration datasets. IRIS factorizes the control problem into a goal-conditioned low-level controller that imitates short demonstration sequences and a high-level goal selection mechanism that sets goals for the low-level and selectively combines parts of suboptimal solutions leading to more successful task completions. We evaluate IRIS across three datasets, including the RoboTurk Cans dataset collected by humans via crowdsourcing, and show that performant policies can be learned from purely offline learning. Additional results at https://sites.google.com/stanford.edu/iris/ .

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Learning Physical Graph Representations from Visual Scenes

Convolutional Neural Networks (CNNs) have proved exceptional at learning representations for visual object categorization. However, CNNs do not explicitly encode objects, parts, and their physical properties, which has limited CNNs' success on tasks that require structured understanding of visual scenes. To overcome these limitations, we introduce the idea of Physical Scene Graphs (PSGs), which represent scenes as hierarchical graphs, with nodes in the hierarchy corresponding intuitively to object parts at different scales, and edges to physical connections between parts. Bound to each node is a vector of latent attributes that intuitively represent object properties such as surface shape and texture. We also describe PSGNet, a network architecture that learns to extract PSGs by reconstructing scenes through a PSG-structured bottleneck. PSGNet augments standard CNNs by including: recurrent feedback connections to combine low and high-level image information; graph pooling and vectorization operations that convert spatially-uniform feature maps into object-centric graph structures; and perceptual grouping principles to encourage the identification of meaningful scene elements. We show that PSGNet outperforms alternative self-supervised scene representation algorithms at scene segmentation tasks, especially on complex real-world images, and generalizes well to unseen object types and scene arrangements. PSGNet is also able learn from physical motion, enhancing scene estimates even for static images. We present a series of ablation studies illustrating the importance of each component of the PSGNet architecture, analyses showing that learned latent attributes capture intuitive scene properties, and illustrate the use of PSGs for compositional scene inference.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Procedure Planning in Instructional Videos

In this paper, we study the problem of procedure planning in instructional videos, which can be seen as a step towards enabling autonomous agents to plan for complex tasks in everyday settings such as cooking. Given the current visual observation of the world and a visual goal, we ask the question "What actions need to be taken in order to achieve the goal?". The key technical challenge is to learn structured and plannable state and action spaces directly from unstructured videos. We address this challenge by proposing Dual Dynamics Networks (DDN), a framework that explicitly leverages the structured priors imposed by the conjugate relationships between states and actions in a learned plannable latent space. We evaluate our method on real-world instructional videos. Our experiments show that DDN learns plannable representations that lead to better planning performance compared to existing planning approaches and neural network policies.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Vision-based Estimation of MDS-UPDRS Gait Scores for Assessing Parkinson's Disease Motor Severity

Parkinson's disease (PD) is a progressive neurological disorder primarily affecting motor function resulting in tremor at rest, rigidity, bradykinesia, and postural instability. The physical severity of PD impairments can be quantified through the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS), a widely used clinical rating scale. Accurate and quantitative assessment of disease progression is critical to developing a treatment that slows or stops further advancement of the disease. Prior work has mainly focused on dopamine transport neuroimaging for diagnosis or costly and intrusive wearables evaluating motor impairments. For the first time, we propose a computer vision-based model that observes non-intrusive video recordings of individuals, extracts their 3D body skeletons, tracks them through time, and classifies the movements according to the MDS-UPDRS gait scores. Experimental results show that our proposed method performs significantly better than chance and competing methods with an F1-score of 0.83 and a balanced accuracy of 81%. This is the first benchmark for classifying PD patients based on MDS-UPDRS gait severity and could be an objective biomarker for disease severity. Our work demonstrates how computer-assisted technologies can be used to non-intrusively monitor patients and their motor impairments. The code is available at https://github.com/mlu355/PD-Motor-Severity-Estimation.

0 citations0 reviewsNo code linkedOpen access
preprint2017arXiv

Using Deep Learning and Google Street View to Estimate the Demographic Makeup of the US

The United States spends more than $1B each year on initiatives such as the American Community Survey (ACS), a labor-intensive door-to-door study that measures statistics relating to race, gender, education, occupation, unemployment, and other demographic factors. Although a comprehensive source of data, the lag between demographic changes and their appearance in the ACS can exceed half a decade. As digital imagery becomes ubiquitous and machine vision techniques improve, automated data analysis may provide a cheaper and faster alternative. Here, we present a method that determines socioeconomic trends from 50 million images of street scenes, gathered in 200 American cities by Google Street View cars. Using deep learning-based computer vision techniques, we determined the make, model, and year of all motor vehicles encountered in particular neighborhoods. Data from this census of motor vehicles, which enumerated 22M automobiles in total (8% of all automobiles in the US), was used to accurately estimate income, race, education, and voting patterns, with single-precinct resolution. (The average US precinct contains approximately 1000 people.) The resulting associations are surprisingly simple and powerful. For instance, if the number of sedans encountered during a 15-minute drive through a city is higher than the number of pickup trucks, the city is likely to vote for a Democrat during the next Presidential election (88% chance); otherwise, it is likely to vote Republican (82%). Our results suggest that automated systems for monitoring demographic trends may effectively complement labor-intensive approaches, with the potential to detect trends with fine spatial resolution, in close to real time.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A Glimpse Far into the Future: Understanding Long-term Crowd Worker Quality

Microtask crowdsourcing is increasingly critical to the creation of extremely large datasets. As a result, crowd workers spend weeks or months repeating the exact same tasks, making it necessary to understand their behavior over these long periods of time. We utilize three large, longitudinal datasets of nine million annotations collected from Amazon Mechanical Turk to examine claims that workers fatigue or satisfice over these long periods, producing lower quality work. We find that, contrary to these claims, workers are extremely stable in their quality over the entire period. To understand whether workers set their quality based on the task's requirements for acceptance, we then perform an experiment where we vary the required quality for a large crowdsourcing task. Workers did not adjust their quality based on the acceptance threshold: workers who were above the threshold continued working at their usual quality level, and workers below the threshold self-selected themselves out of the task. Capitalizing on this consistency, we demonstrate that it is possible to predict workers' long-term quality using just a glimpse of their quality on the first five tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning

When building artificial intelligence systems that can reason and answer questions about visual data, we need diagnostic tests to analyze our progress and discover shortcomings. Existing benchmarks for visual question answering can help, but have strong biases that models can exploit to correctly answer questions without reasoning. They also conflate multiple sources of error, making it hard to pinpoint model weaknesses. We present a diagnostic dataset that tests a range of visual reasoning abilities. It contains minimal biases and has detailed annotations describing the kind of reasoning each question requires. We use this dataset to analyze a variety of modern visual reasoning systems, providing novel insights into their abilities and limitations.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Connectionist Temporal Modeling for Weakly Supervised Action Labeling

We propose a weakly-supervised framework for action labeling in video, where only the order of occurring actions is required during training time. The key challenge is that the per-frame alignments between the input (video) and label (action) sequences are unknown during training. We address this by introducing the Extended Connectionist Temporal Classification (ECTC) framework to efficiently evaluate all possible alignments via dynamic programming and explicitly enforce their consistency with frame-to-frame visual similarities. This protects the model from distractions of visually inconsistent or degenerated alignments without the need of temporal supervision. We further extend our framework to the semi-supervised case when a few frames are sparsely annotated in a video. With less than 1% of labeled frames per video, our method is able to outperform existing semi-supervised approaches and achieve comparable performance to that of fully supervised approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Crowdsourcing in Computer Vision

Computer vision systems require large amounts of manually annotated data to properly learn challenging visual concepts. Crowdsourcing platforms offer an inexpensive method to capture human knowledge and understanding, for a vast number of visual perception tasks. In this survey, we describe the types of annotations computer vision researchers have collected using crowdsourcing, and how they have ensured that this data is of high quality while annotation effort is minimized. We begin by discussing data collection on both classic (e.g., object recognition) and recent (e.g., visual story-telling) vision tasks. We then summarize key design decisions for creating effective data collection interfaces and workflows, and present strategies for intelligently selecting the most important data instances to annotate. Finally, we conclude with some thoughts on the future of crowdsourcing in computer vision.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Detecting events and key actors in multi-person videos

Multi-person event recognition is a challenging task, often with many people active in the scene but only a small subset contributing to an actual event. In this paper, we propose a model which learns to detect events in such videos while automatically "attending" to the people responsible for the event. Our model does not use explicit annotations regarding who or where those people are during training and testing. In particular, we track people in videos and use a recurrent neural network (RNN) to represent the track features. We learn time-varying attention weights to combine these features at each time-instant. The attended features are then processed using another RNN for event detection/classification. Since most video datasets with multiple people are restricted to a small number of videos, we also collected a new basketball dataset comprising 257 basketball games with 14K event annotations corresponding to 11 event classes. Our model outperforms state-of-the-art methods for both event classification and detection on this new dataset. Additionally, we show that the attention mechanism is able to consistently localize the relevant players.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Embracing Error to Enable Rapid Crowdsourcing

Microtask crowdsourcing has enabled dataset advances in social science and machine learning, but existing crowdsourcing schemes are too expensive to scale up with the expanding volume of data. To scale and widen the applicability of crowdsourcing, we present a technique that produces extremely rapid judgments for binary and categorical labels. Rather than punishing all errors, which causes workers to proceed slowly and deliberately, our technique speeds up workers' judgments to the point where errors are acceptable and even expected. We demonstrate that it is possible to rectify these errors by randomizing task order and modeling response latency. We evaluate our technique on a breadth of common labeling tasks such as image verification, word similarity, sentiment analysis and topic classification. Where prior work typically achieves a 0.25x to 1x speedup over fixed majority vote, our approach often achieves an order of magnitude (10x) speedup.

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preprint2016arXiv

Locally-Optimized Inter-Subject Alignment of Functional Cortical Regions

Inter-subject registration of cortical areas is necessary in functional imaging (fMRI) studies for making inferences about equivalent brain function across a population. However, many high-level visual brain areas are defined as peaks of functional contrasts whose cortical position is highly variable. As such, most alignment methods fail to accurately map functional regions of interest (ROIs) across participants. To address this problem, we propose a locally optimized registration method that directly predicts the location of a seed ROI on a separate target cortical sheet by maximizing the functional correlation between their time courses, while simultaneously allowing for non-smooth local deformations in region topology. Our method outperforms the two most commonly used alternatives (anatomical landmark-based AFNI alignment and cortical convexity-based FreeSurfer alignment) in overlap between predicted region and functionally-defined LOC. Furthermore, the maps obtained using our method are more consistent across subjects than both baseline measures. Critically, our method represents an important step forward towards predicting brain regions without explicit localizer scans and deciphering the poorly understood relationship between the location of functional regions, their anatomical extent, and the consistency of computations those regions perform across people.

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preprint2016arXiv

Perceptual Losses for Real-Time Style Transfer and Super-Resolution

We consider image transformation problems, where an input image is transformed into an output image. Recent methods for such problems typically train feed-forward convolutional neural networks using a \emph{per-pixel} loss between the output and ground-truth images. Parallel work has shown that high-quality images can be generated by defining and optimizing \emph{perceptual} loss functions based on high-level features extracted from pretrained networks. We combine the benefits of both approaches, and propose the use of perceptual loss functions for training feed-forward networks for image transformation tasks. We show results on image style transfer, where a feed-forward network is trained to solve the optimization problem proposed by Gatys et al in real-time. Compared to the optimization-based method, our network gives similar qualitative results but is three orders of magnitude faster. We also experiment with single-image super-resolution, where replacing a per-pixel loss with a perceptual loss gives visually pleasing results.

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preprint2016arXiv

Recurrent Attention Models for Depth-Based Person Identification

We present an attention-based model that reasons on human body shape and motion dynamics to identify individuals in the absence of RGB information, hence in the dark. Our approach leverages unique 4D spatio-temporal signatures to address the identification problem across days. Formulated as a reinforcement learning task, our model is based on a combination of convolutional and recurrent neural networks with the goal of identifying small, discriminative regions indicative of human identity. We demonstrate that our model produces state-of-the-art results on several published datasets given only depth images. We further study the robustness of our model towards viewpoint, appearance, and volumetric changes. Finally, we share insights gleaned from interpretable 2D, 3D, and 4D visualizations of our model's spatio-temporal attention.

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preprint2016arXiv

Target-driven Visual Navigation in Indoor Scenes using Deep Reinforcement Learning

Two less addressed issues of deep reinforcement learning are (1) lack of generalization capability to new target goals, and (2) data inefficiency i.e., the model requires several (and often costly) episodes of trial and error to converge, which makes it impractical to be applied to real-world scenarios. In this paper, we address these two issues and apply our model to the task of target-driven visual navigation. To address the first issue, we propose an actor-critic model whose policy is a function of the goal as well as the current state, which allows to better generalize. To address the second issue, we propose AI2-THOR framework, which provides an environment with high-quality 3D scenes and physics engine. Our framework enables agents to take actions and interact with objects. Hence, we can collect a huge number of training samples efficiently. We show that our proposed method (1) converges faster than the state-of-the-art deep reinforcement learning methods, (2) generalizes across targets and across scenes, (3) generalizes to a real robot scenario with a small amount of fine-tuning (although the model is trained in simulation), (4) is end-to-end trainable and does not need feature engineering, feature matching between frames or 3D reconstruction of the environment. The supplementary video can be accessed at the following link: https://youtu.be/SmBxMDiOrvs.

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preprint2016arXiv

The Unreasonable Effectiveness of Noisy Data for Fine-Grained Recognition

Current approaches for fine-grained recognition do the following: First, recruit experts to annotate a dataset of images, optionally also collecting more structured data in the form of part annotations and bounding boxes. Second, train a model utilizing this data. Toward the goal of solving fine-grained recognition, we introduce an alternative approach, leveraging free, noisy data from the web and simple, generic methods of recognition. This approach has benefits in both performance and scalability. We demonstrate its efficacy on four fine-grained datasets, greatly exceeding existing state of the art without the manual collection of even a single label, and furthermore show first results at scaling to more than 10,000 fine-grained categories. Quantitatively, we achieve top-1 accuracies of 92.3% on CUB-200-2011, 85.4% on Birdsnap, 93.4% on FGVC-Aircraft, and 80.8% on Stanford Dogs without using their annotated training sets. We compare our approach to an active learning approach for expanding fine-grained datasets.

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preprint2016arXiv

Towards Viewpoint Invariant 3D Human Pose Estimation

We propose a viewpoint invariant model for 3D human pose estimation from a single depth image. To achieve this, our discriminative model embeds local regions into a learned viewpoint invariant feature space. Formulated as a multi-task learning problem, our model is able to selectively predict partial poses in the presence of noise and occlusion. Our approach leverages a convolutional and recurrent network architecture with a top-down error feedback mechanism to self-correct previous pose estimates in an end-to-end manner. We evaluate our model on a previously published depth dataset and a newly collected human pose dataset containing 100K annotated depth images from extreme viewpoints. Experiments show that our model achieves competitive performance on frontal views while achieving state-of-the-art performance on alternate viewpoints.

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preprint2016arXiv

Visual Relationship Detection with Language Priors

Visual relationships capture a wide variety of interactions between pairs of objects in images (e.g. "man riding bicycle" and "man pushing bicycle"). Consequently, the set of possible relationships is extremely large and it is difficult to obtain sufficient training examples for all possible relationships. Because of this limitation, previous work on visual relationship detection has concentrated on predicting only a handful of relationships. Though most relationships are infrequent, their objects (e.g. "man" and "bicycle") and predicates (e.g. "riding" and "pushing") independently occur more frequently. We propose a model that uses this insight to train visual models for objects and predicates individually and later combines them together to predict multiple relationships per image. We improve on prior work by leveraging language priors from semantic word embeddings to finetune the likelihood of a predicted relationship. Our model can scale to predict thousands of types of relationships from a few examples. Additionally, we localize the objects in the predicted relationships as bounding boxes in the image. We further demonstrate that understanding relationships can improve content based image retrieval.

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preprint2016arXiv

Visual7W: Grounded Question Answering in Images

We have seen great progress in basic perceptual tasks such as object recognition and detection. However, AI models still fail to match humans in high-level vision tasks due to the lack of capacities for deeper reasoning. Recently the new task of visual question answering (QA) has been proposed to evaluate a model's capacity for deep image understanding. Previous works have established a loose, global association between QA sentences and images. However, many questions and answers, in practice, relate to local regions in the images. We establish a semantic link between textual descriptions and image regions by object-level grounding. It enables a new type of QA with visual answers, in addition to textual answers used in previous work. We study the visual QA tasks in a grounded setting with a large collection of 7W multiple-choice QA pairs. Furthermore, we evaluate human performance and several baseline models on the QA tasks. Finally, we propose a novel LSTM model with spatial attention to tackle the 7W QA tasks.

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preprint2016arXiv

What's the Point: Semantic Segmentation with Point Supervision

The semantic image segmentation task presents a trade-off between test time accuracy and training-time annotation cost. Detailed per-pixel annotations enable training accurate models but are very time-consuming to obtain, image-level class labels are an order of magnitude cheaper but result in less accurate models. We take a natural step from image-level annotation towards stronger supervision: we ask annotators to point to an object if one exists. We incorporate this point supervision along with a novel objectness potential in the training loss function of a CNN model. Experimental results on the PASCAL VOC 2012 benchmark reveal that the combined effect of point-level supervision and objectness potential yields an improvement of 12.9% mIOU over image-level supervision. Further, we demonstrate that models trained with point-level supervision are more accurate than models trained with image-level, squiggle-level or full supervision given a fixed annotation budget.

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preprint2015arXiv

Building a Large-scale Multimodal Knowledge Base System for Answering Visual Queries

The complexity of the visual world creates significant challenges for comprehensive visual understanding. In spite of recent successes in visual recognition, today's vision systems would still struggle to deal with visual queries that require a deeper reasoning. We propose a knowledge base (KB) framework to handle an assortment of visual queries, without the need to train new classifiers for new tasks. Building such a large-scale multimodal KB presents a major challenge of scalability. We cast a large-scale MRF into a KB representation, incorporating visual, textual and structured data, as well as their diverse relations. We introduce a scalable knowledge base construction system that is capable of building a KB with half billion variables and millions of parameters in a few hours. Our system achieves competitive results compared to purpose-built models on standard recognition and retrieval tasks, while exhibiting greater flexibility in answering richer visual queries.

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preprint2015arXiv

Deep Visual-Semantic Alignments for Generating Image Descriptions

We present a model that generates natural language descriptions of images and their regions. Our approach leverages datasets of images and their sentence descriptions to learn about the inter-modal correspondences between language and visual data. Our alignment model is based on a novel combination of Convolutional Neural Networks over image regions, bidirectional Recurrent Neural Networks over sentences, and a structured objective that aligns the two modalities through a multimodal embedding. We then describe a Multimodal Recurrent Neural Network architecture that uses the inferred alignments to learn to generate novel descriptions of image regions. We demonstrate that our alignment model produces state of the art results in retrieval experiments on Flickr8K, Flickr30K and MSCOCO datasets. We then show that the generated descriptions significantly outperform retrieval baselines on both full images and on a new dataset of region-level annotations.

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preprint2015arXiv

DenseCap: Fully Convolutional Localization Networks for Dense Captioning

We introduce the dense captioning task, which requires a computer vision system to both localize and describe salient regions in images in natural language. The dense captioning task generalizes object detection when the descriptions consist of a single word, and Image Captioning when one predicted region covers the full image. To address the localization and description task jointly we propose a Fully Convolutional Localization Network (FCLN) architecture that processes an image with a single, efficient forward pass, requires no external regions proposals, and can be trained end-to-end with a single round of optimization. The architecture is composed of a Convolutional Network, a novel dense localization layer, and Recurrent Neural Network language model that generates the label sequences. We evaluate our network on the Visual Genome dataset, which comprises 94,000 images and 4,100,000 region-grounded captions. We observe both speed and accuracy improvements over baselines based on current state of the art approaches in both generation and retrieval settings.

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preprint2015arXiv

ImageNet Large Scale Visual Recognition Challenge

The ImageNet Large Scale Visual Recognition Challenge is a benchmark in object category classification and detection on hundreds of object categories and millions of images. The challenge has been run annually from 2010 to present, attracting participation from more than fifty institutions. This paper describes the creation of this benchmark dataset and the advances in object recognition that have been possible as a result. We discuss the challenges of collecting large-scale ground truth annotation, highlight key breakthroughs in categorical object recognition, provide a detailed analysis of the current state of the field of large-scale image classification and object detection, and compare the state-of-the-art computer vision accuracy with human accuracy. We conclude with lessons learned in the five years of the challenge, and propose future directions and improvements.

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preprint2015arXiv

Improving Image Classification with Location Context

With the widespread availability of cellphones and cameras that have GPS capabilities, it is common for images being uploaded to the Internet today to have GPS coordinates associated with them. In addition to research that tries to predict GPS coordinates from visual features, this also opens up the door to problems that are conditioned on the availability of GPS coordinates. In this work, we tackle the problem of performing image classification with location context, in which we are given the GPS coordinates for images in both the train and test phases. We explore different ways of encoding and extracting features from the GPS coordinates, and show how to naturally incorporate these features into a Convolutional Neural Network (CNN), the current state-of-the-art for most image classification and recognition problems. We also show how it is possible to simultaneously learn the optimal pooling radii for a subset of our features within the CNN framework. To evaluate our model and to help promote research in this area, we identify a set of location-sensitive concepts and annotate a subset of the Yahoo Flickr Creative Commons 100M dataset that has GPS coordinates with these concepts, which we make publicly available. By leveraging location context, we are able to achieve almost a 7% gain in mean average precision.

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preprint2015arXiv

Learning Temporal Embeddings for Complex Video Analysis

In this paper, we propose to learn temporal embeddings of video frames for complex video analysis. Large quantities of unlabeled video data can be easily obtained from the Internet. These videos possess the implicit weak label that they are sequences of temporally and semantically coherent images. We leverage this information to learn temporal embeddings for video frames by associating frames with the temporal context that they appear in. To do this, we propose a scheme for incorporating temporal context based on past and future frames in videos, and compare this to other contextual representations. In addition, we show how data augmentation using multi-resolution samples and hard negatives helps to significantly improve the quality of the learned embeddings. We evaluate various design decisions for learning temporal embeddings, and show that our embeddings can improve performance for multiple video tasks such as retrieval, classification, and temporal order recovery in unconstrained Internet video.

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preprint2015arXiv

SentenceRacer: A Game with a Purpose for Image Sentence Annotation

Recently datasets that contain sentence descriptions of images have enabled models that can automatically generate image captions. However, collecting these datasets are still very expensive. Here, we present SentenceRacer, an online game that gathers and verifies descriptions of images at no cost. Similar to the game hangman, players compete to uncover words in a sentence that ultimately describes an image. SentenceRacer both generates and verifies that the sentences are accurate descriptions. We show that SentenceRacer generates annotations of higher quality than those generated on Amazon Mechanical Turk (AMT).

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preprint2015arXiv

Visualizing and Understanding Recurrent Networks

Recurrent Neural Networks (RNNs), and specifically a variant with Long Short-Term Memory (LSTM), are enjoying renewed interest as a result of successful applications in a wide range of machine learning problems that involve sequential data. However, while LSTMs provide exceptional results in practice, the source of their performance and their limitations remain rather poorly understood. Using character-level language models as an interpretable testbed, we aim to bridge this gap by providing an analysis of their representations, predictions and error types. In particular, our experiments reveal the existence of interpretable cells that keep track of long-range dependencies such as line lengths, quotes and brackets. Moreover, our comparative analysis with finite horizon n-gram models traces the source of the LSTM improvements to long-range structural dependencies. Finally, we provide analysis of the remaining errors and suggests areas for further study.

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preprint2014arXiv

Affordances Provide a Fundamental Categorization Principle for Visual Scenes

How do we know that a kitchen is a kitchen by looking? Relatively little is known about how we conceptualize and categorize different visual environments. Traditional models of visual perception posit that scene categorization is achieved through the recognition of a scene's objects, yet these models cannot account for the mounting evidence that human observers are relatively insensitive to the local details in an image. Psychologists have long theorized that the affordances, or actionable possibilities of a stimulus are pivotal to its perception. To what extent are scene categories created from similar affordances? Using a large-scale experiment using hundreds of scene categories, we show that the activities afforded by a visual scene provide a fundamental categorization principle. Affordance-based similarity explained the majority of the structure in the human scene categorization patterns, outperforming alternative similarities based on objects or visual features. We all models were combined, affordances provided the majority of the predictive power in the combined model, and nearly half of the total explained variance is captured only by affordances. These results challenge many existing models of high-level visual perception, and provide immediately testable hypotheses for the functional organization of the human perceptual system.

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preprint2014arXiv

Deep Fragment Embeddings for Bidirectional Image Sentence Mapping

We introduce a model for bidirectional retrieval of images and sentences through a multi-modal embedding of visual and natural language data. Unlike previous models that directly map images or sentences into a common embedding space, our model works on a finer level and embeds fragments of images (objects) and fragments of sentences (typed dependency tree relations) into a common space. In addition to a ranking objective seen in previous work, this allows us to add a new fragment alignment objective that learns to directly associate these fragments across modalities. Extensive experimental evaluation shows that reasoning on both the global level of images and sentences and the finer level of their respective fragments significantly improves performance on image-sentence retrieval tasks. Additionally, our model provides interpretable predictions since the inferred inter-modal fragment alignment is explicit.

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preprint2014arXiv

VideoSET: Video Summary Evaluation through Text

In this paper we present VideoSET, a method for Video Summary Evaluation through Text that can evaluate how well a video summary is able to retain the semantic information contained in its original video. We observe that semantics is most easily expressed in words, and develop a text-based approach for the evaluation. Given a video summary, a text representation of the video summary is first generated, and an NLP-based metric is then used to measure its semantic distance to ground-truth text summaries written by humans. We show that our technique has higher agreement with human judgment than pixel-based distance metrics. We also release text annotations and ground-truth text summaries for a number of publicly available video datasets, for use by the computer vision community.

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preprint2014arXiv

Visual Noise from Natural Scene Statistics Reveals Human Scene Category Representations

Our perceptions are guided both by the bottom-up information entering our eyes, as well as our top-down expectations of what we will see. Although bottom-up visual processing has been extensively studied, comparatively little is known about top-down signals. Here, we describe REVEAL (Representations Envisioned Via Evolutionary ALgorithm), a method for visualizing an observer's internal representation of a complex, real-world scene, allowing us to, for the first time, visualize the top-down information in an observer's mind. REVEAL rests on two innovations for solving this high dimensional problem: visual noise that samples from natural image statistics, and a computer algorithm that collaborates with human observers to efficiently obtain a solution. In this work, we visualize observers' internal representations of a visual scene category (street) using an experiment in which the observer views the naturalistic visual noise and collaborates with the algorithm to externalize his internal representation. As no scene information was presented, observers had to use their internal knowledge of the target, matching it with the visual features in the noise. We matched reconstructed images with images of real-world street scenes to enhance visualization. Critically, we show that the visualized mental images can be used to predict rapid scene detection performance, as each observer had faster and more accurate responses to detecting real-world images that were the most similar to his reconstructed street templates. These results show that it is possible to visualize previously unobservable mental representations of real world stimuli. More broadly, REVEAL provides a general method for objectively examining the content of previously private, subjective mental experiences.

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preprint2012arXiv

Efficient Euclidean Projections onto the Intersection of Norm Balls

Using sparse-inducing norms to learn robust models has received increasing attention from many fields for its attractive properties. Projection-based methods have been widely applied to learning tasks constrained by such norms. As a key building block of these methods, an efficient operator for Euclidean projection onto the intersection of $\ell_1$ and $\ell_{1,q}$ norm balls $(q=2\text{or}\infty)$ is proposed in this paper. We prove that the projection can be reduced to finding the root of an auxiliary function which is piecewise smooth and monotonic. Hence, a bisection algorithm is sufficient to solve the problem. We show that the time complexity of our solution is $O(n+g\log g)$ for $q=2$ and $O(n\log n)$ for $q=\infty$, where $n$ is the dimensionality of the vector to be projected and $g$ is the number of disjoint groups; we confirm this complexity by experimentation. Empirical study reveals that our method achieves significantly better performance than classical methods in terms of running time and memory usage. We further show that embedded with our efficient projection operator, projection-based algorithms can solve regression problems with composite norm constraints more efficiently than other methods and give superior accuracy.

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