3D color lookup tables (LUTs) enable precise color manipulation by mapping input RGB values to specific output RGB values. 3D LUTs are instrumental in various applications, including video editing, in-camera processing, photographic filters, computer graphics, and color processing for displays. While an individual LUT does not incur a high memory overhead, software and devices may need to store dozens to hundreds of LUTs that can take over 100 MB. This work aims to develop a neural network architecture that can encode hundreds of LUTs in a single compact representation. To this end, we propose a model with a memory footprint of less than 0.25 MB that can reconstruct 512 LUTs with only minor color distortion (ΔE ≤ 2.0 on average) over the entire color gamut. We also show that our network can weight colors to provide further quality gains on natural image colors (ΔE ≤ 1.0 on average). Finally, we show that minor modifications to the network architecture enable a bijective encoding that produces LUTs that are invertible, allowing for reverse color processing.

There has been extensive progress in the reconstruction and generation of 4D scenes from monocular casually-captured video. While these tasks rely heavily on known camera poses, the problem of finding such poses using structure-from-motion (SfM) often depends on robustly separating static from dynamic parts of a video. The lack of a robust solution to this problem limits the performance of SfM camera-calibration pipelines. We propose a novel approach to video-based motion segmentation to identify the components of a scene that are moving w.r.t. a fixed world frame. Our simple but effective iterative method, RoMo, combines optical flow and epipolar cues with a pre-trained video segmentation model. It outperforms unsupervised baselines for motion segmentation as well as supervised baselines trained from synthetic data. More importantly, the combination of an off-the-shelf SfM pipeline with our segmentation masks establishes a new state-of-the-art on camera calibration for scenes with dynamic content, outperforming existing methods by a substantial margin.

Cryo-EM is a transformational paradigm in molecular biology where computational methods are used to infer 3D molecular structure at atomic resolution from extremely noisy 2D electron microscope images. At the forefront of research is how to model the structure when the imaged particles exhibit non-rigid conformational flexibility and compositional variation where parts are sometimes missing. We introduce a novel 3D reconstruction framework with a hierarchical Gaussian mixture model, inspired in part by Gaussian Splatting for 4D scene reconstruction. In particular, the structure of the model is grounded in an initial process that infers a part-based segmentation of the particle, providing essential inductive bias in order to handle both conformational and compositional variability. The framework, called \methodName, is shown to reveal biologically meaningful structures on complex experimental datasets, and establishes a new state-of-the-art on CryoBench, a benchmark for cryo-EM heterogeneity methods.

Cryo-EM is an increasingly popular method for determining the atomic resolution 3D structure of macromolecular complexes (eg, proteins) from noisy 2D images captured by an electron microscope. The computational task is to reconstruct the 3D density of the particle, along with 3D pose of the particle in each 2D image, for which the posterior pose distribution is highly multi-modal. Recent developments in cryo-EM have focused on deep learning for which amortized inference has been used to predict pose. Here, we address key problems with this approach, and propose a new semi-amortized method, cryoSPIN, in which reconstruction begins with amortized inference and then switches to a form of auto-decoding to refine poses locally using stochastic gradient descent. Through evaluation on synthetic datasets, we demonstrate that cryoSPIN is able to handle multi-modal pose distributions during the amortized inference stage, while the later, more flexible stage of direct pose optimization yields faster and more accurate convergence of poses compared to baselines. On experimental data, we show that cryoSPIN outperforms the state-of-the-art cryoAI in speed and reconstruction quality.

Neural Radiance Fields (NeRFs) have emerged as a popular approach for novel view synthesis. While NeRFs are quickly being adapted for a wider set of applications, intuitively editing NeRF scenes is still an open challenge. One important editing task is the removal of unwanted objects from a 3D scene, such that the replaced region is visually plausible and consistent with its context. We refer to this task as 3D inpainting. In 3D, solutions must be both consistent across multiple views and geometrically valid. In this paper, we propose a novel 3D inpainting method that addresses these challenges. Given a small set of posed images and sparse annotations in a single input image, our framework first rapidly obtains a 3D segmentation mask for a target object. Using the mask, a perceptual optimization-based approach is then introduced that leverages learned 2D image inpainters, distilling their information into 3D space, while ensuring view consistency. We also address the lack of a diverse benchmark for evaluating 3D scene inpainting methods by introducing a dataset comprised of challenging real-world scenes. In particular, our dataset contains views of the same scene with and without a target object, enabling more principled benchmarking of the 3D inpainting task. We first demonstrate the superiority of our approach on multiview segmentation, comparing to NeRF-based methods and 2D segmentation approaches. We then evaluate on the task of 3D inpainting, establishing state-of-the-art performance against other NeRF manipulation algorithms, as well as a strong 2D image inpainter baseline.

The popularity of Neural Radiance Fields (NeRFs) for view synthesis has led to a desire for NeRF editing tools. Here, we focus on inpainting regions in a view-consistent and controllable manner. In addition to the typical NeRF inputs and masks delineating the unwanted region in each view, we require only a single inpainted view of the scene, i.e., a reference view. We use monocular depth estimators to back-project the inpainted view to the correct 3D positions. Then, via a novel rendering technique, a bilateral solver can construct view-dependent effects in non-reference views, making the inpainted region appear consistent from any view. For non-reference disoccluded regions, which cannot be supervised by the single reference view, we devise a method based on image inpainters to guide both the geometry and appearance. Our approach shows superior performance to NeRF inpainting baselines, with the additional advantage that a user can control the output via a single inpainted image. Please visit our project page.

Novel view synthesis from a single input image is a challenging task, where the goal is to generate a new view of a scene from a desired camera pose that may be separated by a large motion. The highly uncertain nature of this synthesis task due to unobserved elements within the scene (i.e. occlusion) and outside the field-of-view makes the use of generative models appealing to capture the variety of possible outputs. In this paper, we propose a novel generative model capable of producing a sequence of photorealistic images consistent with a specified camera trajectory, and a single starting image. Our approach is centred on an autoregressive conditional diffusion-based model capable of interpolating visible scene elements, and extrapolating unobserved regions in a view, in a geometrically consistent manner. Conditioning is limited to an image capturing a single camera view and the (relative) pose of the new camera view. To measure the consistency over a sequence of generated views, we introduce a new metric, the thresholded symmetric epipolar distance (TSED), to measure the number of consistent frame pairs in a sequence. While previous methods have been shown to produce high quality images and consistent semantics across pairs of views, we show empirically with our metric that they are often inconsistent with the desired camera poses. In contrast, we demonstrate that our method produces both photorealistic and view-consistent imagery. Additional material is available on our project page: https://yorkucvil.github.io/Photoconsistent-NVS/.

Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependent on properly tuned parameters, most of which are difficult if not impossible to know a priori for a given target distribution. Adaptive MCMC methods aim to address this by allowing the parameters to be updated during sampling based on previous samples from the chain at the expense of requiring a new theoretical analysis to ensure convergence. In this work we extend the convergence theory of adaptive MCMC methods to a new class of methods built on a powerful class of parametric density estimators known as normalizing flows. In particular, we consider an independent Metropolis-Hastings sampler where the proposal distribution is represented by a normalizing flow whose parameters are updated using stochastic gradient descent. We explore the practical performance of this procedure on both synthetic settings and in the analysis of a physical field system, and compare it against both adaptive and non-adaptive MCMC methods.

Noise modeling and reduction are fundamental tasks in low-level computer vision. They are particularly important for smartphone cameras relying on small sensors that exhibit visually noticeable noise. There has recently been renewed interest in using data-driven approaches to improve camera noise models via neural networks. These data-driven approaches target noise present in the raw-sensor image before it has been processed by the camera's image signal processor (ISP). Modeling noise in the RAW-rgb domain is useful for improving and testing the in-camera denoising algorithm; however, there are situations where the camera's ISP does not apply denoising or additional denoising is desired when the RAW-rgb domain image is no longer available. In such cases, the sensor noise propagates through the ISP to the final rendered image encoded in standard RGB (sRGB). The nonlinear steps on the ISP culminate in a significantly more complex noise distribution in the sRGB domain and existing raw-domain noise models are unable to capture the sRGB noise distribution. We propose a new sRGB-domain noise model based on normalizing flows that is capable of learning the complex noise distribution found in sRGB images under various ISO levels. Our normalizing flows-based approach outperforms other models by a large margin in noise modeling and synthesis tasks. We also show that image denoisers trained on noisy images synthesized with our noise model outperforms those trained with noise from baselines models.

Image noise modeling is a long-standing problem with many applications in computer vision. Early attempts that propose simple models, such as signal-independent additive white Gaussian noise or the heteroscedastic Gaussian noise model (a.k.a., camera noise level function) are not sufficient to learn the complex behavior of the camera sensor noise. Recently, more complex learning-based models have been proposed that yield better results in noise synthesis and downstream tasks, such as denoising. However, their dependence on supervised data (i.e., paired clean images) is a limiting factor given the challenges in producing ground-truth images. This paper proposes a framework for training a noise model and a denoiser simultaneously while relying only on pairs of noisy images rather than noisy/clean paired image data. We apply this framework to the training of the Noise Flow architecture. The noise synthesis and density estimation results show that our framework outperforms previous signal-processing-based noise models and is on par with its supervised counterpart. The trained denoiser is also shown to significantly improve upon both supervised and weakly supervised baseline denoising approaches. The results indicate that the joint training of a denoiser and a noise model yields significant improvements in the denoiser.

Most camera images are rendered and saved in the standard RGB (sRGB) format by the camera's hardware. Due to the in-camera photo-finishing routines, nonlinear sRGB images are undesirable for computer vision tasks that assume a direct relationship between pixel values and scene radiance. For such applications, linear raw-RGB sensor images are preferred. Saving images in their raw-RGB format is still uncommon due to the large storage requirement and lack of support by many imaging applications. Several “raw reconstruction” methods have been proposed that utilize specialized metadata sampled from the raw-RGB image at capture time and embedded in the sRGB image. This metadata is used to parameterize a mapping function to derender the sRGB image back to its original raw-RGB format when needed. Existing raw reconstruction methods rely on simple sampling strategies and global mapping to perform the de-rendering. This paper shows how to improve the derendering results by jointly learning sampling and reconstruction. Our experiments show that our learned sampling can adapt to the image content to produce better raw reconstructions than existing methods. We also describe an online fine-tuning strategy for the reconstruction network to improve results further.

Coordinate networks like Multiplicative Filter Networks (MFNs) and BACON offer some control over the frequency spectrum used to represent continuous signals such as images or 3D volumes. Yet, they are not readily applicable to problems for which coarse-to-fine estimation is required, including various inverse problems in which coarse-to-fine optimization plays a key role in avoiding poor local minima. We introduce a new coordinate network architecture and training scheme that enables coarse-to-fine optimization with fine-grained control over the frequency support of learned reconstructions. This is achieved with two key innovations. First, we incorporate skip connections so that structure at one scale is preserved when fitting finer-scale structure. Second, we propose a novel initialization scheme to provide control over the model frequency spectrum at each stage of optimization. We demonstrate how these modifications enable multiscale optimization for coarse-to-fine fitting to natural images. We then evaluate our model on synthetically generated datasets for the the problem of single-particle cryo-EM reconstruction. We learn high resolution multiscale structures, on par with the state-of-the art. Project webpage: https://shekshaa.github.io/ResidualMFN/.

Auto white balance (AWB) is applied by camera hardware at capture time to remove the color cast caused by the scene illumination. The vast majority of white-balance algorithms assume a single light source illuminates the scene; however, real scenes often have mixed lighting conditions. This paper presents an effective AWB method to deal with such mixed-illuminant scenes. A unique departure from conventional AWB, our method does not require illuminant estimation, as is the case in traditional camera AWB modules. Instead, our method proposes to render the captured scene with a small set of predefined white-balance settings. Given this set of rendered images, our method learns to estimate weighting maps that are used to blend the rendered images to generate the final corrected image. Through extensive experiments, we show this proposed method produces promising results compared to other alternatives for single-and mixed-illuminant scene color correction.

While generative adversarial networks (GANs) can successfully produce high-quality images, they can be challenging to control. Simplifying GAN-based image generation is critical for their adoption in graphic design and artistic work. This goal has led to significant interest in methods that can intuitively control the appearance of images generated by GANs. In this paper, we present HistoGAN, a color histogram-based method for controlling GAN-generated images’ colors. We focus on color histograms as they provide an intuitive way to describe image color while remaining decoupled from domain-specific semantics. Specifically, we introduce an effective modification of the recent StyleGAN architecture [31] to control the colors of GAN-generated images specified by a target color histogram feature. We then describe how to expand HistoGAN to recolor real images. For image recoloring, we jointly train an encoder network along with HistoGAN. The recoloring model, ReHistoGAN, is an unsupervised approach trained to encourage the network to keep the original image’s content while changing the colors based on the given target histogram. We show that this histogram-based approach offers a better way to control GAN-generated and real images’ colors while producing more compelling results compared to existing alternative strategies.

Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has practical benefits, including the ability to generate continuous trajectories and to perform inference on previously unseen time stamps. Despite exciting progress in this area, the existing models still face challenges in terms of their representational power and the quality of their variational approximations. We tackle these challenges with continuous latent process flows (CLPF), a principled architecture decoding continuous latent processes into continuous observable processes using a time-dependent normalizing flow driven by a stochastic differential equation. To optimize our model using maximum likelihood, we propose a novel piecewise construction of a variational posterior process and derive the corresponding variational lower bound using trajectory re-weighting. Our ablation studies demonstrate the effectiveness of our contributions in various inference tasks on irregular time grids. Comparisons to state-of-the-art baselines show our model's favourable performance on both synthetic and real-world time-series data.

Normalizing Flows are generative models which produce tractable distributions where both sampling and density evaluation can be efficient and exact. The goal of this survey article is to give a coherent and comprehensive review of the literature around the construction and use of Normalizing Flows for distribution learning. We aim to provide context and explanation of the models, review current state-of-the-art literature, and identify open questions and promising future directions.

Knowledge graphs (KGs) typically contain temporal facts indicating relationships among entities at different times. Due to their incompleteness, several approaches have been proposed to infer new facts for a KG based on the existing ones–a problem known as KG completion. KG embedding approaches have proved effective for KG completion, however, they have been developed mostly for static KGs. Developing temporal KG embedding models is an increasingly important problem. In this paper, we build novel models for temporal KG completion through equipping static models with a diachronic entity embedding function which provides the characteristics of entities at any point in time. This is in contrast to the existing temporal KG embedding approaches where only static entity features are provided. The proposed embedding function is model-agnostic and can be potentially combined with any static model. We prove that combining it with SimplE, a recent model for static KG embedding, results in a fully expressive model for temporal KG completion. Our experiments indicate the superiority of our proposal compared to existing baselines.

We investigate the ability of popular flow models to capture tail-properties of a target density by studying the increasing triangular maps used in these flow methods acting on a tractable source density. We show that the density quantile functions of the source and target density provide a precise characterization of the slope of transformation required to capture tails in a target density. We further show that any Lipschitz-continuous transport map acting on a source density will result in a density with similar tail properties as the source, highlighting the trade-off between the importance of choosing a complex source density and a sufficiently expressive transformation to capture desirable properties of a target density. Subsequently, we illustrate that flow models like Real-NVP, MAF, and Glow as implemented lack the ability to capture a distribution with non-Gaussian tails. We circumvent this problem by proposing tail-adaptive flows consisting of a source distribution that can be learned simultaneously with the triangular map to capture tail-properties of a target density. We perform several synthetic and real-world experiments to complement our theoretical findings.

Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by a differential deformation of the continuous-time Wiener process. As a result, we obtain a rich time series model whose observable process inherits many of the appealing properties of its base process, such as efficient computation of likelihoods and marginals. Furthermore, our continuous treatment provides a natural framework for irregular time series with an independent arrival process, including straightforward interpolation. We illustrate the desirable properties of the proposed model on popular stochastic processes and demonstrate its superior flexibility to variational RNN and latent ODE baselines in a series of experiments on synthetic and real-world data.

Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is their significant training cost, sometimes requiring months of GPU training time to achieve state-of-the-art results. This paper introduces Wavelet Flow, a multi-scale, normalizing flow architecture based on wavelets. A Wavelet Flow has an explicit representation of signal scale that inherently includes models of lower resolution signals and conditional generation of higher resolution signals, i.e., super resolution. A major advantage of Wavelet Flow is the ability to construct generative models for high resolution data (e.g., 1024 × 1024 images) that are impractical with previous models. Furthermore, Wavelet Flow is competitive with previous normalizing flows in terms of bits per dimension on standard (low resolution) benchmarks while being up to 15× faster to train.

Abstract We present a probabilistic framework to generate character animations based on weak control signals, such that the synthesized motions are realistic while retaining the stochastic nature of human movement. The proposed architecture, which is designed as a hierarchical recurrent model, maps each sub‐sequence of motions into a stochastic latent code using a variational autoencoder extended over the temporal domain. We also propose an objective function which respects the impact of each joint on the pose and compares the joint angles based on angular distance. We use two novel quantitative protocols and human qualitative assessment to demonstrate the ability of our model to generate convincing and diverse periodic and non‐periodic motion sequences without the need for strong control signals.

Modeling and synthesizing image noise is an important aspect in many computer vision applications. The long-standing additive white Gaussian and heteroscedastic (signal-dependent) noise models widely used in the literature provide only a coarse approximation of real sensor noise. This paper introduces Noise Flow, a powerful and accurate noise model based on recent normalizing flow architectures. Noise Flow combines well-established basic parametric noise models (e.g., signal-dependent noise) with the flexibility and expressiveness of normalizing flow networks. The result is a single, comprehensive, compact noise model containing fewer than 2500 parameters yet able to represent multiple cameras and gain factors. Noise Flow dramatically outperforms existing noise models, with 0.42 nats/pixel improvement over the camera-calibrated noise level functions, which translates to 52% improvement in the likelihood of sampled noise. Noise Flow represents the first serious attempt to go beyond simple parametric models to one that leverages the power of deep learning and data-driven noise distributions.

Carefully crafted, often imperceptible, adversarial perturbations have been shown to cause state-of-the-art models to yield extremely inaccurate outputs, rendering them unsuitable for safety-critical application domains. In addition, recent work has shown that constraining the attack space to a low frequency regime is particularly effective. Yet, it remains unclear whether this is due to generally constraining the attack search space or specifically removing high frequency components from consideration. By systematically controlling the frequency components of the perturbation, evaluating against the top-placing defense submissions in the NeurIPS 2017 competition, we empirically show that performance improvements in both the white-box and black-box transfer settings are yielded only when low frequency components are preserved. In fact, the defended models based on adversarial training are roughly as vulnerable to low frequency perturbations as undefended models, suggesting that the purported robustness of state-of-the-art ImageNet defenses is reliant upon adversarial perturbations being high frequency in nature. We do find that under L-inf-norm constraint 16/255, the competition distortion bound, low frequency perturbations are indeed perceptible. This questions the use of the L-inf-norm, in particular, as a distortion metric, and, in turn, suggests that explicitly considering the frequency space is promising for learning robust models which better align with human perception.

We introduce a two-stream model for dynamic texture synthesis. Our model is based on pre-trained convolutional networks (ConvNets) that target two independent tasks: (i) object recognition, and (ii) optical flow prediction. Given an input dynamic texture, statistics of filter responses from the object recognition ConvNet encapsulate the per-frame appearance of the input texture, while statistics of filter responses from the optical flow ConvNet model its dynamics. To generate a novel texture, a randomly initialized input sequence is optimized to match the feature statistics from each stream of an example texture. Inspired by recent work on image style transfer and enabled by the two-stream model, we also apply the synthesis approach to combine the texture appearance from one texture with the dynamics of another to generate entirely novel dynamic textures. We show that our approach generates novel, high quality samples that match both the framewise appearance and temporal evolution of input texture. Finally, we quantitatively evaluate our texture synthesis approach with a thorough user study.

In this paper we present a robust, efficient and affordable approach to self-localization which requires neither GPS nor knowledge about the appearance of the world. Towards this goal, we utilize freely available cartographic maps and derive a probabilistic model that exploits semantic cues in the form of sun direction, presence of an intersection, road type, speed limit and ego-car trajectory to produce very reliable localization results. Our experimental evaluation shows that our approach can localize much faster (in terms of driving time) with less computation and more robustly than competing approaches, which ignore semantic information.

In this paper, we explore the use of current deep learning methods in the field of computer-aided diagnosis (CAD). Specifically we propose the use of 3D convolutional neural nets (CNN) in classifying lung nodules based off of their appearance in CT scans. We explore the choices of network architectures, learning parameters and problem formulations. Comparing these results to other methods we show that the proposed method has close to perfect performance on the publicly available LIDC dataset, achieving an AUC of 0:9685 and a false positive rate of 0:46% with a true positive rate of 90% where the ground truth is the expert opinion of a radiologist.

Discovering the 3D atomic-resolution structure of molecules such as proteins and viruses is one of the foremost research problems in biology and medicine. Electron Cryomicroscopy (cryo-EM) is a promising vision-based technique for structure estimation which attempts to reconstruct 3D atomic structures from a large set of 2D transmission electron microscope images. This paper presents a new Bayesian framework for cryo-EM structure estimation that builds on modern stochastic optimization techniques to allow one to scale to very large datasets. We also introduce a novel Monte-Carlo technique that reduces the cost of evaluating the objective function during optimization by over five orders of magnitude. The net result is an approach capable of estimating 3D molecular structure from large-scale datasets in about a day on a single CPU workstation.

A deep Gaussian process (DGP) is a deep network in which each layer is modelled with a Gaussian process (GP). It is a flexible model that can capture highly-nonlinear functions for complex data sets. However, the network structure of DGP often makes inference computationally expensive. In this paper, we propose an efficient sequential inference framework for DGP, where the data is processed sequentially. We also propose two DGP extensions to handle heteroscedasticity and multi-task learning. Our experimental evaluation shows the effectiveness of our sequential inference framework on a number of important learning tasks.

Accurate and efficient self-localization is a critical problem for autonomous systems. This paper describes an affordable solution to vehicle self-localization which uses odometry computed from two video cameras and road maps as the sole inputs. The core of the method is a probabilistic model for which an efficient approximate inference algorithm is derived. The inference algorithm is able to utilize distributed computation in order to meet the real-time requirements of autonomous systems in some instances. Because of the probabilistic nature of the model the method is capable of coping with various sources of uncertainty including noise in the visual odometry and inherent ambiguities in the map (e.g., in a Manhattan world). By exploiting freely available, community developed maps and visual odometry measurements, the proposed method is able to localize a vehicle to 4 m on average after 52 seconds of driving on maps which contain more than 2,150 km of drivable roads.

Discovering the 3D atomic structure of molecules such as proteins and viruses is a fundamental research problem in biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising vision-based technique for structure estimation which attempts to reconstruct 3D structures from 2D images. This paper addresses the challenging problem of 3D reconstruction from 2D Cryo-EM images. A new framework for estimation is introduced which relies on modern stochastic optimization techniques to scale to large datasets. We also introduce a novel technique which reduces the cost of evaluating the objective function during optimization by over five orders or magnitude. The net result is an approach capable of estimating 3D molecular structure from large scale datasets in about a day on a single workstation.

We propose an efficient optimization algorithm to select a subset of training data as the inducing set for sparse Gaussian process regression. Previous methods either use different objective functions for inducing set and hyperparameter selection, or else optimize the inducing set by gradient-based continuous optimization. The former approaches are harder to interpret and suboptimal, whereas the latter cannot be applied to discrete input domains or to kernel functions that are not differentiable with respect to the input. The algorithm proposed in this work estimates an inducing set and the hyperparameters using a single objective. It can be used to optimize either the marginal likelihood or a variational free energy. Space and time complexity are linear in training set size, and the algorithm can be applied to large regression problems on discrete or continuous domains. Empirical evaluation shows state-of-art performance in discrete cases, competitive prediction results as well as a favorable trade-off between training and test time in continuous cases.

In this paper we propose an affordable solution to self-localization, which utilizes visual odometry and road maps as the only inputs. To this end, we present a probabilistic model as well as an efficient approximate inference algorithm, which is able to utilize distributed computation to meet the real-time requirements of autonomous systems. Because of the probabilistic nature of the model we are able to cope with uncertainty due to noisy visual odometry and inherent ambiguities in the map (e.g., in a Manhattan world). By exploiting freely available, community developed maps and visual odometry measurements, we are able to localize a vehicle up to 3m after only a few seconds of driving on maps which contain more than 2,150km of drivable roads.

We propose an efficient discrete optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates this inducing set and the hyperparameters using a single objective, either the marginal likelihood or a variational free energy. The space and time complexity are linear in the training set size, and the algorithm can be applied to large regression problems on discrete or continuous domains. Empirical evaluation shows state-of-art performance in the discrete case and competitive results in the continuous case.

MOTIVATION: Electron cryo-microscopy can be used to infer 3D structures of large macromolecules with high resolution, but the large amounts of data captured necessitate the development of appropriate statistical models to describe the data generation process, and to perform structure inference. We present a new method for performing ab initio inference of the 3D structures of macromolecules from single particle electron cryo-microscopy experiments using class average images. RESULTS: We demonstrate this algorithm on one phantom, one synthetic dataset and three real (experimental) datasets (ATP synthase, V-type ATPase and GroEL). Structures consistent with the known structures were inferred for all datasets. AVAILABILITY: The software and source code for this method is available for download from our website: http://compbio.cs.toronto.edu/cryoem/.

Motion and interaction with the environment are fundamentally intertwined. Few people-tracking algorithms exploit such interactions, and those that do assume that surface geometry and dynamics are given. This paper concerns the converse problem, i.e., the inference of contact and environment properties from motion. For 3D human motion, with a 12-segment articulated body model, we show how one can estimate the forces acting on the body in terms of internal forces (joint torques), gravity, and the parameters of a contact model (e.g., the geometry and dynamics of a spring-based model). This is tested on motion capture data and video-based tracking data, with walking, jogging, cartwheels, and jumping.

The Kneed Walker is a physics-based model derived from a planar biomechanical characterization of human locomotion. By controlling torques at the knees, hips and torso, the model captures a full range of walking motions with foot contact and balance. Constraints are used to properly handle ground collisions and joint limits. A prior density over walking motions is based on dynamics that are optimized for efficient cyclic gaits over a wide range of natural human walking speeds and step lengths, on different slopes. The generative model used for monocular tracking comprises the Kneed Walker prior, a 3D kinematic model constrained to be consistent with the underlying dynamics, and a simple measurement model in terms of appearance and optical flow. The tracker is applied to people walking with varying speeds, on hills, and with occlusion.

We introduce a physics-based model for 3D person tracking. Based on a biomechanical characterization of lower-body dynamics, the model captures important physical properties of bipedal locomotion such as balance and ground contact, generalizes naturally to variations in style due to changes in speed, step-length, and mass, and avoids common problems such as footskate that arise with existing trackers. The model dynamics comprises a two degree-of-freedom representation of human locomotion with inelastic ground contact. A stochastic controller generates impulsive forces during the toe-off stage of walking and spring-like forces between the legs. A higher-dimensional kinematic observation model is then conditioned on the underlying dynamics. We use the model for tracking walking people from video, including examples with turning, occlusion, and varying gait.