Neural models for amortized probabilistic clustering yield samples of cluster labels given a set-structured input, while avoiding lengthy Markov chain runs and the need for explicit data likelihoods. Existing methods which label each data point sequentially, like the Neural Clustering Process, often lead to cluster assignments highly dependent on the data order. Alternatively, methods that sequentially create full clusters, do not provide assignment probabilities. In this paper, we introduce GFNCP, a novel framework for amortized clustering. GFNCP is formulated as a Generative Flow Network with a shared energy-based parametrization of policy and reward. We show that the flow matching conditions are equivalent to consistency of the clustering posterior under marginalization, which in turn implies order invariance. GFNCP also outperforms existing methods in clustering performance on both synthetic and real-world data.

Synchronizing videos captured simultaneously from multiple cameras in the same scene is often easy and typically requires only simple time shifts. However, synchronizing videos from different scenes or, more recently, generative AI videos, poses a far more complex challenge due to diverse subjects, backgrounds, and nonlinear temporal misalignment. We propose Temporal Prototype Learning (TPL), a prototype-based framework that constructs a shared, compact 1D representation from high-dimensional embeddings extracted by any of various pretrained models. TPL robustly aligns videos by learning a unified prototype sequence that anchors key action phases, thereby avoiding exhaustive pairwise matching. Our experiments show that TPL improves synchronization accuracy, efficiency, and robustness across diverse datasets, including fine-grained frame retrieval and phase classification tasks. Importantly, TPL is the first approach to mitigate synchronization issues in multiple generative AI videos depicting the same action. Our code and a new multiple video synchronization dataset are available at https://bgu-cs-vil.github.io/TPL/

Message-Passing Neural Networks (MPNNs) have become a cornerstone for processing and analyzing graph-structured data. However, their effectiveness is often hindered by phenomena such as over-squashing, where long-range dependencies or interactions are inadequately captured and expressed in the MPNN output. This limitation mirrors the challenges of the Effective Receptive Field (ERF) in Convolutional Neural Networks (CNNs), where the theoretical receptive field is underutilized in practice. In this work, we show and theoretically explain the limited ERF problem in MPNNs. Furthermore, inspired by recent advances in ERF augmentation for CNNs, we propose an Interleaved Multiscale Message-Passing Neural Networks (IM-MPNN) architecture to address these problems in MPNNs. Our method incorporates a hierarchical coarsening of the graph, enabling message-passing across multiscale representations and facilitating long-range interactions without excessive depth or parameterization. Through extensive evaluations on benchmarks such as the Long-Range Graph Benchmark (LRGB), we demonstrate substantial improvements over baseline MPNNs in capturing long-range dependencies while maintaining computational efficiency.

Diffusion models, widely recognized for their success in generative tasks, have not yet been applied to clustering. We introduce Clustering via Diffusion (CLUDI), a self-supervised framework that combines the generative power of diffusion models with pre-trained Vision Transformer features to achieve robust and accurate clustering. CLUDI is trained via a teacher–student paradigm: the teacher uses stochastic diffusion-based sampling to produce diverse cluster assignments, which the student refines into stable predictions. This stochasticity acts as a novel data augmentation strategy, enabling CLUDI to uncover intricate structures in high-dimensional data. Extensive evaluations on challenging datasets demonstrate that CLUDI achieves state-of-the-art performance in unsupervised classification, setting new benchmarks in clustering robustness and adaptability to complex data distributions.

Fast and scalable alignment of time series is a fundamental challenge in many domains. The standard solution, Dynamic Time Warping (DTW), struggles with poor scalability and sensitivity to noise. We introduce TimePoint, a self-supervised method that dramatically accelerates DTW-based alignment while typically improving alignment accuracy by learning keypoints and descriptors from synthetic data. Inspired by 2D keypoint detection but carefully adapted to the unique challenges of 1D signals, TimePoint leverages efficient 1D diffeomorphisms, which effectively model nonlinear time warping, to generate realistic training data. This adaptation, along with fully convolutional and wavelet convolutional architectures, enables the extraction of informative keypoints and descriptors. Applying DTW to these sparse representations yields major speedups and typically higher alignment accuracy than standard DTW applied to the full signals. Despite being trained solely on synthetic data, TimePoint generalizes well to real-world time series. Extensive experiments demonstrate that TimePoint consistently achieves faster and more accurate alignments than standard DTW, making it a scalable solution for time-series analysis. Our code is available at https://github.com/ BGU-CS-VIL/TimePoint.

Joint Alignment (JA) of images aims to align a collection of images into a unified coordinate frame, such that semantically-similar features appear at corresponding spatial locations. Most existing approaches often require long training times, large-capacity models, and extensive hyperparameter tuning. We introduce FastJAM, a rapid, graph-based method that drastically reduces the computational complexity of joint alignment tasks. FastJAM leverages pairwise matches computed by an off-the-shelf image matcher, together with a rapid nonparametric clustering, to construct a graph representing intra- and inter-image keypoint relations. A graph neural network propagates and aggregates these correspondences, efficiently predicting per-image homography parameters via image-level pooling. Utilizing an inverse-compositional loss, that eliminates the need for a regularization term over the predicted transformations (and thus also obviates the hyperparameter tuning associated with such terms), FastJAM performs image JA quickly and effectively. Experimental results on several benchmarks demonstrate that FastJAM achieves results better than existing modern JA methods in terms of alignment quality, while reducing computation time from hours or minutes to mere seconds. Our code is available at our project webpage, https://bgu-cs-vil.github.io/FastJAM/.

In time-series analysis, nonlinear temporal misalignment is a major problem that forestalls even simple averaging. An effective learning-based solution for this problem is the Diffeomorphic Temporal Alignment Net (DTAN), that, by relying on a diffeomorphic temporal transformer net and the amortization of the joint-alignment task, eliminates drawbacks of traditional alignment methods. Unfortunately, existing DTAN formulations crucially depend on a regularization term whose optimal hyperparameters are dataset-specific and usually searched via a large number of experiments. Here we propose a regularization-free DTAN that obviates the need to perform such an expensive, and often impractical, search. Concretely, we propose a new well-behaved loss that we call the Inverse Consistency Averaging Error (ICAE), as well as a related new triplet loss. Extensive experiments on 128 UCR datasets show that the proposed method outperforms contemporary methods despite not using a regularization. Moreover, ICAE also gives rise to the first DTAN that supports variable-length signals. Our code is available at https://github.com/BGU-CS-VIL/RF-DTAN.

In the task of semi-supervised video object segmentation, the input is the binary mask of an object in the first frame, and the desired output consists of the corresponding masks of that object in the subsequent frames. Existing leading solutions have two main drawbacks: 1) an expensive and typically-supervised training on videos; 2) a large memory footprint during inference. Here we present a training-free solution, with a low-memory footprint, that yields state-of-the-art results. The proposed method combines pre-trained deep learning-based features (trained on still images) with more classical methods for streaming-data clustering. Designed to adapt to temporal concept drifts and generalize to diverse video content without relying on annotated images or videos, the method eliminates the need for additional training or fine-tuning, ensuring fast inference and immediate applicability to new videos. Concretely, we represent an object via a dynamic ensemble of temporally- and spatially-coherent mixtures over a representation built from pre-trained ViT features and positional embeddings. A convolutional conditional random field further improves spatial coherence and helps reject outliers. We demonstrate the efficacy of the method on key benchmarks: the DAVIS-2017 and YouTube-VOS 2018 validation datasets. Moreover, by the virtue of the low-memory footprint of the compact cluster-based representation, the method scales gracefully to high-resolution ViT features. Our code is available at https://github.com/BGU-CS-VIL/Training-Free-VOS

Practical tools for clustering streaming data must be fast enough to handle the arrival rate of the observations. Typically, they also must adapt on the fly to possible lack of stationarity; i.e., the data statistics may be time-dependent due to various forms of drifts, changes in the number of clusters, etc. The Dirichlet Process Mixture Model (DPMM), whose Bayesian nonparametric nature allows it to adapt its complexity to the data, seems a natural choice for the streaming-data case. In its classical formulation, however, the DPMM cannot capture common types of drifts in the data statistics. Moreover, and regardless of that limitation, existing methods for online DPMM inference are too slow to handle rapid data streams. In this work we propose adapting both the DPMM and a known DPMM sampling-based non-streaming inference method for streaming-data clustering. We demonstrate the utility of the proposed method on several challenging settings, where it obtains state-of-the-art results while being on par with other methods in terms of speed.

The Dirichlet Process Gaussian Mixture Model (DPGMM) is often used to cluster data when the number of clusters is unknown. One main DPGMM inference paradigm relies on sampling. Here we consider a known state-of-art sampler (proposed by Chang and Fisher III (2013) and improved by Dinari et al. (2019)), analyze its failure modes, and show how to improve it, often drastically. Concretely, in that sampler, whenever a new cluster is formed it is augmented with two subclusters whose labels are initialized at random. Upon their evolution, the subclusters serve to propose a split of the parent cluster. We show that the random initialization is often problematic and hurts the otherwise-effective sampler. Specifically, we demonstrate that this initialization tends to lead to poor split proposals and/or too many iterations before a desired split is accepted. This slows convergence and can damage the clustering. As a remedy, we propose two drop-in-replacement options for the subcluster-initialization subroutine. The first is an intuitive heuristic while the second is based on deep learning. We show that the proposed approach yields better splits, which in turn translate to substantial improvements in performance, results, and stability. Our code is publicly available.

Deep Learning (DL) has shown great promise in the unsupervised task of clustering. That said, while in classical (i.e., non-deep) clustering the benefits of the nonparametric approach are well known, most deep-clustering methods are parametric: namely, they require a predefined and fixed number of clusters, denoted by K. When$K$is unknown, however, using model-selection criteria to choose its optimal value might become computationally expensive, especially in DL as the training process would have to be repeated numerous times. In this work, we bridge this gap by introducing an effective deep-clustering method that does not require knowing the value of$K$as it infers it during the learning. Using a split/merge framework, a dynamic architecture that adapts to the changing$K$, and a novel loss, our proposed method outperforms existing nonparametric methods (both classical and deep ones). While the very few existing deep nonparametric methods lack scalability, we demonstrate ours by being the first to report the performance of such a method on ImageNet. We also demonstrate the importance of inferring$K$by showing how methods that fix it deteriorate in performance when their assumed$K$value gets further from the ground-truth one, especially on imbalanced datasets. Our code is available at https://github.com/BGU-CS-VIL/DeepDPM.

One popular deep-learning approach for the task of Out-Of-Distribution (OOD) detection is based on thresholding the values of per-class Gaussian likelihood of deep features. However, two issues arise with that approach: first, the distributions are often far from being Gaussian; second, many OOD data points fall within the effective support of the known classes’ Gaussians. Thus, either way it is hard to find a good threshold. In contrast, our proposed solution for OOD detection is based on a new latent space where: 1) each known class is well captured by a nearly-isotropic Gaussian; 2) those Gaussians are far from each other and from the origin of the space (together, these properties effectively leave the area around the origin free for OOD data). Concretely, given a (possibly-trained) backbone deep net of choice, we use it to train a conditional variational model via a Kullback Leibler loss, a triplet loss, and a new distancing loss that pushes classes away from each other. During inference, the class-dependent log-likelihood values of a deep feature ensemble of the test point are also weighted based on reconstruction errors, improving further the decision rule. Experiments on popular benchmarks show that our method yields state-of-the-art results, a feat achieved despite the fact that, unlike some competitors, we make no use of OOD data for training or hyperparameter tuning. Our code is available at \url{https://github.com/BGU-CS-VIL/vmdls}.

DP-means, a nonparametric generalization of K-means, extends the latter to the case where the number of clusters is unknown. Unlike K-means, however, DP-means is hard to parallelize, a limitation hindering its usage in large-scale tasks. This work bridges this practicality gap by rendering the DP-means approach a viable, fast, and highly-scalable solution. First, we study the strengths and weaknesses of previous attempts to parallelize the DP-means algorithm. Next, we propose a new parallel algorithm, called PDC-DP-Means (Parallel Delayed Cluster DP-Means), based in part on delayed creation of clusters. Compared with DP-Means, PDC-DP-Means provides not only a major speedup but also performance gains. Finally, we propose two extensions of PDC-DP-Means. The first combines it with an existing method, leading to further speedups. The second extends PDC-DP-Means to a Mini-Batch setting (with an optional support for an online mode), allowing for another major speedup. We verify the utility of the proposed methods on multiple datasets. We also show that the proposed methods outperform other nonparametric methods (e.g., DBSCAN). Our highly-efficient code can be used to reproduce our experiments and is available at https://github.com/BGU-CS-VIL/pdc-dp-means

Shape analysis is a key task in image processing. A common method for representing a 2D shape is via a polygon, where the latter is a discretized version of the contour outlining the shape. However, due to the problem of curve reparameterization (i. e., points “sliding” along the contour), even if several shapes are very similar, their representations might be misleadingly far from each other. This misalignment problem confounds shape analysis. As a remedy, we propose a deep-learning framework, based on the recently-proposed diffeomorphic transformers nets. The proposed method handles either a single class (in an unsupervised manner) or multiple classes (in a semi-supervised manner), and is amenable to the warp-around effect exhibited in closed contours. Moreover, unlike typical alignment methods unrelated to learning, the proposed method aligns not only the original (“training”) shapes but also generalizes to test shapes (even if no class labels are given during the test). Our code is publicly available at https://git;hub.com/BGU-CS-VIL/CDTNCA.

Background models are widely used in computer vision. While successful Static-camera Background (SCB) models exist, Moving-camera Background (MCB) models are limited. Seemingly, there is a straightforward solution: 1) align the video frames; 2) learn an SCB model; 3) warp either original or previously-unseen frames toward the model. This approach, however, has drawbacks, especially when the accumulative camera motion is large and/or the video is long. Here we propose a purely-2D unsupervised modular method that systematically eliminates those issues. First, to estimate warps in the original video, we solve a joint-alignment problem while leveraging a certifiably-correct initialization. Next, we learn both multiple partially-overlapping local subspaces and how to predict alignments. Lastly, in test time, we warp a previously-unseen frame, based on the prediction, and project it on a subset of those subspaces to obtain a background/foreground separation. We show the method handles even large scenes with a relatively-free camera motion (provided the camera-to-scene distance does not change much) and that it not only yields State-of-the-Art results on the original video but also generalizes gracefully to previously-unseen videos of the same scene. Our code is available at https://github.com/BGU-CS-VIL/JA-POLS.

Adaptive clustering of grouped data is often done via the Hierarchical Dirichlet Process Mixture Model (HDPMM). That approach, however, is limited in its flexibility and usually does not scale well. As a remedy, we propose another, but closely related, hierarchical Bayesian nonparametric framework. Our main contributions are as follows. 1) a new model, called the Versatile HDPMM (vHDPMM), with two possible settings: full and reduced. While the latter is akin to the HDPMM’s setting, the former supports not only global features (as HDPMM does) but also local ones. 2) An effective mechanism for detecting global features. 3) A new sampler that addresses the challenges posed by the vHDPMM and, in the reduced setting, scales better than HDPMM samplers. 4) An efficient, distributed, and easily-modifiable implementation that offers more flexibility (even in the reduced setting) than publicly-available HDPMM implementations. Finally, we show the utility of the approach in applications such as image cosegmentation, visual topic modeling, and clustering with missing data.

Due to the increasing availability of large data sets, the need for general-purpose massively-parallel analysis tools become ever greater. In unsupervised learning, Bayesian nonparametric mixture models, exemplified by the Dirichlet-Process Mixture Model (DPMM), provide a principled Bayesian approach to adapt model complexity to the data. Despite their potential, however, DPMMs have yet to become a popular tool. This is partly due to the lack of friendly software tools that can handle large datasets efficiently. Here we show how, using Julia, one can achieve efficient and easily-modifiable implementation of distributed inference in DPMMs. Particularly, we show how a recent parallel MCMC inference algorithm - originally implemented in C++ for a single multi-core machine - can be distributed efficiently across multiple multi-core machines using a distributed-memory model. This leads to speedups, alleviates memory and storage limitations, and lets us learn DPMMs from significantly larger datasets and of higher dimensionality. It also turned out that even on a single machine the proposed Julia implementation handles higher dimensions more gracefully (at least for Gaussians) than the original C++ implementation. Finally, we use the proposed implementation to learn a model of image patches and apply the learned model for image denoising. While we speculate that a highly-optimized distributed implementation in, say, C++ could have been faster than the proposed implementation in Julia, from our perspective as machine-learning researchers (as opposed to HPC researchers), the latter also offers a practical and monetary value due to the ease of development and abstraction level. Our code is publicly available at https://github.com/dinarior/dpmm subclusters.jl

Superpixels provide a useful intermediate image representation. Existing superpixel methods, however, suffer from at least some of the following drawbacks: 1) topology is handled heuristically; 2) the number of superpixels is either predefined or estimated at a prohibitive cost; 3) lack of adaptiveness. As a remedy, we propose a novel probabilistic model, self-coined Bayesian Adaptive Superpixel Segmentation (BASS), together with an efficient inference. BASS is a Bayesian nonparametric mixture model that also respects topology and favors spatial coherence. The optimizationbased and topology-aware inference is parallelizable and implemented in GPU. Quantitatively, BASS achieves results that are either better than the state-of-the-art or close to it, depending on the performance index and/or dataset. Qualitatively, we argue it achieves the best results; we demonstrate this by not only subjective visual inspection but also objective quantitative performance evaluation of the downstream application of face detection. Our code is available at https://github.com/uzielroy/BASS.

Time-series analysis is confounded by nonlinear time warping of the data. Traditional methods for joint alignment do not generalize: after aligning a given signal ensemble, they lack a mechanism, that does not require solving a new optimization problem, to align previously-unseen signals. In the multi-class case, they must also first classify the test data before aligning it. Here we propose the Diffeomorphic Temporal alignment Net (DTAN), a learning-based method for time-series joint alignment. Via flexible temporal transformer layers, DTAN learns and applies an input-dependent nonlinear time warping to its input signal. Once learned, DTAN easily aligns previously-unseen signals by its inexpensive forward pass. In a single-class case, the method is unsupervised: the ground-truth alignments are unknown. In the multi-class case, it is semi-supervised in the sense that class labels (but not the ground-truth alignments) are used during learning; in test time, however, the class labels are unknown. As we show, DTAN not only outperforms existing joint-alignment methods in aligning training data but also generalizes well to test data. Our code is available at https://github.com/BGU-CS-VIL/dtan.

Spatial Transformer layers allow neural networks, at least in principle, to be invariant to large spatial transformations in image data. The model has, however, seen limited uptake as most practical implementations support only transformations that are too restricted, e.g. affine or homographic maps, and/or destructive maps, such as thin plate splines. We investigate the use of flexible diffeomorphic image transformations within such networks and demonstrate that significant performance gains can be attained over currently-used models. The learned transformations are found to be both simple and intuitive, thereby providing insights into individual problem domains. With the proposed framework, a standard convolutional neural network matches state-of-the-art results on face verification with only two extra lines of simple TensorFlow code.

Objects and structures within man-made environments typically exhibit a high degree of organization in the form of orthogonal and parallel planes. Traditional approaches utilize these regularities via the restrictive, and rather local, Manhattan World (MW) assumption which posits that every plane is perpendicular to one of the axes of a single coordinate system. The aforementioned regularities are especially evident in the surface normal distribution of a scene where they manifest as orthogonally-coupled clusters. This motivates the introduction of the Manhattan-Frame (MF) model which captures the notion of an MW in the surface normals space, the unit sphere, and two probabilistic MF models over this space. First, for a single MF we propose novel real-time MAP inference algorithms, evaluate their performance and their use in drift-free rotation estimation. Second, to capture the complexity of real-world scenes at a global scale, we extend the MF model to a probabilistic mixture of Manhattan Frames (MMF). For MMF inference we propose a simple MAP inference algorithm and an adaptive Markov-Chain Monte-Carlo sampling algorithm with Metropolis-Hastings split/merge moves that let us infer the unknown number of mixture components. We demonstrate the versatility of the MMF model and inference algorithm across several scales of man-made environments.

We propose novel finite-dimensional spaces of well-behaved transformations. The latter are obtained by (fast and highly-accurate) integration of continuous piecewise-affine velocity fields. The proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volume preservation and/or boundary conditions), and supports convenient modeling choices such as smoothing priors and coarse-to-fine analysis. Importantly, the proposed approach, partly due to its rapid likelihood evaluations and partly due to its other properties, facilitates tractable inference over rich transformation spaces, including using Markov-Chain Monte-Carlo methods. Its applications include, but are not limited to: monotonic regression (more generally, optimization over monotonic functions); modeling cumulative distribution functions or histograms; time-warping; image warping; image registration; real-time diffeomorphic image editing; data augmentation for image classifiers. Our GPU-based code is publicly available.

Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g. new images are formed by rotating old ones. Current augmentation schemes, however, rely on manual specification of the applied transformations, making data augmentation an implicit form of feature engineering. With an eye towards true end-to-end learning, we suggest learning the applied transformations on a per-class basis. Particularly, we align image pairs within each class under the assumption that the spatial transformation between images belongs to a large class of diffeomorphisms. We then learn a class-specific probabilistic generative models of the transformations in a Riemannian submanifold of the Lie group of diffeomorphisms. We demonstrate significant performance improvements in training deep neural nets over manually-specified augmentation schemes. Our code and augmented datasets are available online.

Directional data, naturally represented as points on the unit sphere, appear in many applications. However, unlike the case of Euclidean data, flexible mixture models on the sphere that can capture correlations, handle an unknown number of components and extend readily to high-dimensional data have yet to be suggested. For this purpose we propose a Dirichlet process mixture model of Gaussian distributions in distinct tangent spaces (DP-TGMM) to the sphere. Importantly, the formulation of the proposed model allows the extension of recent advances in efficient inference for Bayesian nonparametric models to the spherical domain. Experiments on synthetic data as well as real-world 3D surface normal and 20-dimensional semantic word vector data confirm the expressiveness and applicability of the DP-TGMM.

We propose novel finite-dimensional spaces of Rn→ Rntransformations, n ∈ {1, 2, 3}, derived from (continuously-defined) parametric stationary velocity fields. Particularly, we obtain these transformations, which are diffeomorphisms, by fast and highly-accurate integration of continuous piecewise-affine velocity fields, we also provide an exact solution for n = 1. The simple-yet-highly-expressive proposed representation handles optional constraints (e.g., volume preservation) easily and supports convenient modeling choices and rapid likelihood evaluations (facilitating tractable inference over latent transformations). Its applications include, but are not limited to: unconstrained optimization over monotonic functions, modeling cumulative distribution functions or histograms, time warping, image registration, landmark-based warping, real-time diffeomorphic image editing. Our code is available at https://github.com/freifeld/cpabDiffeo.

Superpixel segmentation is a key step in many image processing and vision tasks. Our recently-proposed connectivity-constrained probabilistic model [1] yields high-quality super-pixels. Seemingly, however, connectivity constraints preclude parallelized inference. As such, the implementation from [1] is serial. The contributions of this work are as follows. First, we demonstrate that effective parallelization is possible via a fast GPU implementation that scales gracefully with both the number of pixels and number of superpixels. Second, we show that the superpixels are improved by replacing the fixed and restricted spatial covariances from [1] with a flexible Bayesian prior. Quantitative evaluation on public benchmarks shows the proposed method outperforms the state-of-the-art. We make our implementation publicly available.

We propose an integrated probabilistic model for multi-modal fusion of aerial imagery, LiDAR data, and (optional) GPS measurements. The model allows for analysis and dense reconstruction (in terms of both geometry and appearance) of large 3D scenes. An advantage of the approach is that it explicitly models uncertainty and allows for missing data. As compared with image-based methods, dense reconstructions of complex urban scenes are feasible with fewer observations. Moreover, the proposed model allows one to estimate absolute scale and orientation and reason about other aspects of the scene, e.g., detection of moving objects. As formulated, the model lends itself to massively-parallel computing. We exploit this in an efficient inference scheme that utilizes both general purpose and domain-specific hardware components. We demonstrate results on large-scale reconstruction of urban terrain from LiDAR and aerial photography data.

We consider the intersection of two research fields: transfer learning and statistics on manifolds. In particular, we consider, for manifold-valued data, transfer learning of tangent-space models such as Gaussians distributions, PCA, regression, or classifiers. Though one would hope to simply use ordinary Rn-transfer learning ideas, the manifold structure prevents it. We overcome this by basing our method on inner-product-preserving parallel transport, a well-known tool widely used in other problems of statistics on manifolds in computer vision. At first, this straight-forward idea seems to suffer from an obvious shortcoming: Transporting large datasets is prohibitively expensive, hindering scalability. Fortunately, with our approach, we never transport data. Rather, we show how the statistical models themselves can be transported, and prove that for the tangent-space models above, the transport "commutes" with learning. Consequently, our compact framework, ap- plicable to a large class of manifolds, is not restricted by the size of either the training or test sets. We demonstrate the approach by transferring PCA and logistic-regression models of real-world data involving 3D shapes and image descriptors.

Objects and structures within man-made environments typically exhibit a high degree of organization in the form of orthogonal and parallel planes. Traditional approaches to scene representation exploit this phenomenon via the somewhat restrictive assumption that every plane is perpendicular to one of the axes of a single coordinate system. Known as the Manhattan-World model, this assumption is widely used in computer vision and robotics. The complexity of many real-world scenes, however, necessitates a more flexible model. We propose a novel probabilistic model that describes the world as a mixture of Manhattan frames: each frame defines a different orthogonal coordinate system. This results in a more expressive model that still exploits the orthogonality constraints. We propose an adaptive Markov-Chain Monte-Carlo sampling algorithm with Metropolis-Hastings split/merge moves that utilizes the geometry of the unit sphere. We demonstrate the versatility of our Mixture-of-Manhattan-Frames model by describing complex scenes using depth images of indoor scenes as well as aerial-LiDAR measurements of an urban center. Additionally, we show that the model lends itself to focal-length calibration of depth cameras and to plane segmentation.

Pictorial Structures (PS) define a probabilistic model of 2D articulated objects in images. Typical PS models assume an object can be represented by a set of rigid parts connected with pairwise constraints that define the prior probability of part configurations. These models are widely used to represent non-rigid articulated objects such as humans and animals despite the fact that such objects have parts that deform non-rigidly. Here we define a new Deformable Structures (DS) model that is a natural extension of previous PS models and that captures the non-rigid shape deformation of the parts. Each part in a DS model is represented by a low-dimensional shape deformation space and pairwise potentials between parts capture how the shape varies with pose and the shape of neighboring parts. A key advantage of such a model is that it more accurately models object boundaries. This enables image likelihood models that are more discriminative than previous PS likelihoods. This likelihood is learned using training imagery annotated using a DS “puppet.” We focus on a human DS model learned from 2D projections of a realistic 3D human body model and use it to infer human poses in images using a form of non-parametric belief propagation.

Multi-metric learning techniques learn local metric tensors in different parts of a feature space. With such an approach, even simple classifiers can be competitive with the state-of-the-art because the distance measure locally adapts to the structure of the data. The learned distance measure is, however, non-metric, which has prevented multi-metric learning from generalizing to tasks such as dimensionality reduction and regression in a principled way. We prove that, with appropriate changes, multi-metric learning corresponds to learning the structure of a Riemannian manifold. We then show that this structure gives us a principled way to perform dimensionality reduction and regression according to the learned metrics. Algorithmically, we provide the first practical algorithm for computing geodesics according to the learned metrics, as well as algorithms for computing exponential and logarithmic maps on the Riemannian manifold. Together, these tools let many Euclidean algorithms take advantage of multi-metric learning. We illustrate the approach on regression and dimensionality reduction tasks that involve predicting measurements of the human body from shape data.

We define a new “contour person” model of the human body that has the expressive power of a detailed 3D model and the computational benefits of a simple 2D part-based model. The contour person (CP) model is learned from a 3D SCAPE model of the human body that captures natural shape and pose variations; the projected contours of this model, along with their segmentation into parts forms the training set. The CP model factors deformations of the body into three components: shape variation, viewpoint change and part rotation. This latter model also incorporates a learned non-rigid deformation model. The result is a 2D articulated model that is compact to represent, simple to compute with and more expressive than previous models. We demonstrate the value of such a model in 2D pose estimation and segmentation. Given an initial pose from a standard pictorial-structures method, we refine the pose and shape using an objective function that segments the scene into foreground and background regions. The result is a parametric, human-specific, image segmentation.