This work presents a unified framework for the unsupervised prediction of physically plausible interpolations between two 3D articulated shapes and the automatic estimation of dense correspondence between them. Interpolation is modelled as a diffeomorphic transformation using a smooth, time-varying flow field governed by Neural Ordinary Differential Equations (ODEs). This ensures topological consistency and non-intersecting trajectories while accommodating hard constraints, such as volume preservation, and soft constraints, e.g. physical priors. Correspondence is recovered using an efficient Varifold formulation, that is effective on high-fidelity surfaces with differing parameterisations. By providing a simple skeleton for the source shape only, we impose physically motivated constraints on the deformation field and resolve symmetric ambiguities. This is achieved without relying on skinning weights or any prior knowledge of the skeleton's target pose configuration. Qualitative and quantitative results demonstrate competitive or superior performance over existing state-of-the-art approaches in both shape correspondence and interpolation tasks across standard datasets.

We present an unsupervised framework for physically plausible shape interpolation and dense correspondence estimation between 3D articulated shapes. Our approach intentionally focuses upon pose variation within the same identity, which we believe is a meaningful and challenging problem in its own right. Our method uses Neural Ordinary Differential Equations (NODEs) to generate smooth flow fields that define diffeomorphic transformations, ensuring topological consistency and preventing self-intersections while accommodating hard constraints, such as volume preservation. By incorporating a lightweight skeletal structure, we impose kinematic constraints that resolve symmetries without requiring manual skinning or predefined poses. We enhance physical realism by interpolating skeletal motion with dual quaternions and applying constrained optimisation to align the flow field with the skeleton, preserving local rigidity. Additionally, we employ an efficient formulation of Normal Cycles, a metric from geometric measure theory, to capture higher-order surface details like curvature, enabling precise alignment between complex articulated structures and recovery of accurate dense correspondence mapping. Evaluations on multiple benchmarks show notable improvements over state-of-the-art methods in both interpolation quality and correspondence accuracy, with consistent performance across different skeletal configurations, demonstrating broad utility for shape matching and animation tasks.

Multi-task learning requires accurate identification of the correlations between tasks. In real-world time-series, tasks are rarely perfectly temporally aligned; traditional multi-task models do not account for this and subsequent errors in correlation estimation will result in poor predictive performance and uncertainty quantification. We introduce a method that automatically accounts for temporal misalignment in a unified generative model that improves predictive performance. Our method uses Gaussian processes (GPs) to model the correlations both within and between the tasks. Building on the previous work by Kazlauskaite et al. (2019), we include a separate monotonic warp of the input data to model temporal misalignment. In contrast to previous work, we formulate a lower bound that accounts for uncertainty in both the estimates of the warping process and the underlying functions. Also, our new take on a monotonic stochastic process, with efficient path-wise sampling for the warp functions, allows us to perform full Bayesian inference in the model rather than MAP estimates. Missing data experiments, on synthetic and real time-series, demonstrate the advantages of accounting for misalignments (vs standard unaligned method) as well as modelling the uncertainty in the warping process (vs baseline MAP alignment approach).

This paper proposes using a sparse-structured multivari-ate Gaussian to provide a closed-form approximator for the output of probabilistic ensemble models used for dense im-age prediction tasks. This is achieved through a convolutional neural network that predicts the mean and covari-ance of the distribution, where the inverse covariance is parameterised by a sparsely structured Cholesky matrix. Similarly to distillation approaches, our single network is trained to maximise the probability of samples from pre-trained probabilistic models, in this work we use a fixed en-semble of networks. Once trained, our compact represen-tation can be used to efficiently draw spatially correlated samples from the approximated output distribution. Impor-tantly, this approach captures the uncertainty and struc-tured correlations in the predictions explicitly in a formal distribution, rather than implicitly through sampling alone. This allows direct introspection of the model, enabling vi-sualisation of the learned structure. Moreover, this formu-lation provides two further benefits: estimation of a sample probability, and the introduction of arbitrary spatial conditioning at test time. We demonstrate the merits of our approach on monocular depth estimation and show that the advantages of our approach are obtained with comparable quantitative performance.

Shape models have been used extensively to regularise segmentation of objects of interest in images, e.g. bones in medical x-ray radiographs, given supervised training examples. However, approaches usually adopt simple linear models that do not capture uncertainty and require extensive annotation effort to label a large number of set template landmarks for training. Conversely, supervised deep learning methods have been used on appearance directly (no explicit shape modelling) but these fail to capture detailed features that are clinically important.We present a supervised approach that combines both a non-linear generative shape model and a discriminative appearance-based convolutional neural network whilst quantifying uncertainty and relaxes the need for detailed, template based alignment for the training data. Our Bayesian framework couples the uncertainty from both the generator and the discriminator; our main contribution is the marginalisation of an intractable integral through the use of radial basis function approximations. We illustrate this model on the problem of segmenting bones from Psoriatic Arthritis hand radiographs and demonstrate that we can accurately measure the clinically important joint space gap between neighbouring bones.

We propose a new framework for imposing monotonicity constraints in a Bayesian non-parametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty. We demonstrate the efficacy of the proposed model by providing competitive results to other probabilistic monotonic models on a number of benchmark functions. In addition, we consider the utility of a monotonic random process as a part of a hierarchical probabilistic model; we examine the task of temporal alignment of time-series data where it is beneficial to use a monotonic random process in order to preserve the uncertainty in the temporal warpings.

Deep neural networks have recently been used to edit images with great success, in particular for faces. However, they are often limited to only being able to work at a restricted range of resolutions. Many methods are so flexible that face edits can often result in an unwanted loss of identity. This work proposes to learn how to perform semantic image edits through the application of smooth warp fields. Previous approaches that attempted to use warping for semantic edits required paired data, i.e. example images of the same subject with different semantic attributes. In contrast, we employ recent advances in Generative Adversarial Networks that allow our model to be trained with unpaired data. We demonstrate face editing at very high resolutions (4k images) with a single forward pass of a deep network at a lower resolution. We also show that our edits are substantially better at preserving the subject's identity. The robustness of our approach is demonstrated by showing plausible image editing results on the Cub200 birds dataset. To our knowledge this has not been previously accomplished, due the challenging nature of the dataset.

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a posterior distribution of compositions of multiple functions giving rise to the observations. However, exact Bayesian inference is intractable for DGPs, motivating the use of various approximations. We show that the application of simplifying mean-field assumptions across the hierarchy leads to the layers of a DGP collapsing to near-deterministic transformations. We argue that such an inference scheme is suboptimal, not taking advantage of the potential of the model to discover the compositional structure in the data. To address this issue, we examine alternative variational inference schemes allowing for dependencies across different layers and discuss their advantages and limitations.

We present a model that can automatically learn alignments between high-dimensional data in an unsupervised manner. Our proposed method casts alignment learning in a framework where both alignment and data are modelled simultaneously. Further, we automatically infer groupings of different types of sequences within the same dataset. We derive a probabilistic model built on non-parametric priors that allows for flexible warps while at the same time providing means to specify interpretable constraints. We demonstrate the efficacy of our approach with superior quantitative performance to the state-of-the-art approaches and provide examples to illustrate the versatility of our model in automatic inference of sequence groupings, absent from previous approaches, as well as easy specification of high level priors for different modalities of data.

We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of the Dirichlet process as a specific structural prior allows our model to circumvent issues associated with previous Gaussian process latent variable models. Inference is performed by deriving an efficient variational bound on the marginal log-likelihood of the model. We demonstrate the efficacy of our approach via analysis of discovered structure and superior quantitative performance on missing data imputation.

We present a new technique for the learning of continuous energy functions that we refer to as Wibergian Learning. One common approach to inverse problems is to cast them as an energy minimisation problem, where the minimum cost solution found is used as an estimator of hidden parameters. Our new approach formally characterises the dependency between weights that control the shape of the energy function, and the location of minima, by describing minima as fixed points of optimisation methods. This allows for the use of gradient-based end-to- end training to integrate deep-learning and the classical inverse problem methods. We show how our approach can be applied to obtain state-of-the-art results in the diverse applications of tracker fusion and multiview 3D reconstruction.

The ubiquity of smart mobile devices, such as phones and tablets, enables users to casually capture 360° panoramas with a single camera sweep to share and relive experiences. However, panoramas lack motion parallax as they do not provide different views for different viewpoints. The motion parallax induced by translational head motion is a crucial depth cue in daily life. Alternatives, such as omnidirectional stereo panoramas, provide different views for each eye (binocular disparity), but they also lack motion parallax as the left and right eye panoramas are stitched statically. Methods based on explicit scene geometry reconstruct textured 3D geometry, which provides motion parallax, but suffers from visible reconstruction artefacts. The core of our method is a novel multi-perspective panorama representation, which can be casually captured and rendered with motion parallax for each eye on the fly. This provides a more realistic perception of panoramic environments which is particularly useful for virtual reality applications. Our approach uses a single consumer video camera to acquire 200-400 views of a real 360° environment with a single sweep. By using novel-view synthesis with flow-based blending, we show how to turn these input views into an enriched 360° panoramic experience that can be explored in real time, without relying on potentially unreliable reconstruction of scene geometry. We compare our results with existing omnidirectional stereo and image-based rendering methods to demonstrate the benefit of our approach, which is the first to enable casual consumers to capture and view high-quality 360° panoramas with motion parallax.

This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices [15]. Our novel model learns to predict a full Gaussian covariance matrix for each reconstruction, which permits efficient sampling and likelihood evaluation. We demonstrate that our model can accurately reconstruct ground truth correlated residual distributions for synthetic datasets and generate plausible high frequency samples for real face images. We also illustrate the use of these predicted covariances for structure preserving image denoising.

Many structured prediction tasks in machine vision have a collection of acceptable answers, instead of one definitive ground truth answer. Segmentation of images, for example, is subject to human labeling bias. Similarly, there are multiple possible pixel values that could plausibly complete occluded image regions. State-of-the art supervised learning methods are typically optimized to make a single test-time prediction for each query, failing to find other modes in the output space. Existing methods that allow for sampling often sacrifice speed or accuracy. We introduce a simple method for training a neural network, which enables diverse structured predictions to be made for each test-time query. For a single input, we learn to predict a range of possible answers. We compare favorably to methods that seek diversity through an ensemble of networks. Such stochastic multiple choice learning faces mode collapse, where one or more ensemble members fail to receive any training signal. Our best performing solution can be deployed for various tasks, and just involves small modifications to the existing single-mode architecture, loss function, and training regime. We demonstrate that our method results in quantitative improvements across three challenging tasks: 2D image completion, 3D volume estimation, and flow prediction.

We propose technology to enable a new medium of expression, where video elements can be looped, merged, and triggered, interactively. Like audio, video is easy to sample from the real world, but hard to segment into clean reusable elements. Reusing a video clip means non-linear editing, and compositing with novel footage. The new context dictates how carefully a clip must be prepared, so our end-to-end approach enables previewing and easy iteration. We convert static-camera videos into loopable sequences, synthesizing them in response to simple end-user requests. This is hard because a) users want essentially semantic-level control over the synthesized video content, and b) automatic loop-finding is brittle and leaves users limited opportunity to work through problems. We propose a human-in-the-loop system where adding effort gives the user progressively more creative control. Artists help us evaluate how our trigger interfaces can be used for authoring of videos and video-performances.

Quadrics are a compact mathematical formulation for a range of primitive surfaces. A problem arises when there are not enough data points to compute the model but knowledge of the shape is available. This paper presents a method for fitting a quadric with a Bayesian prior. We use a matrix normal prior in order to favour ellipsoids when fitting to ambiguous data. The results show the algorithm copes well when there are few points in the point cloud, competing with contemporary techniques in the area.

Rotoscoping (cutting out different characters/objects/layers in raw video footage) is a ubiquitous task in modern post-production and represents a significant investment in person-hours. In this work, we study the particular task of professional rotoscoping for high-end, live action movies and propose a new framework that works with roto-artists to accelerate the workflow and improve their productivity. Working with the existing keyframing paradigm, our first contribution is the development of a shape model that is updated as artists add successive keyframes. This model is used to improve the output of traditional interpolation and tracking techniques, reducing the number of keyframes that need to be specified by the artist. Our second contribution is to use the same shape model to provide a new interactive tool that allows an artist to reduce the time spent editing each keyframe. The more keyframes that are edited, the better the interactive tool becomes, accelerating the process and making the artist more efficient without compromising their control. Finally, we also provide a new, professionally rotoscoped dataset that enables truly representative, real-world evaluation of rotoscoping methods. We used this dataset to perform a number of experiments, including an expert study with professional roto-artists, to show, quantitatively, the advantages of our approach.

Subspace models have been very successful at modeling the appearance of structured image datasets when the visual objects have been aligned in the images (e.g., faces). Even with extensions that allow for global transformations or dense warps of the image, the set of visual objects whose appearance may be modeled by such methods is limited. They are unable to account for visual objects where occlusion leads to changing visibility of different object parts (without a strict layered structure) and where a one-to-one mapping between parts is not preserved. For example bunches of bananas contain different numbers of bananas but each individual banana shares an appearance subspace. In this work we remove the image space alignment limitations of existing subspace models by conditioning the models on a shape dependent context that allows for the complex, non-linear structure of the appearance of the visual object to be captured and shared. This allows us to exploit the advantages of subspace appearance models with non-rigid, deformable objects whilst also dealing with complex occlusions and varying numbers of parts. We demonstrate the effectiveness of our new model with examples of structured inpainting and appearance transfer.

In this paper we tackle the problem of capturing the dense, detailed 3D geometry of generic, complex non-rigid meshes using a single RGB-only commodity video camera and a direct approach. While robust and even real-time solutions exist to this problem if the observed scene is static, for non-rigid dense shape capture current systems are typically restricted to the use of complex multi-camera rigs, take advantage of the additional depth channel available in RGB-D cameras, or deal with specific shapes such as faces or planar surfaces. In contrast, our method makes use of a single RGB video as input, it can capture the deformations of generic shapes, and the depth estimation is dense, per-pixel and direct. We first compute a dense 3D template of the shape of the object, using a short rigid sequence, and subsequently perform online reconstruction of the non-rigid mesh as it evolves over time. Our energy optimization approach minimizes a robust photometric cost that simultaneously estimates the temporal correspondences and 3D deformations with respect to the template mesh. In our experimental evaluation we show a range of qualitative results on novel datasets, we compare against an existing method that requires multi-frame optical flow, and perform a quantitative evaluation against other template-based approaches on a ground truth dataset.

Abstract We present an interactive system for composing realistic images of an object under arbitrary pose and appearance specified by sketching. Our system draws inspiration from a traditional illustration workflow: The user first sketches rough ‘masses’ of the object, as ellipses, to define an initial abstract pose that can then be refined with more detailed contours as desired. The system is made robust to partial or inaccurate sketches using a reduced‐dimensionality model of pose space learnt from a labelled collection of photos. Throughout the composition process, interactive visual feedback is provided to guide the user. Finally, the user's partial or complete sketch, complemented with appearance requirements, is used to constrain the automatic synthesis of a novel, high‐quality, realistic image.

To train good supervised and semi-supervised object classifiers, it is critical that we not waste the time of the human experts who are providing the training labels. Existing active learning strategies can have uneven performance, being efficient on some datasets but wasteful on others, or inconsistent just between runs on the same dataset. We propose perplexity based graph construction and a new hierarchical subquery evaluation algorithm to combat this variability, and to release the potential of Expected Error Reduction. Under some specific circumstances, Expected Error Reduction has been one of the strongest-performing informativeness criteria for active learning. Until now, it has also been prohibitively costly to compute for sizeable datasets. We demonstrate our highly practical algorithm, comparing it to other active learning measures on classification datasets that vary in sparsity, dimensionality, and size. Our algorithm is consistent over multiple runs and achieves high accuracy, while querying the human expert for labels at a frequency that matches their desired time budget.

The design and manipulation of typefaces and fonts is an area requiring substantial expertise; it can take many years of study to become a proficient typographer. At the same time, the use of typefaces is ubiquitous; there are many users who, while not experts, would like to be more involved in tweaking or changing existing fonts without suffering the learning curve of professional typography packages. Given the wealth of fonts that are available today, we would like to exploit the expertise used to produce these fonts, and to enable everyday users to create, explore, and edit fonts. To this end, we build a generative manifold of standard fonts. Every location on the manifold corresponds to a unique and novel typeface, and is obtained by learning a non-linear mapping that intelligently interpolates and extrapolates existing fonts. Using the manifold, we can smoothly interpolate and move between existing fonts. We can also use the manifold as a constraint that makes a variety of new applications possible. For instance, when editing a single character, we can update all the other glyphs in a font simultaneously to keep them compatible with our changes.

Conditional Random Fields (CRFs) are used for diverse tasks, ranging from image denoising to object recognition. For images, they are commonly defined as a graph with nodes corresponding to individual pixels and pairwise links that connect nodes to their immediate neighbors. Recent work has shown that fully-connected CRFs, where each node is connected to every other node, can be solved efficiently under the restriction that the pairwise term is a Gaussian kernel over a Euclidean feature space. In this paper, we generalize the pairwise terms to a non-linear dissimilarity measure that is not required to be a distance metric. To this end, we propose a density estimation technique to derive conditional pairwise potentials in a non-parametric manner. We then use an efficient embedding technique to estimate an approximate Euclidean feature space for these potentials, in which the pairwise term can still be expressed as a Gaussian kernel. We demonstrate that the use of non-parametric models for the pairwise interactions, conditioned on the input data, greatly increases expressive power whilst maintaining efficient inference.

We propose an algorithm for automatically obtaining a segmentation of a rigid object in a sequence of images that are calibrated for camera pose and intrinsic parameters. Until recently, the best segmentation results have been obtained by interactive methods that require manual labelling of image regions. Our method requires no user input but instead relies on the camera fixating on the object of interest during the sequence. We begin by learning a model of the object is colour, from the image pixels around the fixation points. We then extract image edges and combine these with the object colour information in a volumetric binary MRF model. The globally optimal segmentation of 3D space is obtained by a graph-cut optimisation. From this segmentation an improved colour model is extracted and the whole process is iterated until convergence. Our first finding is that the fixation constraint, which requires that the object of interest is more or less central in the image, is enough to determine what to segment and initialise an automatic segmentation process. Second, we find that by performing a single segmentation in 3D, we implicitly exploit a 3D rigidity constraint, expressed as silhouette coherency, which significantly improves silhouette quality over independent 2D segmentations. We demonstrate the validity of our approach by providing segmentation results on real sequences.