Ameesh Makadia

Varun Jampani, Kevis-Kokitsi Maninis, Andreas Engelhardt et al. · deepmind

Recent advances in neural reconstruction enable high-quality 3D object reconstruction from casually captured image collections. Current techniques mostly analyze their progress on relatively simple image collections where Structure-from-Motion (SfM) techniques can provide ground-truth (GT) camera poses. We note that SfM techniques tend to fail on in-the-wild image collections such as image search results with varying backgrounds and illuminations. To enable systematic research progress on 3D reconstruction from casual image captures, we propose NAVI: a new dataset of category-agnostic image collections of objects with high-quality 3D scans along with per-image 2D-3D alignments providing near-perfect GT camera parameters. These 2D-3D alignments allow us to extract accurate derivative annotations such as dense pixel correspondences, depth and segmentation maps. We demonstrate the use of NAVI image collections on different problem settings and show that NAVI enables more thorough evaluations that were not possible with existing datasets. We believe NAVI is beneficial for systematic research progress on 3D reconstruction and correspondence estimation. Project page: https://navidataset.github.io

Kamal Gupta, Varun Jampani, Carlos Esteves et al. · deepmind

We present a method for joint alignment of sparse in-the-wild image collections of an object category. Most prior works assume either ground-truth keypoint annotations or a large dataset of images of a single object category. However, neither of the above assumptions hold true for the long-tail of the objects present in the world. We present a self-supervised technique that directly optimizes on a sparse collection of images of a particular object/object category to obtain consistent dense correspondences across the collection. We use pairwise nearest neighbors obtained from deep features of a pre-trained vision transformer (ViT) model as noisy and sparse keypoint matches and make them dense and accurate matches by optimizing a neural network that jointly maps the image collection into a learned canonical grid. Experiments on CUB and SPair-71k benchmarks demonstrate that our method can produce globally consistent and higher quality correspondences across the image collection when compared to existing self-supervised methods. Code and other material will be made available at \url{https://kampta.github.io/asic}.

Carlos Esteves, Jean-Jacques Slotine, Ameesh Makadia

Spherical CNNs generalize CNNs to functions on the sphere, by using spherical convolutions as the main linear operation. The most accurate and efficient way to compute spherical convolutions is in the spectral domain (via the convolution theorem), which is still costlier than the usual planar convolutions. For this reason, applications of spherical CNNs have so far been limited to small problems that can be approached with low model capacity. In this work, we show how spherical CNNs can be scaled for much larger problems. To achieve this, we make critical improvements including novel variants of common model components, an implementation of core operations to exploit hardware accelerator characteristics, and application-specific input representations that exploit the properties of our model. Experiments show our larger spherical CNNs reach state-of-the-art on several targets of the QM9 molecular benchmark, which was previously dominated by equivariant graph neural networks, and achieve competitive performance on multiple weather forecasting tasks. Our code is available at https://github.com/google-research/spherical-cnn.

Mohammed Suhail, Carlos Esteves, Leonid Sigal et al.

Neural rendering has received tremendous attention since the advent of Neural Radiance Fields (NeRF), and has pushed the state-of-the-art on novel-view synthesis considerably. The recent focus has been on models that overfit to a single scene, and the few attempts to learn models that can synthesize novel views of unseen scenes mostly consist of combining deep convolutional features with a NeRF-like model. We propose a different paradigm, where no deep features and no NeRF-like volume rendering are needed. Our method is capable of predicting the color of a target ray in a novel scene directly, just from a collection of patches sampled from the scene. We first leverage epipolar geometry to extract patches along the epipolar lines of each reference view. Each patch is linearly projected into a 1D feature vector and a sequence of transformers process the collection. For positional encoding, we parameterize rays as in a light field representation, with the crucial difference that the coordinates are canonicalized with respect to the target ray, which makes our method independent of the reference frame and improves generalization. We show that our approach outperforms the state-of-the-art on novel view synthesis of unseen scenes even when being trained with considerably less data than prior work.

Zezhou Cheng, Carlos Esteves, Varun Jampani et al.

A critical obstacle preventing NeRF models from being deployed broadly in the wild is their reliance on accurate camera poses. Consequently, there is growing interest in extending NeRF models to jointly optimize camera poses and scene representation, which offers an alternative to off-the-shelf SfM pipelines which have well-understood failure modes. Existing approaches for unposed NeRF operate under limited assumptions, such as a prior pose distribution or coarse pose initialization, making them less effective in a general setting. In this work, we propose a novel approach, LU-NeRF, that jointly estimates camera poses and neural radiance fields with relaxed assumptions on pose configuration. Our approach operates in a local-to-global manner, where we first optimize over local subsets of the data, dubbed mini-scenes. LU-NeRF estimates local pose and geometry for this challenging few-shot task. The mini-scene poses are brought into a global reference frame through a robust pose synchronization step, where a final global optimization of pose and scene can be performed. We show our LU-NeRF pipeline outperforms prior attempts at unposed NeRF without making restrictive assumptions on the pose prior. This allows us to operate in the general SE(3) pose setting, unlike the baselines. Our results also indicate our model can be complementary to feature-based SfM pipelines as it compares favorably to COLMAP on low-texture and low-resolution images.

Yipeng Gao, Lei Shu, Genzhi Ye et al.

Procedural 3D modeling through code is emerging as a versatile paradigm, offering deterministic, engine-ready, and precisely editable assets that neural 3D generators inherently lack. Authoring such procedural content, however, demands deep expertise in 3D software APIs, parametric design, and code-level geometric reasoning. In this paper, we propose 3DCodeBench, a systematic benchmark for evaluating vision-language model (VLM) agents for procedural 3D generation in 3D modeling software. Specifically, 3DCodeBench evaluates how effectively 12 advanced VLMs can serve as procedural 3D modelers by translating text and image references into procedural code for 3D modeling software. Recognizing that automated metrics may not fully capture the perceptual quality of 3D shapes, we build 3DCodeArena, a ranking platform based on pairwise human preferences over generated 3D outputs. From extensive evaluations and results, we observe that: (1) Failures mostly arise from API mismatches, while successful renders still suffer from disconnected or floating 3D geometric components. (2) Test-time scaling, such as higher thinking budgets and multi-turn refinement, improves performance overall. Our findings highlight a critical need for high-quality procedural coding data to advance commercial VLMs. Furthermore, effective procedural 3D modeling requires a robust execution environment that provides high-fidelity feedback for iterative refinement. We release 3DCodeBench, including the curated large-scale dataset of multimodal (text/image) prompts, procedural code, 3D object triplets, evaluation protocol, and the public 3DCodeArena platform as a foundational toolkit for exploring VLM-based procedural 3D modelers.

Richard Li, Carlos Esteves, Ameesh Makadia et al.

We present a system for accurately predicting stable orientations for diverse rigid objects. We propose to overcome the critical issue of modelling multimodality in the space of rotations by using a conditional generative model to accurately classify contact surfaces. Our system is capable of operating from noisy and partially-observed pointcloud observations captured by real world depth cameras. Our method substantially outperforms the current state-of-the-art systems on a simulated stacking task requiring highly accurate rotations, and demonstrates strong sim2real zero-shot transfer results across a variety of unseen objects on a real world reorientation task. Project website: \url{https://richardrl.github.io/stable-reorientation/}

Utkarsh Singhal, Carlos Esteves, Ameesh Makadia et al.

Computer vision research has long aimed to build systems that are robust to spatial transformations found in natural data. Traditionally, this is done using data augmentation or hard-coding invariances into the architecture. However, too much or too little invariance can hurt, and the correct amount is unknown a priori and dependent on the instance. Ideally, the appropriate invariance would be learned from data and inferred at test-time. We treat invariance as a prediction problem. Given any image, we use a normalizing flow to predict a distribution over transformations and average the predictions over them. Since this distribution only depends on the instance, we can align instances before classifying them and generalize invariance across classes. The same distribution can also be used to adapt to out-of-distribution poses. This normalizing flow is trained end-to-end and can learn a much larger range of transformations than Augerino and InstaAug. When used as data augmentation, our method shows accuracy and robustness gains on CIFAR 10, CIFAR10-LT, and TinyImageNet.

Carlos Esteves, Ameesh Makadia

Denoising diffusion models are widely used for high-quality image and video generation. Their performance depends on noise schedules, which define the distribution of noise levels applied during training and the sequence of noise levels traversed during sampling. Noise schedules are typically handcrafted and require manual tuning across different resolutions. In this work, we propose a principled way to design per-instance noise schedules for pixel diffusion, based on the image's spectral properties. By deriving theoretical bounds on the efficacy of minimum and maximum noise levels, we design ``tight'' noise schedules that eliminate redundant steps. During inference, we propose to conditionally sample such noise schedules. Experiments show that our noise schedules improve generative quality of single-stage pixel diffusion models, particularly in the low-step regime.

Jasmine Bayrooti, Weiwei Kong, Natalia Ponomareva et al.

Generative models trained on sensitive image datasets risk memorizing and reproducing individual training examples, making strong privacy guarantees essential. While differential privacy (DP) provides a principled framework for such guarantees, standard DP finetuning (e.g., with DP-SGD) often results in severe degradation of image quality, particularly in high-frequency textures, due to the indiscriminate addition of noise across all model parameters. In this work, we propose a spectral DP framework based on the hypothesis that the most privacy-sensitive portions of an image are often low-frequency components in the wavelet space (e.g., facial features and object shapes) while high-frequency components are largely generic and public. Based on this hypothesis, we propose the following two-stage framework for DP image generation with coarse image intermediaries: (1) DP finetune an autoregressive spectral image tokenizer model on the low-resolution wavelet coefficients of the sensitive images, and (2) perform high-resolution upsampling using a publicly pretrained super-resolution model. By restricting the privacy budget to the global structures of the image in the first stage, and leveraging the post-processing property of DP for detail refinement, we achieve promising trade-offs between privacy and utility. Experiments on the MS-COCO and MM-CelebA-HQ datasets show that our method generates images with improved quality and style capture relative to other leading DP image frameworks.

Thomas W. Mitchel, Carlos Esteves, Ameesh Makadia

We introduce a framework for intrinsic latent diffusion models operating directly on the surfaces of 3D shapes, with the goal of synthesizing high-quality textures. Our approach is underpinned by two contributions: field latents, a latent representation encoding textures as discrete vector fields on the mesh vertices, and field latent diffusion models, which learn to denoise a diffusion process in the learned latent space on the surface. We consider a single-textured-mesh paradigm, where our models are trained to generate variations of a given texture on a mesh. We show the synthesized textures are of superior fidelity compared those from existing single-textured-mesh generative models. Our models can also be adapted for user-controlled editing tasks such as inpainting and label-guided generation. The efficacy of our approach is due in part to the equivariance of our proposed framework under isometries, allowing our models to seamlessly reproduce details across locally similar regions and opening the door to a notion of generative texture transfer.

Carlos Esteves, Mohammed Suhail, Ameesh Makadia

Image tokenizers map images to sequences of discrete tokens, and are a crucial component of autoregressive transformer-based image generation. The tokens are typically associated with spatial locations in the input image, arranged in raster scan order, which is not ideal for autoregressive modeling. In this paper, we propose to tokenize the image spectrum instead, obtained from a discrete wavelet transform (DWT), such that the sequence of tokens represents the image in a coarse-to-fine fashion. Our tokenizer brings several advantages: 1) it leverages that natural images are more compressible at high frequencies, 2) it can take and reconstruct images of different resolutions without retraining, 3) it improves the conditioning for next-token prediction -- instead of conditioning on a partial line-by-line reconstruction of the image, it takes a coarse reconstruction of the full image, 4) it enables partial decoding where the first few generated tokens can reconstruct a coarse version of the image, 5) it enables autoregressive models to be used for image upsampling. We evaluate the tokenizer reconstruction metrics as well as multiscale image generation, text-guided image upsampling and editing.

Mohammed Suhail, Carlos Esteves, Leonid Sigal et al.

Latent variable generative models have emerged as powerful tools for generative tasks including image and video synthesis. These models are enabled by pretrained autoencoders that map high resolution data into a compressed lower dimensional latent space, where the generative models can subsequently be developed while requiring fewer computational resources. Despite their effectiveness, the direct application of latent variable models to higher dimensional domains such as videos continues to pose challenges for efficient training and inference. In this paper, we propose an autoencoder that projects volumetric data onto a four-plane factorized latent space that grows sublinearly with the input size, making it ideal for higher dimensional data like videos. The design of our factorized model supports straightforward adoption in a number of conditional generation tasks with latent diffusion models (LDMs), such as class-conditional generation, frame prediction, and video interpolation. Our results show that the proposed four-plane latent space retains a rich representation needed for high-fidelity reconstructions despite the heavy compression, while simultaneously enabling LDMs to operate with significant improvements in speed and memory.

Mohammed Suhail, Carlos Esteves, Leonid Sigal et al.

Classical light field rendering for novel view synthesis can accurately reproduce view-dependent effects such as reflection, refraction, and translucency, but requires a dense view sampling of the scene. Methods based on geometric reconstruction need only sparse views, but cannot accurately model non-Lambertian effects. We introduce a model that combines the strengths and mitigates the limitations of these two directions. By operating on a four-dimensional representation of the light field, our model learns to represent view-dependent effects accurately. By enforcing geometric constraints during training and inference, the scene geometry is implicitly learned from a sparse set of views. Concretely, we introduce a two-stage transformer-based model that first aggregates features along epipolar lines, then aggregates features along reference views to produce the color of a target ray. Our model outperforms the state-of-the-art on multiple forward-facing and 360° datasets, with larger margins on scenes with severe view-dependent variations.

Kieran Murphy, Carlos Esteves, Varun Jampani et al.

Single image pose estimation is a fundamental problem in many vision and robotics tasks, and existing deep learning approaches suffer by not completely modeling and handling: i) uncertainty about the predictions, and ii) symmetric objects with multiple (sometimes infinite) correct poses. To this end, we introduce a method to estimate arbitrary, non-parametric distributions on SO(3). Our key idea is to represent the distributions implicitly, with a neural network that estimates the probability given the input image and a candidate pose. Grid sampling or gradient ascent can be used to find the most likely pose, but it is also possible to evaluate the probability at any pose, enabling reasoning about symmetries and uncertainty. This is the most general way of representing distributions on manifolds, and to showcase the rich expressive power, we introduce a dataset of challenging symmetric and nearly-symmetric objects. We require no supervision on pose uncertainty -- the model trains only with a single pose per example. Nonetheless, our implicit model is highly expressive to handle complex distributions over 3D poses, while still obtaining accurate pose estimation on standard non-ambiguous environments, achieving state-of-the-art performance on Pascal3D+ and ModelNet10-SO(3) benchmarks.

Kefan Chen, Noah Snavely, Ameesh Makadia

Modern deep learning techniques that regress the relative camera pose between two images have difficulty dealing with challenging scenarios, such as large camera motions resulting in occlusions and significant changes in perspective that leave little overlap between images. These models continue to struggle even with the benefit of large supervised training datasets. To address the limitations of these models, we take inspiration from techniques that show regressing keypoint locations in 2D and 3D can be improved by estimating a discrete distribution over keypoint locations. Analogously, in this paper we explore improving camera pose regression by instead predicting a discrete distribution over camera poses. To realize this idea, we introduce DirectionNet, which estimates discrete distributions over the 5D relative pose space using a novel parameterization to make the estimation problem tractable. Specifically, DirectionNet factorizes relative camera pose, specified by a 3D rotation and a translation direction, into a set of 3D direction vectors. Since 3D directions can be identified with points on the sphere, DirectionNet estimates discrete distributions on the sphere as its output. We evaluate our model on challenging synthetic and real pose estimation datasets constructed from Matterport3D and InteriorNet. Promising results show a near 50% reduction in error over direct regression methods.

Tomas Jakab, Richard Tucker, Ameesh Makadia et al.

We introduce KeypointDeformer, a novel unsupervised method for shape control through automatically discovered 3D keypoints. We cast this as the problem of aligning a source 3D object to a target 3D object from the same object category. Our method analyzes the difference between the shapes of the two objects by comparing their latent representations. This latent representation is in the form of 3D keypoints that are learned in an unsupervised way. The difference between the 3D keypoints of the source and the target objects then informs the shape deformation algorithm that deforms the source object into the target object. The whole model is learned end-to-end and simultaneously discovers 3D keypoints while learning to use them for deforming object shapes. Our approach produces intuitive and semantically consistent control of shape deformations. Moreover, our discovered 3D keypoints are consistent across object category instances despite large shape variations. As our method is unsupervised, it can be readily deployed to new object categories without requiring annotations for 3D keypoints and deformations.

Shangzhe Wu, Ameesh Makadia, Jiajun Wu et al.

Recent works have shown exciting results in unsupervised image de-rendering -- learning to decompose 3D shape, appearance, and lighting from single-image collections without explicit supervision. However, many of these assume simplistic material and lighting models. We propose a method, termed RADAR, that can recover environment illumination and surface materials from real single-image collections, relying neither on explicit 3D supervision, nor on multi-view or multi-light images. Specifically, we focus on rotationally symmetric artefacts that exhibit challenging surface properties including specular reflections, such as vases. We introduce a novel self-supervised albedo discriminator, which allows the model to recover plausible albedo without requiring any ground-truth during training. In conjunction with a shape reconstruction module exploiting rotational symmetry, we present an end-to-end learning framework that is able to de-render the world's revolutionary artefacts. We conduct experiments on a real vase dataset and demonstrate compelling decomposition results, allowing for applications including free-viewpoint rendering and relighting.

Kieran A. Murphy, Varun Jampani, Srikumar Ramalingam et al.

Representational learning forms the backbone of most deep learning applications, and the value of a learned representation is intimately tied to its information content regarding different factors of variation. Finding good representations depends on the nature of supervision and the learning algorithm. We propose a novel algorithm that utilizes a weak form of supervision where the data is partitioned into sets according to certain inactive (common) factors of variation which are invariant across elements of each set. Our key insight is that by seeking correspondence between elements of different sets, we learn strong representations that exclude the inactive factors of variation and isolate the active factors that vary within all sets. As a consequence of focusing on the active factors, our method can leverage a mix of set-supervised and wholly unsupervised data, which can even belong to a different domain. We tackle the challenging problem of synthetic-to-real object pose transfer, without pose annotations on anything, by isolating pose information which generalizes to the category level and across the synthetic/real domain gap. The method can also boost performance in supervised settings, by strengthening intermediate representations, as well as operate in practically attainable scenarios with set-supervised natural images, where quantity is limited and nuisance factors of variation are more plentiful.

Andrew Liu, Richard Tucker, Varun Jampani et al.

We introduce the problem of perpetual view generation - long-range generation of novel views corresponding to an arbitrarily long camera trajectory given a single image. This is a challenging problem that goes far beyond the capabilities of current view synthesis methods, which quickly degenerate when presented with large camera motions. Methods for video generation also have limited ability to produce long sequences and are often agnostic to scene geometry. We take a hybrid approach that integrates both geometry and image synthesis in an iterative `\emph{render}, \emph{refine} and \emph{repeat}' framework, allowing for long-range generation that cover large distances after hundreds of frames. Our approach can be trained from a set of monocular video sequences. We propose a dataset of aerial footage of coastal scenes, and compare our method with recent view synthesis and conditional video generation baselines, showing that it can generate plausible scenes for much longer time horizons over large camera trajectories compared to existing methods. Project page at https://infinite-nature.github.io/.

Jake Levinson, Carlos Esteves, Kefan Chen et al.

Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D alignment problems solved by orthogonal Procrustes, rotation averaging, or Essential matrix decomposition. Despite its utility in different settings, SVD orthogonalization as a procedure for producing rotation matrices is typically overlooked in deep learning models, where the preferences tend toward classic representations like unit quaternions, Euler angles, and axis-angle, or more recently-introduced methods. Despite the importance of 3D rotations in computer vision and robotics, a single universally effective representation is still missing. Here, we explore the viability of SVD orthogonalization for 3D rotations in neural networks. We present a theoretical analysis that shows SVD is the natural choice for projecting onto the rotation group. Our extensive quantitative analysis shows simply replacing existing representations with the SVD orthogonalization procedure obtains state of the art performance in many deep learning applications covering both supervised and unsupervised training.

Carlos Esteves, Ameesh Makadia, Kostas Daniilidis

Learning equivariant representations is a promising way to reduce sample and model complexity and improve the generalization performance of deep neural networks. The spherical CNNs are successful examples, producing SO(3)-equivariant representations of spherical inputs. There are two main types of spherical CNNs. The first type lifts the inputs to functions on the rotation group SO(3) and applies convolutions on the group, which are computationally expensive since SO(3) has one extra dimension. The second type applies convolutions directly on the sphere, which are limited to zonal (isotropic) filters, and thus have limited expressivity. In this paper, we present a new type of spherical CNN that allows anisotropic filters in an efficient way, without ever leaving the spherical domain. The key idea is to consider spin-weighted spherical functions, which were introduced in physics in the study of gravitational waves. These are complex-valued functions on the sphere whose phases change upon rotation. We define a convolution between spin-weighted functions and build a CNN based on it. The spin-weighted functions can also be interpreted as spherical vector fields, allowing applications to tasks where the inputs or outputs are vector fields. Experiments show that our method outperforms previous methods on tasks like classification of spherical images, classification of 3D shapes and semantic segmentation of spherical panoramas.

Jared Quincy Davis, Krzysztof Choromanski, Jake Varley et al.

Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient, constant memory backpropagation. Neural ODEs are universal approximators only when they are non-autonomous, that is, the dynamics depends explicitly on time. We propose a novel family of Neural ODEs with time-varying weights, where time-dependence is non-parametric, and the smoothness of weight trajectories can be explicitly controlled to allow a tradeoff between expressiveness and efficiency. Using this enhanced expressiveness, we outperform previous Neural ODE variants in both speed and representational capacity, ultimately outperforming standard ResNet and CNN models on select image classification and video prediction tasks.

Chiyu Max Jiang, Avneesh Sud, Ameesh Makadia et al.

Shape priors learned from data are commonly used to reconstruct 3D objects from partial or noisy data. Yet no such shape priors are available for indoor scenes, since typical 3D autoencoders cannot handle their scale, complexity, or diversity. In this paper, we introduce Local Implicit Grid Representations, a new 3D shape representation designed for scalability and generality. The motivating idea is that most 3D surfaces share geometric details at some scale -- i.e., at a scale smaller than an entire object and larger than a small patch. We train an autoencoder to learn an embedding of local crops of 3D shapes at that size. Then, we use the decoder as a component in a shape optimization that solves for a set of latent codes on a regular grid of overlapping crops such that an interpolation of the decoded local shapes matches a partial or noisy observation. We demonstrate the value of this proposed approach for 3D surface reconstruction from sparse point observations, showing significantly better results than alternative approaches.

Jake Levinson, Avneesh Sud, Ameesh Makadia

Generative modeling of 3D shapes has become an important problem due to its relevance to many applications across Computer Vision, Graphics, and VR. In this paper we build upon recently introduced 3D mesh-convolutional Variational AutoEncoders which have shown great promise for learning rich representations of deformable 3D shapes. We introduce a supervised generative 3D mesh model that disentangles the latent shape representation into independent generative factors. Our extensive experimental analysis shows that learning an explicitly disentangled representation can both improve random shape generation as well as successfully address downstream tasks such as pose and shape transfer, shape-invariant temporal synchronization, and pose-invariant shape matching.

Carlos Esteves, Avneesh Sud, Zhengyi Luo et al.

Spherical convolutional networks have been introduced recently as tools to learn powerful feature representations of 3D shapes. Spherical CNNs are equivariant to 3D rotations making them ideally suited to applications where 3D data may be observed in arbitrary orientations. In this paper we learn 2D image embeddings with a similar equivariant structure: embedding the image of a 3D object should commute with rotations of the object. We introduce a cross-domain embedding from 2D images into a spherical CNN latent space. This embedding encodes images with 3D shape properties and is equivariant to 3D rotations of the observed object. The model is supervised only by target embeddings obtained from a spherical CNN pretrained for 3D shape classification. We show that learning a rich embedding for images with appropriate geometric structure is sufficient for tackling varied applications, such as relative pose estimation and novel view synthesis, without requiring additional task-specific supervision.

Carlos Esteves, Kostas Daniilidis, Ameesh Makadia

With the recent proliferation of consumer-grade 360° cameras, it is worth revisiting visual perception challenges with spherical cameras given the potential benefit of their global field of view. To this end we introduce a spherical convolutional hourglass network (SCHN) for the dense labeling on the sphere. The SCHN is invariant to camera orientation (lifting the usual requirement for `upright' panoramic images), and its design is scalable for larger practical datasets. Initial experiments show promising results on a spherical semantic segmentation task.

Or Litany, Alex Bronstein, Michael Bronstein et al.

The availability of affordable and portable depth sensors has made scanning objects and people simpler than ever. However, dealing with occlusions and missing parts is still a significant challenge. The problem of reconstructing a (possibly non-rigidly moving) 3D object from a single or multiple partial scans has received increasing attention in recent years. In this work, we propose a novel learning-based method for the completion of partial shapes. Unlike the majority of existing approaches, our method focuses on objects that can undergo non-rigid deformations. The core of our method is a variational autoencoder with graph convolutional operations that learns a latent space for complete realistic shapes. At inference, we optimize to find the representation in this latent space that best fits the generated shape to the known partial input. The completed shape exhibits a realistic appearance on the unknown part. We show promising results towards the completion of synthetic and real scans of human body and face meshes exhibiting different styles of articulation and partiality.

Carlos Esteves, Christine Allen-Blanchette, Ameesh Makadia et al.

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.

Amir Ali Ahmadi, Georgina Hall, Ameesh Makadia et al.

Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an obstacle) with convex or nearly-convex basic semialgebraic sets, computation of Euclidean distances between two such sets, separation of two convex basic semalgebraic sets that overlap, and tight containment of the union of several basic semialgebraic sets with a single convex one. We use algebraic techniques from sum of squares optimization that reduce all these tasks to semidefinite programs of small size and present numerical experiments in realistic scenarios.