arXiv subjects

Ameesh Makadia

Publications and source records attributed to Ameesh Makadia.

30 records · Page 2Linked to original sources

arXiv2021

Wide-Baseline Relative Camera Pose Estimation with Directional Learning

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.

cs.CV↗

arXiv2021

KeypointDeformer: Unsupervised 3D Keypoint Discovery for Shape Control

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.

cs.CV↗

arXiv2020

Spin-Weighted Spherical CNNs

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.

cs.CV↗

arXiv2020

An Analysis of SVD for Deep Rotation Estimation

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.

cs.CV↗

arXiv2020

Time Dependence in Non-Autonomous Neural ODEs

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.

cs.LG↗

arXiv2020

Local Implicit Grid Representations for 3D Scenes

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.

cs.CV↗

arXiv2019

Latent feature disentanglement for 3D meshes

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.

cs.LG↗

arXiv2019

Cross-Domain 3D Equivariant Image Embeddings

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.

cs.CV↗

arXiv2018

Learning SO(3) Equivariant Representations with Spherical CNNs

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.

cs.CV↗

arXiv2018

Labeling Panoramas with Spherical Hourglass Networks

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.

cs.CV↗

arXiv2018

Deformable Shape Completion with Graph Convolutional Autoencoders

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.

cs.CV↗

arXiv2017

Geometry of 3D Environments and Sum of Squares Polynomials

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.

math.OC↗