In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a unified feature space in a principled manner using kernel methods. Sparse models that generalize well to the test data can be learned in the unified kernel space, and appropriate constraints can be incorporated for application in supervised and unsupervised learning. In this paper, we propose to perform sparse coding and dictionary learning in the multiple kernel space, where the weights of the ensemble kernel are tuned based on graph-embedding principles such that class discrimination is maximized. In our proposed algorithm, dictionaries are inferred using multiple levels of 1-D subspace clustering in the kernel space, and the sparse codes are obtained using a simple levelwise pursuit scheme. Empirical results for object recognition and image clustering show that our algorithm outperforms existing sparse coding based approaches, and compares favorably to other state-of-the-art methods.
We show that unsupervised training of latent capsule layers using only the reconstruction loss, without masking to select the correct output class, causes a loss of equivariances and other desirable capsule qualities. This implies that supervised capsules networks can't be very deep. Unsupervised sparsening of latent capsule layer activity both restores these qualities and appears to generalize better than supervised masking, while potentially enabling deeper capsules networks. We train a sparse, unsupervised capsules network of similar geometry to Sabour et al (2017) on MNIST, and then test c…
In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic distances, we use heat kernels. These can be computed quickly during training as the supervisor signal. Moreover, we propose a curriculum learning strategy using different heat diffusion times which provide different levels of difficulty during optimization without any sampling mechanism or hard example mining. We present the results of our method on differen…
Computer Vision Center(计算机视觉中心);Universitat de Barcelona(巴塞罗那大学)
In this paper we propose the first deep unsupervised approach in human body reconstruction to estimate body surface from a sparse set of landmarks, so called DeepMurf. We apply a denoising autoencoder to estimate missing landmarks. Then we apply an attention model to estimate body joints from landmarks. Finally, a cascading network is applied to regress parameters of a statistical generative model that reconstructs body. Our set of proposed loss functions allows us to train the network in an unsupervised way. Results on four public datasets show that our approach accurately reconstructs the hu…
Unsupervised Domain adaptation is an effective method in addressing the domain shift issue when transferring knowledge from an existing richly labeled domain to a new domain. Existing manifold-based methods either are based on traditional models or largely rely on Grassmannian manifold via minimizing differences of single covariance matrices of two domains. In addition, existing pseudo-labeling algorithms inadequately consider the quality of pseudo labels in aligning the conditional distribution between two domains. In this work, a deep spherical manifold Gaussian kernel (DSGK) framework is pr…
The formation of connections between neural cells is emerging essentially from an unsupervised learning process. For instance, during the development of the primary visual cortex of mammals (V1), we observe the emergence of cells selective to localized and oriented features. This leads to the development of a rough contour-based representation of the retinal image in area V1. We propose a biological model of the formation of this representation along the thalamo-cortical pathway. To achieve this goal, we replicated the Multi-Layer Convolutional Sparse Coding (ML-CSC) algorithm developed by Mic…
Stony Brook University(石溪大学);Oak Ridge National Laboratory(橡树岭国家实验室);Stony Brook University Hospital(石溪大学医院)
Histopathology images are crucial to the study of complex diseases such as cancer. The histologic characteristics of nuclei play a key role in disease diagnosis, prognosis and analysis. In this work, we propose a sparse Convolutional Autoencoder (CAE) for fully unsupervised, simultaneous nucleus detection and feature extraction in histopathology tissue images. Our CAE detects and encodes nuclei in image patches in tissue images into sparse feature maps that encode both the location and appearance of nuclei. Our CAE is the first unsupervised detection network for computer vision applications. T…
Deep kernel video approximation for unsupervised action segmentation
Department of Intellgient Systems (DIS), Tilburg University, Tilburg, NL(智能系统系,蒂尔堡大学,蒂尔堡,荷兰);Division of Image Processing, LUMC, Leiden, NL(图像处理 division,莱顿大学医学中心,莱顿,荷兰)
Indian Institute of Space Science and Technology(印度空间科学与技术研究所)
Kernel based Deep Learning using multi-layer kernel machines(MKMs) was proposed by Y.Cho and L.K. Saul in \cite{saul}. In MKMs they used only one kernel(arc-cosine kernel) at a layer for the kernel PCA-based feature extraction. We propose to use multiple kernels in each layer by taking a convex combination of many kernels following an unsupervised learning strategy. Empirical study is conducted on \textit{mnist-back-rand}, \textit{mnist-back-image} and \textit{mnist-rot-back-image} datasets generated by adding random noise in the image background of MNIST dataset. Experimental results indicate…
Partitioning an image into superpixels based on the similarity of pixels with respect to features such as colour or spatial location can significantly reduce data complexity and improve subsequent image processing tasks. Initial algorithms for unsupervised superpixel generation solely relied on local cues without prioritizing significant edges over arbitrary ones. On the other hand, more recent methods based on unsupervised deep learning either fail to properly address the trade-off between superpixel edge adherence and compactness or lack control over the generated number of superpixels. By u…
University of Electronic Science and Technology of China(电子科技大学);The Chinese University of Hong Kong(香港中文大学);Northeast Normal University(东北师范大学)
Non-blind deblurring methods achieve decent performance under the accurate blur kernel assumption. Since the kernel uncertainty (i.e. kernel error) is inevitable in practice, semi-blind deblurring is suggested to handle it by introducing the prior of the kernel (or induced) error. However, how to design a suitable prior for the kernel (or induced) error remains challenging. Hand-crafted prior, incorporating domain knowledge, generally performs well but may lead to poor performance when kernel (or induced) error is complex. Data-driven prior, which excessively depends on the diversity and abund…
Duke University(杜克大学);University of Minnesota(明尼苏达大学)
A framework for unsupervised group activity analysis from a single video is here presented. Our working hypothesis is that human actions lie on a union of low-dimensional subspaces, and thus can be efficiently modeled as sparse linear combinations of atoms from a learned dictionary representing the action's primitives. Contrary to prior art, and with the primary goal of spatio-temporal action grouping, in this work only one single video segment is available for both unsupervised learning and analysis without any prior training information. After extracting simple features at a single spatio-te…
School of Computer Science, University of Sydney(悉尼大学计算机科学学院);Royal Prince Alfred Hospital(皇家阿尔弗雷德王子医院);Sydney Medical School, University of Sydney(悉尼大学悉尼医学院);Med-X Research Institute, Shanghai Jiao Tong University(上海交通大学Med-X研究院)
The availability of large-scale annotated image datasets and recent advances in supervised deep learning methods enable the end-to-end derivation of representative image features that can impact a variety of image analysis problems. Such supervised approaches, however, are difficult to implement in the medical domain where large volumes of labelled data are difficult to obtain due to the complexity of manual annotation and inter- and intra-observer variability in label assignment. We propose a new convolutional sparse kernel network (CSKN), which is a hierarchical unsupervised feature learning…
Nanjing University of Science and Technology(南京理工大学)
Unsupervised depth completion aims to recover dense depth from the sparse one without using the ground-truth annotation. Although depth measurement obtained from LiDAR is usually sparse, it contains valid and real distance information, i.e., scale-consistent absolute depth values. Meanwhile, scale-agnostic counterparts seek to estimate relative depth and have achieved impressive performance. To leverage both the inherent characteristics, we thus suggest to model scale-consistent depth upon unsupervised scale-agnostic frameworks. Specifically, we propose the decomposed scale-consistent learning…
Portland State University(波特兰州立大学);New Mexico Consortium(新墨西哥联盟);Santa Fe Institute(圣菲研究所);Los Alamos National Laboratory(洛斯阿拉莫斯国家实验室)
Deep Convolutional Neural Networks (DCNN) require millions of labeled training examples for image classification and object detection tasks, which restrict these models to domains where such datasets are available. In this paper, we explore the use of unsupervised sparse coding applied to stereo-video data to help alleviate the need for large amounts of labeled data. We show that replacing a typical supervised convolutional layer with an unsupervised sparse-coding layer within a DCNN allows for better performance on a car detection task when only a limited number of labeled training examples i…
Universitat de Barcelona(巴塞罗那大学);Centre de Visió per Computador(计算机视觉中心)
We propose a meta-parameter free, off-the-shelf, simple and fast unsupervised feature learning algorithm, which exploits a new way of optimizing for sparsity. Experiments on STL-10 show that the method presents state-of-the-art performance and provides discriminative features that generalize well.
In this paper, we propose sparse coding-based approaches for segmentation of tumor regions from MR images. Sparse coding with data-adapted dictionaries has been successfully employed in several image recovery and vision problems. The proposed approaches obtain sparse codes for each pixel in brain magnetic resonance images considering their intensity values and location information. Since it is trivial to obtain pixel-wise sparse codes, and combining multiple features in the sparse coding setup is not straightforward, we propose to perform sparse coding in a high-dimensional feature space where…
Philips Medical Systems Technologies Ltd.(飞利浦医疗系统科技有限公司)
Deep sparse auto-encoders with mixed structure regularization (MSR) in addition to explicit sparsity regularization term and stochastic corruption of the input data with Gaussian noise have the potential to improve unsupervised abnormality detection. Unsupervised abnormality detection based on identifying outliers using deep sparse auto-encoders is a very appealing approach for medical computer aided detection systems as it requires only healthy data for training rather than expert annotated abnormality. In the task of detecting coronary artery disease from Coronary Computed Tomography Angiogr…
We use spatially-sparse two, three and four dimensional convolutional autoencoder networks to model sparse structures in 2D space, 3D space, and 3+1=4 dimensional space-time. We evaluate the resulting latent spaces by testing their usefulness for downstream tasks. Applications are to handwriting recognition in 2D, segmentation for parts in 3D objects, segmentation for objects in 3D scenes, and body-part segmentation for 4D wire-frame models generated from motion capture data.
Unified Unsupervised and Sparsely-Supervised 3D Object Detection by Semantic Pseudo-Labeling and Prototype Learning
Institute of Medical Robotics, Shanghai Jiao Tong University(上海交通大学医疗机器人研究院);Key Laboratory of System Control and Information Processing, Ministry of Education of China(系统控制与信息处理教育部重点实验室)
Sun Yat-Sen University(中山大学);Microsoft Research(微软研究院);Hefei University of Technology(合肥工业大学);University of Central Florida(中佛罗里达大学)
In this paper, we study the problem of designing efficient convolutional neural network architectures with the interest in eliminating the redundancy in convolution kernels. In addition to structured sparse kernels, low-rank kernels and the product of low-rank kernels, the product of structured sparse kernels, which is a framework for interpreting the recently-developed interleaved group convolutions (IGC) and its variants (e.g., Xception), has been attracting increasing interests. Motivated by the observation that the convolutions contained in a group convolution in IGC can be further decompo…
Aligning Instance-Semantic Sparse Representation towards Unsupervised Object Segmentation and Shape Abstraction with Repeatable Primitives
School of Big Data and Software Engineering, Chongqing University(重庆大学大数据与软件学院);Department of Computer Science and Engineering, State University of New York at Buffalo(纽约州立大学布法罗分校计算机科学与工程系)
The University of Tennessee(田纳西大学);Applied Research LLC(应用研究有限责任公司)
In many computer vision applications, obtaining images of high resolution in both the spatial and spectral domains are equally important. However, due to hardware limitations, one can only expect to acquire images of high resolution in either the spatial or spectral domains. This paper focuses on hyperspectral image super-resolution (HSI-SR), where a hyperspectral image (HSI) with low spatial resolution (LR) but high spectral resolution is fused with a multispectral image (MSI) with high spatial resolution (HR) but low spectral resolution to obtain HR HSI. Existing deep learning-based solution…
Tsinghua University(清华大学);Wayne State University(韦恩州立大学)
It is vital to infer signed distance functions (SDFs) from 3D point clouds. The latest methods rely on generalizing the priors learned from large scale supervision. However, the learned priors do not generalize well to various geometric variations that are unseen during training, especially for extremely sparse point clouds. To resolve this issue, we present a neural network to directly infer SDFs from single sparse point clouds without using signed distance supervision, learned priors or even normals. Our insight here is to learn surface parameterization and SDFs inference in an end-to-end ma…
Guangdong University of Technology(广东工业大学);Commonwealth Scientific and Industrial Research Organisation(联邦科学与工业研究组织);The University of Sydney(悉尼大学)
Sparse subspace clustering (SSC), as one of the most successful subspace clustering methods, has achieved notable clustering accuracy in computer vision tasks. However, SSC applies only to vector data in Euclidean space. As such, there is still no satisfactory approach to solve subspace clustering by ${\it self-expressive}$ principle for symmetric positive definite (SPD) matrices which is very useful in computer vision. In this paper, by embedding the SPD matrices into a Reproducing Kernel Hilbert Space (RKHS), a kernel subspace clustering method is constructed on the SPD manifold through an a…
What if deep neural networks can learn from sparsity-inducing priors? When the networks are designed by combining layer modules (CNN, RNN, etc), engineers less exploit the inductive bias, i.e., existing well-known rules or prior knowledge, other than annotated training data sets. We focus on employing sparsity-inducing priors in deep learning to encourage the network to concisely capture the nature of high-dimensional data in an unsupervised way. In order to use non-differentiable sparsity-inducing norms as loss functions, we plug their proximal mappings into the automatic differentiation fram…
University of Firenze(佛罗伦萨大学);University of Udine(乌迪内大学)
Person re-identification is best known as the problem of associating a single person that is observed from one or more disjoint cameras. The existing literature has mainly addressed such an issue, neglecting the fact that people usually move in groups, like in crowded scenarios. We believe that the additional information carried by neighboring individuals provides a relevant visual context that can be exploited to obtain a more robust match of single persons within the group. Despite this, re-identifying groups of people compound the common single person re-identification problems by introduci…
Self-similarity learning has been recognized as a promising method for single image super-resolution (SR) to produce high-resolution (HR) image in recent years. The performance of learning based SR reconstruction, however, highly depends on learned representation coeffcients. Due to the degradation of input image, conventional sparse coding is prone to produce unfaithful representation coeffcients. To this end, we propose a novel kernel based low-rank sparse model with self-similarity learning for single image SR which incorporates nonlocalsimilarity prior to enforce similar patches having sim…
Institute of Information Science, Academia Sinica(中央研究院信息科学研究所)
Blind image restoration is a non-convex problem which involves restoration of images from an unknown blur kernel. The factors affecting the performance of this restoration are how much prior information about an image and a blur kernel are provided and what algorithm is used to perform the restoration task. Prior information on images is often employed to restore the sharpness of the edges of an image. By contrast, no consensus is still present regarding what prior information to use in restoring from a blur kernel due to complex image blurring processes. In this paper, we propose modelling of…
Unsupervised Pre-training with Language-Vision Prompts for Low-Data Instance Segmentation
Northwestern Polytechnical University(西北工业大学);Inception Institute of Artificial Intelligence(Inception人工智能研究院);Hefei University of Technology(合肥工业大学);Baidu Inc.(百度公司)
The paper addresses face presentation attack detection in the challenging conditions of an unseen attack scenario where the system is exposed to novel presentation attacks that were not present in the training step. For this purpose, a pure one-class face presentation attack detection approach based on kernel regression is developed which only utilises bona fide (genuine) samples for training. In the context of the proposed approach, a number of innovations, including multiple kernel fusion, client-specific modelling, sparse regularisation and probabilistic modelling of score distributions are…
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney(悉尼大学航空航天、机械与机电工程学院);Sydney Institute for Robotics and Intelligent Systems(悉尼机器人与智能系统研究院)
While an exciting diversity of new imaging devices is emerging that could dramatically improve robotic perception, the challenges of calibrating and interpreting these cameras have limited their uptake in the robotics community. In this work we generalise techniques from unsupervised learning to allow a robot to autonomously interpret new kinds of cameras. We consider emerging sparse light field (LF) cameras, which capture a subset of the 4D LF function describing the set of light rays passing through a plane. We introduce a generalised encoding of sparse LFs that allows unsupervised learning …
We propose an algorithm for segmenting natural images based on texture and color information, which leverages the co-sparse analysis model for image segmentation within a convex multilabel optimization framework. As a key ingredient of this method, we introduce a novel textural similarity measure, which builds upon the co-sparse representation of image patches. We propose a Bayesian approach to merge textural similarity with information about color and location. Combined with recently developed convex multilabel optimization methods this leads to an efficient algorithm for both supervised and …
Georgia Institute of Technology(佐治亚理工学院);DeepMind Technologies(DeepMind科技公司);Princeton University(普林斯顿大学);The City College of New York(纽约城市学院);University of Virginia(弗吉尼亚大学)
In this paper, we propose a new unsupervised feature learning framework, namely Deep Sparse Coding (DeepSC), that extends sparse coding to a multi-layer architecture for visual object recognition tasks. The main innovation of the framework is that it connects the sparse-encoders from different layers by a sparse-to-dense module. The sparse-to-dense module is a composition of a local spatial pooling step and a low-dimensional embedding process, which takes advantage of the spatial smoothness information in the image. As a result, the new method is able to learn several levels of sparse represen…
With the development of Earth observation technology, very-high-resolution (VHR) image has become an important data source of change detection. Nowadays, deep learning methods have achieved conspicuous performance in the change detection of VHR images. Nonetheless, most of the existing change detection models based on deep learning require annotated training samples. In this paper, a novel unsupervised model called kernel principal component analysis (KPCA) convolution is proposed for extracting representative features from multi-temporal VHR images. Based on the KPCA convolution, an unsupervi…
University of Hong Kong(香港大学);Microsoft Research Asia(微软亚洲研究院);Texas A&M University(德克萨斯A&M大学)
We present a novel approach for completing and reconstructing 3D shapes from incomplete scanned data by using deep neural networks. Rather than being trained on supervised completion tasks and applied on a testing shape, the network is optimized from scratch on the single testing shape, to fully adapt to the shape and complete the missing data using contextual guidance from the known regions. The ability to complete missing data by an untrained neural network is usually referred to as the deep prior. In this paper, we interpret the deep prior from a neural tangent kernel (NTK) perspective and …
Unsupervised neural nets such as Restricted Boltzmann Machines(RBMs) and Deep Belif Networks(DBNs), are powerful in automatic feature extraction,unsupervised weight initialization and density estimation. In this paper,we demonstrate that the parameters of these neural nets can be dramatically reduced without affecting their performance. We describe a method to reduce the parameters required by RBM which is the basic building block for deep architectures. Further we propose an unsupervised sparse deep architectures selection algorithm to form sparse deep neural networks.Experimental results sho…
New Mexico Consortium(新墨西哥联盟);University of California, Berkeley(加州大学伯克利分校);University of Michigan(密歇根大学);Los Alamos National Laboratory(洛斯阿拉莫斯国家实验室)
In sparse coding it is common to tile an image into nonoverlapping patches, and then use a dictionary to create a sparse representation of each tile independently. In this situation, the overcompleteness of the dictionary is the number of dictionary elements divided by the patch size. In deconvolutional neural networks (DCNs), dictionaries learned on nonoverlapping tiles are replaced by a family of convolution kernels. Hence adjacent points in the feature maps (V1 layers) have receptive fields in the image that are translations of each other. The translational distance is determined by the dim…
Northwestern Polytechnical University(西北工业大学);Zhejiang Lab(之江实验室);Inception Institute of Artificial Intelligence(起源人工智能研究院);University of Chinese Academy of Sciences(中国科学院大学);NetEase(网易);Huazhong University of Science and Technology(华中科技大学)
Recently, inspired by DETR variants, query-based end-to-end instance segmentation (QEIS) methods have outperformed CNN-based models on large-scale datasets. Yet they would lose efficacy when only a small amount of training data is available since it's hard for the crucial queries/kernels to learn localization and shape priors. To this end, this work offers a novel unsupervised pre-training solution for low-data regimes. Inspired by the recent success of the Prompting technique, we introduce a new pre-training method that boosts QEIS models by giving Saliency Prompt for queries/kernels. Our met…
University of Maryland Institute for Advanced Computer Studies(马里兰大学高级计算机研究所);Institute for Physical Science and Technology, University of Maryland(马里兰大学物理科学与技术研究所)
In this work we present a lightweight, unsupervised learning pipeline for \textit{dense} depth, optical flow and egomotion estimation from sparse event output of the Dynamic Vision Sensor (DVS). To tackle this low level vision task, we use a novel encoder-decoder neural network architecture - ECN. Our work is the first monocular pipeline that generates dense depth and optical flow from sparse event data only. The network works in self-supervised mode and has just 150k parameters. We evaluate our pipeline on the MVSEC self driving dataset and present results for depth, optical flow and and egom…
University of Oulu(奥卢大学);University College London(伦敦大学学院)
Multi-energy computed tomography (CT) with photon counting detectors (PCDs) enables spectral imaging as PCDs can assign the incoming photons to specific energy channels. However, PCDs with many spectral channels drastically increase the computational complexity of the CT reconstruction, and bespoke reconstruction algorithms need fine-tuning to varying noise statistics. \rev{Especially if many projections are taken, a large amount of data has to be collected and stored. Sparse view CT is one solution for data reduction. However, these issues are especially exacerbated when sparse imaging scenar…
Unsupervised Self-Prior Embedding Neural Representation for Iterative Sparse-View CT Reconstruction
School of Information Science and Technology, ShanghaiTech University(上海科技大学信息科学与技术学院);Lingang Laboratory(临港实验室);University of Michigan(密歇根大学);Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology(华中科技大学同济医学院附属同济医院);School of Biomedical Engineering, Shanghai Jiao Tong University(上海交通大学生物医学工程学院)
Minimalistic Unsupervised Learning with the Sparse Manifold Transform
Meta AI;Center for Data Science(数据科学中心);EECS Dept.(电子工程与计算机科学系);Redwood Center(雷德伍德中心);Helen Wills Neuroscience Inst., UC Berkeley(加州大学伯克利分校海伦·威尔斯神经科学研究所);Courant Institute, New York University(纽约大学柯朗研究所)
NICTA(澳大利亚国家信息与通信技术研究院);University of Queensland(昆士兰大学);Australian National University(澳大利亚国立大学)
Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of symmetric positive definite matrices, which form a Riemannian manifold. With the aid of the recently introduced Stein kernel (related to a symmetric version of Bregman matrix divergence), we propose to perform sparse coding by embedding Riemannian manifolds into reproducing kernel Hilbert spaces. This leads to a convex and kernel version of the Lasso problem, which…
Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary advances in sparsity-aware modeling and processing, promotes the nonparametric basis pursuit advocated in this paper as the overarching framework for the confluence of kernel-based learning (KBL) approaches leveraging sparse linear regression, nuclear-norm regularization, and dictionary learning. The novel sparse KBL toolbox goes beyond translating sparse param…
Unsupervised Representation Learning from Sparse Transformation Analysis
Computing and Mathematical Sciences, Caltech, CA(计算与数学科学系,加州理工学院);Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University, MA(自然与人工智能研究学院,哈佛大学);Amsterdam Machine Learning Lab, University of Amsterdam, the Netherlands(阿姆斯特丹机器学习实验室,阿姆斯特丹大学)
The Chinese University of Hong Kong(香港中文大学);MEGVII Technology(旷视科技);The University of Hong Kong(香港大学)
Recent advance in 2D CNNs has revealed that large kernels are important. However, when directly applying large convolutional kernels in 3D CNNs, severe difficulties are met, where those successful module designs in 2D become surprisingly ineffective on 3D networks, including the popular depth-wise convolution. To address this vital challenge, we instead propose the spatial-wise partition convolution and its large-kernel module. As a result, it avoids the optimization and efficiency issues of naive 3D large kernels. Our large-kernel 3D CNN network, LargeKernel3D, yields notable improvement in 3…
Independent Component Analysis (ICA) is an effective unsupervised tool to learn statistically independent representation. However, ICA is not only sensitive to whitening but also difficult to learn an over-complete basis. Consequently, ICA with soft Reconstruction cost(RICA) was presented to learn sparse representations with over-complete basis even on unwhitened data. Whereas RICA is infeasible to represent the data with nonlinear structure due to its intrinsic linearity. In addition, RICA is essentially an unsupervised method and can not utilize the class information. In this paper, we propo…
We describe a method to infer dense depth from camera motion and sparse depth as estimated using a visual-inertial odometry system. Unlike other scenarios using point clouds from lidar or structured light sensors, we have few hundreds to few thousand points, insufficient to inform the topology of the scene. Our method first constructs a piecewise planar scaffolding of the scene, and then uses it to infer dense depth using the image along with the sparse points. We use a predictive cross-modal criterion, akin to `self-supervision,' measuring photometric consistency across time, forward-backward…