Data-Driven, Soft Alignment of Functional Data Using Shapes and Landmarks

Alignment or registration of functions is a fundamental problem in statistical analysis of functions and shapes. While there are several approaches available, a more recent approach based on Fisher-Rao metric and square-root velocity functions (SRVFs) has been shown to have good performance. However, this SRVF method has two limitations: (1) it is susceptible to over alignment, i.e., alignment of noise as well as the signal, and (2) in case there is additional information in form of landmarks, the original formulation does not prescribe a way to incorporate that information. In this paper we propose an extension that allows for incorporation of landmark information to seek a compromise between matching curves and landmarks. This results in a soft landmark alignment that pushes landmarks closer, without requiring their exact overlays to finds a compromise between contributions from functions and landmarks. The proposed method is demonstrated to be superior in certain practical scenarios.

Implicit Data Augmentation Using Feature Interpolation for Diversified Low-Shot Image Generation

Training of generative models especially Generative Adversarial Networks can easily diverge in low-data setting. To mitigate this issue, we propose a novel implicit data augmentation approach which facilitates stable training and synthesize diverse samples. Specifically, we view the discriminator as a metric embedding of the real data manifold, which offers proper distances between real data points. We then utilize information in the feature space to develop a data-driven augmentation method. We further bring up a simple metric to evaluate the diversity of synthesized samples. Experiments on few-shot generation tasks show our method improves FID and diversity of results compared to current methods, and allows generating high-quality and diverse images with less than 100 training samples.

MixSiam: A Mixture-based Approach to Self-supervised Representation Learning

Recently contrastive learning has shown significant progress in learning visual representations from unlabeled data. The core idea is training the backbone to be invariant to different augmentations of an instance. While most methods only maximize the feature similarity between two augmented data, we further generate more challenging training samples and force the model to keep predicting discriminative representation on these hard samples. In this paper, we propose MixSiam, a mixture-based approach upon the traditional siamese network. On the one hand, we input two augmented images of an instance to the backbone and obtain the discriminative representation by performing an element-wise maximum of two features. On the other hand, we take the mixture of these augmented images as input, and expect the model prediction to be close to the discriminative representation. In this way, the model could access more variant data samples of an instance and keep predicting invariant discriminative representations for them. Thus the learned model is more robust compared to previous contrastive learning methods. Extensive experiments on large-scale datasets show that MixSiam steadily improves the baseline and achieves competitive results with state-of-the-art methods. Our code will be released soon.

LIGA-Stereo: Learning LiDAR Geometry Aware Representations for Stereo-based 3D Detector

Stereo-based 3D detection aims at detecting 3D object bounding boxes from stereo images using intermediate depth maps or implicit 3D geometry representations, which provides a low-cost solution for 3D perception. However, its performance is still inferior compared with LiDAR-based detection algorithms. To detect and localize accurate 3D bounding boxes, LiDAR-based models can encode accurate object boundaries and surface normal directions from LiDAR point clouds. However, the detection results of stereo-based detectors are easily affected by the erroneous depth features due to the limitation of stereo matching. To solve the problem, we propose LIGA-Stereo (LiDAR Geometry Aware Stereo Detector) to learn stereo-based 3D detectors under the guidance of high-level geometry-aware representations of LiDAR-based detection models. In addition, we found existing voxel-based stereo detectors failed to learn semantic features effectively from indirect 3D supervisions. We attach an auxiliary 2D detection head to provide direct 2D semantic supervisions. Experiment results show that the above two strategies improved the geometric and semantic representation capabilities. Compared with the state-of-the-art stereo detector, our method has improved the 3D detection performance of cars, pedestrians, cyclists by 10.44%, 5.69%, 5.97% mAP respectively on the official KITTI benchmark. The gap between stereo-based and LiDAR-based 3D detectors is further narrowed.

Statistical shape analysis of brain arterial networks (BAN)

Structures of brain arterial networks (BANs) - that are complex arrangements of individual arteries, their branching patterns, and inter-connectivities - play an important role in characterizing and understanding brain physiology. One would like tools for statistically analyzing the shapes of BANs, i.e. quantify shape differences, compare population of subjects, and study the effects of covariates on these shapes. This paper mathematically represents and statistically analyzes BAN shapes as elastic shape graphs. Each elastic shape graph is made up of nodes that are connected by a number of 3D curves, and edges, with arbitrary shapes. We develop a mathematical representation, a Riemannian metric and other geometrical tools, such as computations of geodesics, means and covariances, and PCA for analyzing elastic graphs and BANs. This analysis is applied to BANs after separating them into four components -- top, bottom, left, and right. This framework is then used to generate shape summaries of BANs from 92 subjects, and to study the effects of age and gender on shapes of BAN components. We conclude that while gender effects require further investigation, the age has a clear, quantifiable effect on BAN shapes. Specifically, we find an increased variance in BAN shapes as age increases.

Representations, Metrics and Statistics For Shape Analysis of Elastic Graphs

Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the current literature offers only topological methods. This paper introduces a far-reaching geometric approach for analyzing shapes of graphical objects, such as road networks, blood vessels, brain fiber tracts, etc. It represents such objects, exhibiting differences in both geometries and topologies, as graphs made of curves with arbitrary shapes (edges) and connected at arbitrary junctions (nodes). To perform statistical analyses, one needs mathematical representations, metrics and other geometrical tools, such as geodesics, means, and covariances. This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis and analytical statistical testing and modeling of graphical shapes. The efficacy of this framework is demonstrated using various simulated as well as the real data from neurons and brain arterial networks.

A Quotient Space Formulation for Statistical Analysis of Graphical Data

Complex analyses involving multiple, dependent random quantities often lead to graphical models: a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical analyses for graphical data, one needs mathematical representations and metrics for matching and comparing graphs, and other geometrical tools, such as geodesics, means, and covariances, on representation spaces of graphs. This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis, linear dimension reduction, and analytical statistical modeling. The efficacy of this framework is demonstrated using datasets taken from several problem areas, including alphabets, video summaries, social networks, and biochemical structures.

Group-wise Correlation Stereo Network

Stereo matching estimates the disparity between a rectified image pair, which is of great importance to depth sensing, autonomous driving, and other related tasks. Previous works built cost volumes with cross-correlation or concatenation of left and right features across all disparity levels, and then a 2D or 3D convolutional neural network is utilized to regress the disparity maps. In this paper, we propose to construct the cost volume by group-wise correlation. The left features and the right features are divided into groups along the channel dimension, and correlation maps are computed among each group to obtain multiple matching cost proposals, which are then packed into a cost volume. Group-wise correlation provides efficient representations for measuring feature similarities and will not lose too much information like full correlation. It also preserves better performance when reducing parameters compared with previous methods. The 3D stacked hourglass network proposed in previous works is improved to boost the performance and decrease the inference computational cost. Experiment results show that our method outperforms previous methods on Scene Flow, KITTI 2012, and KITTI 2015 datasets. The code is available at https://github.com/xy-guo/GwcNet

Unsupervised Cross-spectral Stereo Matching by Learning to Synthesize

Unsupervised cross-spectral stereo matching aims at recovering disparity given cross-spectral image pairs without any supervision in the form of ground truth disparity or depth. The estimated depth provides additional information complementary to individual semantic features, which can be helpful for other vision tasks such as tracking, recognition and detection. However, there are large appearance variations between images from different spectral bands, which is a challenge for cross-spectral stereo matching. Existing deep unsupervised stereo matching methods are sensitive to the appearance variations and do not perform well on cross-spectral data. We propose a novel unsupervised cross-spectral stereo matching framework based on image-to-image translation. First, a style adaptation network transforms images across different spectral bands by cycle consistency and adversarial learning, during which appearance variations are minimized. Then, a stereo matching network is trained with image pairs from the same spectra using view reconstruction loss. At last, the estimated disparity is utilized to supervise the spectral-translation network in an end-to-end way. Moreover, a novel style adaptation network F-cycleGAN is proposed to improve the robustness of spectral translation. Our method can tackle appearance variations and enhance the robustness of unsupervised cross-spectral stereo matching. Experimental results show that our method achieves good performance without using depth supervision or explicit semantic information.

Learning Monocular Depth by Distilling Cross-domain Stereo Networks

Monocular depth estimation aims at estimating a pixelwise depth map for a single image, which has wide applications in scene understanding and autonomous driving. Existing supervised and unsupervised methods face great challenges. Supervised methods require large amounts of depth measurement data, which are generally difficult to obtain, while unsupervised methods are usually limited in estimation accuracy. Synthetic data generated by graphics engines provide a possible solution for collecting large amounts of depth data. However, the large domain gaps between synthetic and realistic data make directly training with them challenging. In this paper, we propose to use the stereo matching network as a proxy to learn depth from synthetic data and use predicted stereo disparity maps for supervising the monocular depth estimation network. Cross-domain synthetic data could be fully utilized in this novel framework. Different strategies are proposed to ensure learned depth perception capability well transferred across different domains. Our extensive experiments show state-of-the-art results of monocular depth estimation on KITTI dataset.