AutoSweep: Recovering 3D Editable Objectsfrom a Single Photograph

This paper presents a fully automatic framework for extracting editable 3D objects directly from a single photograph. Unlike previous methods which recover either depth maps, point clouds, or mesh surfaces, we aim to recover 3D objects with semantic parts and can be directly edited. We base our work on the assumption that most human-made objects are constituted by parts and these parts can be well represented by generalized primitives. Our work makes an attempt towards recovering two types of primitive-shaped objects, namely, generalized cuboids and generalized cylinders. To this end, we build a novel instance-aware segmentation network for accurate part separation. Our GeoNet outputs a set of smooth part-level masks labeled as profiles and bodies. Then in a key stage, we simultaneously identify profile-body relations and recover 3D parts by sweeping the recognized profile along their body contour and jointly optimize the geometry to align with the recovered masks. Qualitative and quantitative experiments show that our algorithm can recover high quality 3D models and outperforms existing methods in both instance segmentation and 3D reconstruction. The dataset and code of AutoSweep are available at https://chenxin.tech/AutoSweep.html.

Towards 3D Human Shape Recovery Under Clothing

We present a learning-based scheme for robustly and accurately estimating clothing fitness as well as the human shape on clothed 3D human scans. Our approach maps the clothed human geometry to a geometry image that we call clothed-GI. To align clothed-GI under different clothing, we extend the parametric human model and employ skeleton detection and warping for reliable alignment. For each pixel on the clothed-GI, we extract a feature vector including color/texture, position, normal, etc. and train a modified conditional GAN network for per-pixel fitness prediction using a comprehensive 3D clothing. Our technique significantly improves the accuracy of human shape prediction, especially under loose and fitted clothing. We further demonstrate using our results for human/clothing segmentation and virtual clothes fitting at a high visual realism.

Model Assisted Variable Clustering: Minimax-optimal Recovery and Algorithms

Model-based clustering defines population level clusters relative to a model that embeds notions of similarity. Algorithms tailored to such models yield estimated clusters with a clear statistical interpretation. We take this view here and introduce the class of $G$-block covariance models as a background model for variable clustering. In such models, two variables in a cluster are deemed similar if they have similar associations will all other variables. This can arise, for instance, when groups of variables are noise corrupted versions of the same latent factor. We quantify the difficulty of clustering data generated from a $G$-block covariance model in terms of cluster proximity, measured with respect to two related, but different, cluster separation metrics. We derive minimax cluster separation thresholds, which are the metric values below which no algorithm can recover the model-defined clusters exactly, and show that they are different for the two metrics. We therefore develop two algorithms, COD and PECOK, tailored to G-block covariance models, and study their minimax-optimality with respect to each metric. Of independent interest is the fact that the analysis of the PECOK algorithm, which is based on a corrected convex relaxation of the popular $K$-means algorithm, provides the first statistical analysis of such algorithms for variable clustering. Additionally, we contrast our methods with another popular clustering method, spectral clustering, specialized to variable clustering, and show that ensuring exact cluster recovery via this method requires clusters to have a higher separation, relative to the minimax threshold. Extensive simulation studies, as well as our data analyses, confirm the applicability of our approach.

Granger Mediation Analysis of Multiple Time Series with an Application to fMRI

It becomes increasingly popular to perform mediation analysis for complex data from sophisticated experimental studies. In this paper, we present Granger Mediation Analysis (GMA), a new framework for causal mediation analysis of multiple time series. This framework is motivated by a functional magnetic resonance imaging (fMRI) experiment where we are interested in estimating the mediation effects between a randomized stimulus time series and brain activity time series from two brain regions. The stable unit treatment assumption for causal mediation analysis is thus unrealistic for this type of time series data. To address this challenge, our framework integrates two types of models: causal mediation analysis across the variables and vector autoregressive models across the temporal observations. We further extend this framework to handle multilevel data to address individual variability and correlated errors between the mediator and the outcome variables. These models not only provide valid causal mediation for time series data but also model the causal dynamics across time. We show that the modeling parameters in our models are identifiable, and we develop computationally efficient methods to maximize the likelihood-based optimization criteria. Simulation studies show that our method reduces the estimation bias and improve statistical power, compared to existing approaches. On a real fMRI data set, our approach not only infers the causal effects of brain pathways but accurately captures the feedback effect of the outcome region on the mediator region.

Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset.

Pathway Lasso: Estimate and Select Sparse Mediation Pathways with High Dimensional Mediators

In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as products of coefficients. However, it becomes unstable to fit such models with high dimensional mediators, especially for a general setting where all the mediators are causally dependent but the exact causal relationships between them are unknown. This paper proposes a sparse mediation model using a regularized SEM approach, where sparsity here means that a small number of mediators have nonzero mediation effects between a treatment and an outcome. To address the model selection challenge, we innovate by introducing a new penalty called Pathway Lasso. This penalty function is a convex relaxation of the non-convex product function, and it enables a computationally tractable optimization criterion to estimate and select many pathway effects simultaneously. We develop a fast ADMM-type algorithm to compute the model parameters, and we show that the iterative updates can be expressed in closed form. On both simulated data and a real fMRI dataset, the proposed approach yields higher pathway selection accuracy and lower estimation bias than other competing methods.

A Hierarchical Graphical Model for Big Inverse Covariance Estimation with an Application to fMRI

Brain networks has attracted the interests of many neuroscientists. From functional MRI (fMRI) data, statistical tools have been developed to recover brain networks. However, the dimensionality of whole-brain fMRI, usually in hundreds of thousands, challenges the applicability of these methods. We develop a hierarchical graphical model (HGM) to remediate this difficulty. This model introduces a hidden layer of networks based on sparse Gaussian graphical models, and the observed data are sampled from individual network nodes. In fMRI, the network layer models the underlying signals of different brain functional units, and how these units directly interact with each other. The introduction of this hierarchical structure not only provides a formal and interpretable approach, but also enables efficient computation for inferring big networks with hundreds of thousands of nodes. Based on the conditional convexity of our formulation, we develop an alternating update algorithm to compute the HGM model parameters simultaneously. The effectiveness of this approach is demonstrated on simulated data and a real dataset from a stop/go fMRI experiment.