Object recognition using shape-from-shading

This paper investigates whether surface topography information extracted from intensity images using a recently reported shape-from-shading (SFS) algorithm can be used for the purposes of 3D object recognition. We consider how curvature and shape-index information delivered by this algorithm can be used to recognize objects based on their surface topography. We explore two contrasting object recognition strategies. The first of these is based on a low-level attribute summary and uses histograms of curvature and orientation measurements. The second approach is based on the structural arrangement of constant shape-index maximal patches and their associated region attributes. We show that region curvedness and a string ordering of the regions according to size provides recognition accuracy of about 96 percent. By polling various recognition schemes. including a graph matching method. we show that a recognition rate of 98-99 percent is achievable

Static/Dynamic Filtering for Mesh Geometry

The joint bilateral filter, which enables feature-preserving signal smoothing according to the structural information from a guidance, has been applied for various tasks in geometry processing. Existing methods either rely on a static guidance that may be inconsistent with the input and lead to unsatisfactory results, or a dynamic guidance that is automatically updated but sensitive to noises and outliers. Inspired by recent advances in image filtering, we propose a new geometry filtering technique called static/dynamic filter, which utilizes both static and dynamic guidances to achieve state-of-the-art results. The proposed filter is based on a nonlinear optimization that enforces smoothness of the signal while preserving variations that correspond to features of certain scales. We develop an efficient iterative solver for the problem, which unifies existing filters that are based on static or dynamic guidances. The filter can be applied to mesh face normals followed by vertex position update, to achieve scale-aware and feature-preserving filtering of mesh geometry. It also works well for other types of signals defined on mesh surfaces, such as texture colors. Extensive experimental results demonstrate the effectiveness of the proposed filter for various geometry processing applications such as mesh denoising, geometry feature enhancement, and texture color filtering

A View of Damped Trend as Incorporating a Tracking Signal into a State Space Model

Damped trend exponential smoothing has previously been established as an important forecasting method. Here, it is shown to have close links to simple exponential smoothing with a smoothed error tracking signal. A special case of damped trend exponential smoothing emerges from our analysis, one that is more parsimonious because it effectively relies on one less parameter. This special case is compared with its traditional counterpart in an application to the annual data from the M3 competition and is shown to be quite competitive.Exponential smoothing, monitoring forecasts, structural change, adjusting forecasts, state space models, damped trend

Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning

Many interesting problems in machine learning are being revisited with new deep learning tools. For graph-based semisupervised learning, a recent important development is graph convolutional networks (GCNs), which nicely integrate local vertex features and graph topology in the convolutional layers. Although the GCN model compares favorably with other state-of-the-art methods, its mechanisms are not clear and it still requires a considerable amount of labeled data for validation and model selection. In this paper, we develop deeper insights into the GCN model and address its fundamental limits. First, we show that the graph convolution of the GCN model is actually a special form of Laplacian smoothing, which is the key reason why GCNs work, but it also brings potential concerns of over-smoothing with many convolutional layers. Second, to overcome the limits of the GCN model with shallow architectures, we propose both co-training and self-training approaches to train GCNs. Our approaches significantly improve GCNs in learning with very few labels, and exempt them from requiring additional labels for validation. Extensive experiments on benchmarks have verified our theory and proposals.Comment: AAAI-2018 Oral Presentatio

Marginal integration for nonparametric causal inference

We consider the problem of inferring the total causal effect of a single variable intervention on a (response) variable of interest. We propose a certain marginal integration regression technique for a very general class of potentially nonlinear structural equation models (SEMs) with known structure, or at least known superset of adjustment variables: we call the procedure S-mint regression. We easily derive that it achieves the convergence rate as for nonparametric regression: for example, single variable intervention effects can be estimated with convergence rate $n^{-2/5}$ assuming smoothness with twice differentiable functions. Our result can also be seen as a major robustness property with respect to model misspecification which goes much beyond the notion of double robustness. Furthermore, when the structure of the SEM is not known, we can estimate (the equivalence class of) the directed acyclic graph corresponding to the SEM, and then proceed by using S-mint based on these estimates. We empirically compare the S-mint regression method with more classical approaches and argue that the former is indeed more robust, more reliable and substantially simpler.Comment: 40 pages, 14 figure

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Geometric Multi-Model Fitting with a Convex Relaxation Algorithm

We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by minimising the energy of the overall classification. Our approach is similar to state-of-the-art energy minimisation techniques which use a global energy. However, we deal with the scaling factor (as the number of models increases) of the original combinatorial problem by relaxing the solution. This relaxation brings two advantages: first, by operating in the continuous domain we can parallelize the calculations. Second, it allows for the use of different metrics which results in a more general formulation. We demonstrate the versatility of our technique on two different problems of estimating structure from images: plane extraction from RGB-D data and homography estimation from pairs of images. In both cases, we report accurate results on publicly available datasets, in most of the cases outperforming the state-of-the-art