Matthew Berger

State of the Art in Surface Reconstruction from Point Clouds

The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contains a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece-wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations -- not necessarily the explicit geometry. This state-of-the-art report surveys the field of surface reconstruction, providing a categorization with respect to priors, data imperfections, and reconstruction output. By considering a holistic view of surface reconstruction, this report provides a detailed characterization of the field, highlights similarities between diverse reconstruction techniques, and provides directions for future work in surface reconstruction.

A benchmark for surface reconstruction

We present a benchmark for the evaluation and comparison of algorithms which reconstruct a surface from point cloud data. Although a substantial amount of effort has been dedicated to the problem of surface reconstruction, a comprehensive means of evaluating this class of algorithms is noticeably absent. We propose a simple pipeline for measuring surface reconstruction algorithms, consisting of three main phases: surface modeling, sampling, and evaluation. We use implicit surfaces for modeling shapes which are capable of representing details of varying size and sharp features. From these implicit surfaces, we produce point clouds by synthetically generating range scans which resemble realistic scan data produced by an optical triangulation scanner. We validate our synthetic sampling scheme by comparing against scan data produced by a commercial optical laser scanner, where we scan a 3D-printed version of the original surface. Last, we perform evaluation by comparing the output reconstructed surface to a dense uniformly distributed sampling of the implicit surface. We decompose our benchmark into two distinct sets of experiments. The first set of experiments measures reconstruction against point clouds of complex shapes sampled under a wide variety of conditions. Although these experiments are quite useful for comparison, they lack a fine-grain analysis. To complement this, the second set of experiments measures specific properties of surface reconstruction, in terms of sampling characteristics and surface features. Together, these experiments depict a detailed examination of the state of surface reconstruction algorithms.

A Survey of Surface Reconstruction from Point Clouds

The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contain a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece‐wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations—not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques and provide directions for future work in surface reconstruction.

Medial Kernels

We introduce the medial kernel, an association measure which provides for a robust construction of volume‐aware distances defined directly on point clouds. The medial kernel is a similarity measure defined as the likelihood of two points belonging to a common interior medial ball. We use the medial kernel to construct a random walk on the point cloud, where movement in the walk is restricted to regions containing similar medial balls. Our distances are defined as the diffusion distances of this random walk, assigning low distance to points belonging to similar medial regions. These distances allow for a robust means of processing incomplete point clouds, capable of distinguishing nearby yet separate undersampled components, while also associating points which are far in Euclidean distance yet mutually share an interior volume. We leverage these distances for several applications: volumetric part segmentation, the construction of function bases, and reconstruction‐by‐parts – a surface reconstruction method which adheres to the medial kernel.

cite2vec: Citation-Driven Document Exploration via Word Embeddings

Effectively exploring and browsing document collections is a fundamental problem in visualization. Traditionally, document visualization is based on a data model that represents each document as the set of its comprised words, effectively characterizing what the document is. In this paper we take an alternative perspective: motivated by the manner in which users search documents in the research process, we aim to visualize documents via their usage, or how documents tend to be used. We present a new visualization scheme - cite2vec - that allows the user to dynamically explore and browse documents via how other documents use them, information that we capture through citation contexts in a document collection. Starting from a usage-oriented word-document 2D projection, the user can dynamically steer document projections by prescribing semantic concepts, both in the form of phrase/document compositions and document:phrase analogies, enabling the exploration and comparison of documents by their use. The user interactions are enabled by a joint representation of words and documents in a common high-dimensional embedding space where user-specified concepts correspond to linear operations of word and document vectors. Our case studies, centered around a large document corpus of computer vision research papers, highlight the potential for usage-based document visualization.

Subspace Tracking under Dynamic Dimensionality for Online Background Subtraction

Long-term modeling of background motion in videos is an important and challenging problem used in numerous applications such as segmentation and event recognition. A major challenge in modeling the background from point trajectories lies in dealing with the variable length duration of trajectories, which can be due to such factors as trajectories entering and leaving the frame or occlusion from different depth layers. This work proposes an online method for background modeling of dynamic point trajectories via tracking of a linear subspace describing the background motion. To cope with variability in trajectory durations, we cast subspace tracking as an instance of subspace estimation under missing data, using a least-absolute deviations formulation to robustly estimate the background in the presence of arbitrary foreground motion. Relative to previous works, our approach is very fast and scales to arbitrarily long videos as our method processes new frames sequentially as they arrive.

Classifying swarm behavior via compressive subspace learning

Bio-inspired robot swarms encompass a rich space of dynamics and collective behaviors. Given some agent measurements of a swarm at a particular time instance, an important problem is the classification of the swarm behavior. This is challenging in practical scenarios where information from only a small number of agents may be available, resulting in limited agent samples for classification. Another challenge is recognizing emerging behavior: the prediction of swarm behavior prior to convergence of the attracting state. In this paper we address these challenges by modeling a swarms collective motion as a low-dimensional linear subspace. We illustrate that for both synthetic and real data, these behaviors manifest as low-dimensional subspaces, and that these subspaces are highly discriminative. We also show that these subspaces generalize well to predicting emerging behavior, highlighting that there exists low-dimensional structure in transient agent behavior. In order to learn distinct behavior subspaces, we extend previous work on subspace estimation and identification from missing data to that of compressive measurements, where compressive measurements arise due to agent positions scattered throughout the domain. We demonstrate improvement in performance over prior works with respect to limited agent samples over a wide range of agent models and scenarios.

Multi-agent Planning in Sokoban

The issue of multi-agent planning in highly dynamic environments is a major impediment to conventional planning solutions. Plan repair and replanning solutions alike have difficulty adapting to frequently changing environment states. To adequately handle such situations, this paper instead focuses on preserving individual agent plans through multi-agent coordination techniques. We describe a reactive agent system architecture in which the main focus of an agent is to be able to achieve its subgoals without interfering with any other agent. The system is a 3-level architecture, where each level is guided by the following fundamental principles, respectively: whenis it valid to generate a plan for a subgoal, whois most appropriate for completing the subgoal, and howshould the plan be carried out.

On Time-Series Topological Data Analysis: New Data and Opportunities

This work introduces a new dataset and framework for the exploration of topological data analysis (TDA) techniques applied to time-series data. We examine the end-toend TDA processing pipeline for persistent homology applied to time-delay embeddings of time series – embeddings that capture the underlying system dynamics from which time series data is acquired. In particular, we consider stability with respect to time series length, the approximation accuracy of sparse filtration methods, and the discriminating ability of persistence diagrams as a feature for learning. We explore these properties across a wide range of time-series datasets spanning multiple domains for single source multi-segment signals as well as multi-source single segment signals. Our analysis and dataset captures the entire TDA processing pipeline and includes time-delay embeddings, persistence diagrams, topological distance measures, as well as kernels for similarity learning and classification tasks for a broad set of time-series data sources. We outline the TDA framework and rationale behind the dataset and provide insights into the role of TDA for time-series analysis as well as opportunities for new work.

Nonrigid Matching of Undersampled Shapes via Medial Diffusion

We introduce medial diffusion for the matching of undersampled shapes undergoing a nonrigid deformation. We construct a diffusion process with respect to the medial axis of a shape, and use the quantity of heat diffusion as a measure which is both tolerant of missing data and approximately invariant to nonrigid deformations. A notable aspect of our approach is that we do not define the diffusion on the shapes medial axis, or similar medial representation. Instead, we construct the diffusion process directly on the shape. This permits the diffusion process to better capture surface features, such as varying spherical and cylindrical parts, as well as combine with other surface‐based diffusion processes. We show how to use medial diffusion to detect intrinsic symmetries, and for computing correspondences between pairs of shapes, wherein shapes contain substantial missing data.