Using Hierarchical EM to Extract Planes from 3D Range Scans

©2005 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Presented at the 2005 IEEE International Conference on Robotics and Automation (ICRA), 18-22 April 2005, Barcelona, Spain.DOI: 10.1109/ROBOT.2005.1570803Recently, the acquisition of three-dimensional maps has become more and more popular. This is motivated by the fact that robots act in the three-dimensional world and several tasks such as path planning or localizing objects can be carried out more reliable using three-dimensional representations. In this paper we consider the problem of extracting planes from three-dimensional range data. In contrast to previous approaches our algorithm uses a hierarchical variant of the popular Expectation Maximization (EM) algorithm [1] to simultaneously learn the main directions of the planar structures. These main directions are then used to correct the position and orientation of planes. In practical experiments carried out with real data and in simulations we demonstrate that our algorithm can accurately extract planes and their orientation from range data

Graph-based segmentation of range data with applications to 3D urban mapping

This paper presents an efficient graph-based algorithm for the segmentation of planar regions out of 3D range maps of urban areas. Segmentation of planar surfaces in urban scenarios is challenging because the data acquired is typically sparsely sampled, incomplete, and noisy. The algorithm is motivated by Felzenszwalb’s algorithm to 2D image segmentation [8], and is extended to deal with non-uniformly sampled 3D range data using an approximate nearest neighbor search. Interpoint distances are sorted in increasing order and this list of distances is traversed growing planar regions that satisfy both local and global variation of distance and curvature. The algorithm runs in O(n log n) and compares favorably with other region growing mechanisms based on Expectation Maximization. Experiments carried out with real data acquired in an outdoor urban environment demonstrate that our approach is well-suited to segment planar surfaces from noisy 3D range data. A pair of applications of the segmented results are shown, a) to derive traversability maps, and b) to calibrate a camera network.Peer ReviewedPostprint (published version

A Mixture of Manhattan Frames: Beyond the Manhattan World

Objects and structures within man-made environments typically exhibit a high degree of organization in the form of orthogonal and parallel planes. Traditional approaches to scene representation exploit this phenomenon via the somewhat restrictive assumption that every plane is perpendicular to one of the axes of a single coordinate system. Known as the Manhattan-World model, this assumption is widely used in computer vision and robotics. The complexity of many real-world scenes, however, necessitates a more flexible model. We propose a novel probabilistic model that describes the world as a mixture of Manhattan frames: each frame defines a different orthogonal coordinate system. This results in a more expressive model that still exploits the orthogonality constraints. We propose an adaptive Markov-Chain Monte-Carlo sampling algorithm with Metropolis-Hastings split/merge moves that utilizes the geometry of the unit sphere. We demonstrate the versatility of our Mixture-of-Manhattan-Frames model by describing complex scenes using depth images of indoor scenes as well as aerial-LiDAR measurements of an urban center. Additionally, we show that the model lends itself to focal-length calibration of depth cameras and to plane segmentation.United States. Office of Naval Research. Multidisciplinary University Research Initiative (Award N00014-11-1-0688)United States. Defense Advanced Research Projects Agency (Award FA8650-11-1-7154)Technion, Israel Institute of Technology (MIT Postdoctoral Fellowship Program

A Sparsity-Inducing Optimization-Based Algorithm for Planar Patches Extraction from Noisy Point-Cloud Data

Currently, much of the manual labor needed to generate as-built Building Information Models (BIMs) of existing facilities is spent converting raw Point Cloud Datasets (PCDs) to BIMs descriptions. Automating the PCD conversion process can drastically reduce the cost of generating as-built BIMs. Due to the widespread existence of planar structures in civil infrastructures, detecting and extracting planar patches from raw PCDs is a fundamental step in the conversion pipeline from PCDs to BIMs. However, existing methods cannot effectively address both automatically detecting and extracting planar patches from infrastructure PCDs. The existing methods cannot resolve the problem due to the large scale and model complexity of civil infrastructure, or due to the requirements of extra constraints or known information. To address the problem, this paper presents a novel framework for automatically detecting and extracting planar patches from large-scale and noisy raw PCDs. The proposed method automatically detects planar structures, estimates the parametric plane models, and determines the boundaries of the planar patches. The first step recovers existing linear dependence relationships amongst points in the PCD by solving a group-sparsity inducing optimization problem. Next, a spectral clustering procedure based on the recovered linear dependence relationships segments the PCD. Then, for each segmented group, model parameters of the extracted planes are estimated via Singular Value Decomposition (SVD) and Maximum Likelihood Estimation Sample Consensus (MLESAC). Finally, the α-shape algorithm detects the boundaries of planar structures based on a projection of the data to the planar model. The proposed approach is evaluated comprehensively by experiments on two types of PCDs from real-world infrastructures, one captured directly by laser scanners and the other reconstructed from video using structure-from-motion techniques. In order to evaluate the performance comprehensively, five evaluation metrics are proposed which measure different aspects of performance. Experimental results reveal that the proposed method outperforms the existing methods, in the sense that the method automatically and accurately extracts planar patches from large-scaled raw PCDs without any extra constraints nor user assistance.This is the accepted manuscript. The final version is available from Wiley at http://onlinelibrary.wiley.com/doi/10.1111/mice.12063/abstract

Using hierarchical EM to extract planes from 3d range scans

Abstract — Recently, the acquisition of three-dimensional maps has become more and more popular. This is motivated by the fact that robots act in the three-dimensional world and several tasks such as path planning or localizing objects can be carried out more reliable using three-dimensional representations. In this paper we consider the problem of extracting planes from three-dimensional range data. In contrast to previous approaches our algorithm uses a hierarchical variant of the popular Expectation Maximization (EM) algorithm [1] to simultaneously learn the main directions of the planar structures. These main directions are then used to correct the position and orientation of planes. In practical experiments carried out with real data and in simulations we demonstrate that our algorithm can accurately extract planes and their orientation from range data. I

Active shape models with focus on overlapping problems applied to plant detection and soil pore analysis

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The robot's vista space : a computational 3D scene analysis

Swadzba A. The robot's vista space : a computational 3D scene analysis. Bielefeld (Germany): Bielefeld University; 2011.The space that can be explored quickly from a fixed view point without locomotion is known as the vista space. In indoor environments single rooms and room parts follow this definition. The vista space plays an important role in situations with agent-agent interaction as it is the directly surrounding environment in which the interaction takes place. A collaborative interaction of the partners in and with the environment requires that both partners know where they are, what spatial structures they are talking about, and what scene elements they are going to manipulate. This thesis focuses on the analysis of a robot's vista space. Mechanisms for extracting relevant spatial information are developed which enable the robot to recognize in which place it is, to detect the scene elements the human partner is talking about, and to segment scene structures the human is changing. These abilities are addressed by the proposed holistic, aligned, and articulated modeling approach. For a smooth human-robot interaction, the computed models should be aligned to the partner's representations. Therefore, the design of the computational models is based on the combination of psychological results from studies on human scene perception with basic physical properties of the perceived scene and the perception itself. The holistic modeling realizes a categorization of room percepts based on the observed 3D spatial layout. Room layouts have room type specific features and fMRI studies have shown that some of the human brain areas being active in scene recognition are sensitive to the 3D geometry of a room. With the aligned modeling, the robot is able to extract the hierarchical scene representation underlying a scene description given by a human tutor. Furthermore, it is able to ground the inferred scene elements in its own visual perception of the scene. This modeling follows the assumption that cognition and language schematize the world in the same way. This is visible in the fact that a scene depiction mainly consists of relations between an object and its supporting structure or between objects located on the same supporting structure. Last, the articulated modeling equips the robot with a methodology for articulated scene part extraction and fast background learning under short and disturbed observation conditions typical for human-robot interaction scenarios. Articulated scene parts are detected model-less by observing scene changes caused by their manipulation. Change detection and background learning are closely coupled because change is defined phenomenologically as variation of structure. This means that change detection involves a comparison of currently visible structures with a representation in memory. In range sensing this comparison can be nicely implement as subtraction of these two representations. The three modeling approaches enable the robot to enrich its visual perceptions of the surrounding environment, the vista space, with semantic information about meaningful spatial structures useful for further interaction with the environment and the human partner

Exploiting biological pathways to infer temporal gene interaction models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 156-166).An important goal in genomic research is the reconstruction of the complete picture of temporal interactions among all genes, but this inference problem is not tractable because of the large number of genes, the small number of experimental observations for each gene, and the complexity of biological networks. We focus instead on the B cell receptor (BCR) signaling pathway, which narrows the inference problem and provides a clinical application, as B cell chronic lymphocytic leukemia (B-CLL) is believed to be related to BCR response. In this work, we infer population-dependent gene networks of temporal interaction within the BCR signaling pathway. We develop simple statistical models that capture the temporal behavior of differentially expressed genes and then estimate the parameters in an Expectation-Maximization framework, resulting in clusters with a biological interpretation for each subject population. Using the cluster labels to define a small number of modes of interaction and imposing sparsity constraints to effectively limit the number of genes influencing each target gene makes the ill-posed problem of network inference tractable.(cont.) For both the clustering and the inference of the predictive models, we have statistical results that show that we successfully capture the temporal structure of and the interactions between the genes relevant to the BCR. signaling pathway. We have confirmatory results from a biological standpoint, in which genes that we have identified as playing key roles in the networks have already been shown in previous work to be relevant to BCR. stimulation, but we also have results that guide future experiments in the study of other related genes, in order to further the long term goal of a full understanding of how and why B-CLL cells behave abnormally.by Corey Ann Kemper.Ph.D