Yu-Shen Liu

The IFC-based path planning for 3D indoor spaces

Path planning is a fundamental problem, especially for various AEC applications, such as architectural design, indoor and outdoor navigation, and emergency evacuation. However, the conventional approaches mainly operate path planning on 2D drawings or building layouts by simply considering geometric information, while losing abundant semantic information of building components. To address this issue, this paper introduces a new method to cope with path planning for 3D indoor space through an IFC (Industry Foundation Classes) file as input. As a major data exchange standard for Building Information Modeling (BIM), the IFC standard is capable of restoring both geometric information and rich semantic information of building components to support lifecycle data sharing. The method consists of three main steps: (1) extracting both geometric and semantic information of building components defined within the IFC file, (2) discretizing and mapping the extracted information into a planar grid, (3) and finally finding the shortest path based on the mapping for path planning using Fast Marching Method. The paper aims to process different kinds of building components and their corresponding properties to obtain rich semantic information that can enhance applications of path planning. In addition, the IFC-based distributed data sharing and management is implemented for path planning. The paper also presents some experiments to demonstrate the accuracy, efficiency and adaptability of the method. Video demonstration is available from http://cgcad.thss.tsinghua.edu.cn/liuyushen/ifcpath/.

Salient critical points for meshes

A novel method for extracting the salient critical points of meshes, possibly with noise, is presented by combining mesh saliency with Morse theory. In this paper, we use the idea of mesh saliency as a measure of regional importance for meshes. The proposed method defines the salient critical points in a scalar function space using a center-surround filter operator on Gaussian-weighted average of the scalar of vertices. Compared to using a purely geometric measure of shape, such as curvature, our method yields more satisfactory results with the lower number of critical points. We demonstrate the effectiveness of this approach by comparing our results with the results of the conventional approaches in a number of examples. Furthermore, this work has a variety of potential applications. We give a direct application to the hierarchical topological representation for meshes by combining the salient critical points with the Morse-Smale complex.

IDSS: deformation invariant signatures for molecular shape comparison

BackgroundMany molecules of interest are flexible and undergo significant shape deformation as part of their function, but most existing methods of molecular shape comparison (MSC) treat them as rigid bodies, which may lead to incorrect measure of the shape similarity of flexible molecules.ResultsTo address the issue we introduce a new shape descriptor, called Inner Distance Shape Signature (IDSS), for describing the 3D shapes of flexible molecules. The inner distance is defined as the length of the shortest path between landmark points within the molecular shape, and it reflects well the molecular structure and deformation without explicit decomposition. Our IDSS is stored as a histogram which is a probability distribution of inner distances between all sample point pairs on the molecular surface. We show that IDSS is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. Our approach reduces the 3D shape comparison problem of flexible molecules to the comparison of IDSS histograms.ConclusionThe proposed algorithm is robust and does not require any prior knowledge of the flexible regions. We demonstrate the effectiveness of IDSS within a molecular search engine application for a benchmark containing abundant conformational changes of molecules. Such comparisons in several thousands per second can be carried out. The presented IDSS method can be considered as an alternative and complementary tool for the existing methods for rigid MSC. The binary executable program for Windows platform and database are available from https://engineering.purdue.edu/PRECISE/IDSS.

Computing the Inner Distances of Volumetric Models for Articulated Shape Description with a Visibility Graph

A new visibility graph-based algorithm is presented for computing the inner distances of a 3D shape represented by a volumetric model. The inner distance is defined as the length of the shortest path between landmark points within the shape. The inner distance is robust to articulation and can reflect the deformation of a shape structure well without an explicit decomposition. Our method is based on the visibility graph approach. To check the visibility between pairwise points, we propose a novel, fast, and robust visibility checking algorithm based on a clustering technique which operates directly on the volumetric model without any surface reconstruction procedure, where an octree is used for accelerating the computation. The inner distance can be used as a replacement for other distance measures to build a more accurate description for complex shapes, especially for those with articulated parts. The binary executable program for the Windows platform is available from https://engineering.purdue.edu/PRECISE/VMID.

Robust principal axes determination for point-based shapes using least median of squares

A robust technique for determining the principal axes of a 3D shape represented by a point set, possibly with noise, is presented. We use techniques from robust statistics to guide the classical principal component analysis (PCA) computation. Our algorithm is based on a robust statistics method: least median of squares (LMS), for outlier detection. Using this method, an outlier-free major region of the shape is extracted, which ignores the effect on other minor regions regarded as the outliers of the shape.In order to effectively approximate the LMS optimization, the forward search technique is utilized. We start from a small outlier-free subset robustly chosen as the major region, where an octree is used for accelerating computation. Then the region is iteratively increased by adding samples at a time. Finally, by treating the points on minor regions as outliers, we are able to define the principal axes of the shape as one of the major region. One of the advantages of our algorithm is that it automatically disregards outliers and distinguishes the shape as the major and minor regions during the principal axes determination without any extra segmentation procedure. The presented algorithm is simple and effective and gives good results for point-based shapes. The application on shape alignment is considered for demonstration purpose.

Three dimensional shape comparison of flexible proteins using the local-diameter descriptor.

BackgroundTechniques for inferring the functions of the protein by comparing their shape similarity have been receiving a lot of attention. Proteins are functional units and their shape flexibility occupies an essential role in various biological processes. Several shape descriptors have demonstrated the capability of protein shape comparison by treating them as rigid bodies. But this may give rise to an incorrect comparison of flexible protein shapes.ResultsWe introduce an efficient approach for comparing flexible protein shapes by adapting a local diameter (LD) descriptor. The LD descriptor, developed recently to handle skeleton based shape deformations [1], is adapted in this work to capture the invariant properties of shape deformations caused by the motion of the protein backbone. Every sampled point on the protein surface is assigned a value measuring the diameter of the 3D shape in the neighborhood of that point. The LD descriptor is built in the form of a one dimensional histogram from the distribution of the diameter values. The histogram based shape representation reduces the shape comparison problem of the flexible protein to a simple distance calculation between 1D feature vectors. Experimental results indicate how the LD descriptor accurately treats the protein shape deformation. In addition, we use the LD descriptor for protein shape retrieval and compare it to the effectiveness of conventional shape descriptors. A sensitivity-specificity plot shows that the LD descriptor performs much better than the conventional shape descriptors in terms of consistency over a family of proteins and discernibility across families of different proteins.ConclusionOur study provides an effective technique for comparing the shape of flexible proteins. The experimental results demonstrate the insensitivity of the LD descriptor to protein shape deformation. The proposed method will be potentially useful for molecule retrieval with similar shapes and rapid structure retrieval for proteins. The demos and supplemental materials are available on https://engineering.purdue.edu/PRECISE/LDD.

Automatic least-squares projection of points onto point clouds with applications in reverse engineering

A novel method for projecting points onto a point cloud, possibly with noise, is presented based on the point directed projection (DP) algorithm proposed by Azariadis P., Sapidis N. [Drawing curves onto a cloud of points for point-based modelling. Computer-Aided Design 2005; 37(1): 109-22]. The new method operates directly on the point cloud without any explicit or implicit surface reconstruction procedure. The presented method uses a simple, robust, and efficient algorithm: least-squares projection (LSP), which projects points onto the point cloud in a least-squares sense without any specification of the projection vector. The main contribution of this novel method is the automatic computation of the projection vector. Furthermore, we demonstrate the effectiveness of this approach through a number of application examples including thinning a point cloud, point normal estimation, projecting curves onto a point cloud and others.

A quasi-Monte Carlo method for computing areas of point-sampled surfaces

A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy-Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction.

Using diffusion distances for flexible molecular shape comparison.

BackgroundMany molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition.ResultsIn this paper, we present a new shape descriptor, named Diffusion Distance Shape Descriptor (DDSD), for comparing 3D shapes of flexible molecules. The diffusion distance in our work is considered as an average length of paths connecting two landmark points on the molecular shape in a sense of inner distances. The diffusion distance is robust to flexible shape deformation, in particular to topological changes, and it reflects well the molecular structure and deformation without explicit decomposition. Our DDSD is stored as a histogram which is a probability distribution of diffusion distances between all sample point pairs on the molecular surface. Finally, the problem of flexible MSC is reduced to comparison of DDSD histograms.ConclusionsWe illustrate that DDSD is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. The presented algorithm is robust and does not require any prior knowledge of the flexible regions.

Using least median of squares for structural superposition of flexible proteins

BackgroundThe conventional superposition methods use an ordinary least squares (LS) fit for structural comparison of two different conformations of the same protein. The main problem of the LS fit that it is sensitive to outliers, i.e. large displacements of the original structures superimposed.ResultsTo overcome this problem, we present a new algorithm to overlap two protein conformations by their atomic coordinates using a robust statistics technique: least median of squares (LMS). In order to effectively approximate the LMS optimization, the forward search technique is utilized. Our algorithm can automatically detect and superimpose the rigid core regions of two conformations with small or large displacements. In contrast, most existing superposition techniques strongly depend on the initial LS estimating for the entire atom sets of proteins. They may fail on structural superposition of two conformations with large displacements. The presented LMS fit can be considered as an alternative and complementary tool for structural superposition.ConclusionThe proposed algorithm is robust and does not require any prior knowledge of the flexible regions. Furthermore, we show that the LMS fit can be extended to multiple level superposition between two conformations with several rigid domains. Our fit tool has produced successful superpositions when applied to proteins for which two conformations are known. The binary executable program for Windows platform, tested examples, and database are available from https://engineering.purdue.edu/PRECISE/LMSfit.