Enclosing trees

A method is described for representing voxel-based objects by means of enclosing trees. An enclosing tree is a tree which totally covers a voxel-based object, the vertices of the enclosing tree correspond to the vertices of the enclosing surface of the analyzed voxel-based object. An enclosing tree is represented by a chain of base-five digit strings suitably combined by means of parentheses. The enclosing-tree notation is invariant under rotation and translation. Furthermore, using this notation it is possible to obtain the mirror image of any voxel-based object with ease. The enclosing-tree notation preserves the shape of voxel-based objects, allowing us to know some of their topological and geometrical properties. Also, the proposed enclosing-tree notation is a good tool for storing of voxel-based objects.     

树木结构层次细化的立体树木图像构建

目的 2维转3维技术可以将现有的丰富2维图像资源快速有效地转为立体图像,但是现有方法只能对树木的整体进行深度估计,所生成的图像无法表现出树木的立体结构。为此,提出一种树木结构层次细化的立体树木图像构建方法。方法 首先利用Lab颜色模型下的像素色差区别将2维树木图像的树干区域和树冠区域分割开来,并对树冠区域进行再分割;然后,在深度梯度假设思想基础上建立多种类型的深度模板,结合深度模板和树冠的区域信息为典型树木对象构建初始深度图,并通过基础深度梯度图组合的方式为非典型树木进行个性化深度构建;最后,根据应用场景对树木深度信息进行自适应调整与优化,将树木图像合成到背景图像中,并构建立体图像。结果 对5组不同的树木图像及背景图像进行了立体树木图像的构建与合成。结果表明,不同形态的树木图像都能生成具有层次感的深度图并自适应地合成到立体背景图像中,构建树木图像深度图的时间与原始树木图像的尺寸成正比,而构建立体树木图像并合成到背景中所需时间在24 s之间。对立体图像质量的主观评价测试中,这些图像的评分均达到良好级别以上,部分立体图像达到了优秀级别。结论 该方法充分利用了树木的形态结构特征,能同时适用于典型和非典型树木,所构建的立体树木图像质量较高,具有丰富的层次感,并具有舒适的立体观看效果。     

树的RVA存储结构

本文提出了一种四元树的存储模式——RVA 存储结构。它能使我们用较少的空间存储四元树且保持子树的随机访问功能。我们对 RVA 结构上的图象处理运算的讨论证实了这是一种高效率的四元树存储结构。我们的方法和技术可以方便地推广到三维图象的八元树结构、K 维图象的 K-树结构上去。最后,我们在一般树上拓广了我们的思想,提出了一般树的 RVA 存储结构。     

Graph embedding using tree edit-union

In this paper we address the problem of how to learn a structural prototype that can be used to represent the variations present in a set of trees. The prototype serves as a pattern space representation for the set of trees. To do this we construct a super-tree to span the union of the set of trees. This is a chicken and egg problem, since before the structure can be estimated correspondences between the nodes of the super-tree and the nodes of the sample tree must be to hand. We demonstrate how to simultaneously estimate the structure of the super-tree and recover the required correspondences by minimizing the sum of the tree edit-distances over pairs of trees, subject to edge consistency constraints. Each node of the super-tree corresponds to a dimension of the pattern space, and for each tree we construct a pattern vector in which the elements of the weights corresponding to each of the dimensions of the super-tree. We perform pattern analysis on the set of trees by performing principal components analysis on the vectors. The method is illustrated on a shape analysis problem involving shock-trees extracted from the skeletons of 2D objects.     

基于L-系统的三维分形植物的算法及实现

分形理论适于解决不规则形态物体的建模仿真问题.分形理论和虚拟现实技术结合起来可以生成逼真、复杂的自然景物.该文将分形理论用于VRML 环境中研究植物的计算机模拟算法.首先介绍了常见的2维和3维分形植物生成算法,总结了它们的利弊.然后提出一种在VRML环境下改进的分形植物生成算法.通过描述树的属性（如树的种类、树的繁茂程度、树叶的形状等）,从而自动生成符合用户要求的三维树.最后给出了产生的3维分形树,并给出了一个应用实例.     

3D树木建模技术研究进展

3D树木建模一直都是计算机图形学、计算机视觉、虚拟现实等领域最具有挑战性的研究方向之一,国外学者在该领域做了大量研究工作,但3D树木建模综述性文章的缺乏成为其发展的制约因素。侧重从计算机视觉的角度,将当前国内外经典的3D树木建模方法分为基于图像,基于规则和基于草图等三类,并跟踪了最新的3D树木建模技术进展,对他们的成果进行了深入剖析,重点阐述3D树木建模关键技术。最后,分析和比较了几种主要的3D树木建模技术,提出轻量化3D树木建模技术是今后虚拟场景中的交互应用的发展趋势。此外,根据当前研究的难点提出了基于单张图像的轻量化混合建模的研究思路。     

Approximation algorithms for tree alignment with a given phylogeny

We study the following fundamental problem in computational molecular biology: Given a set of DNA sequences representing some species and a phylogenetic tree depicting the ancestral relationship among these species, compute an optimal alignment of the sequences by the means of constructing a minimum-cost evolutionary tree. The problem is an important variant of multiple sequence alignment, and is widely known astree alignment. We design an efficient approximation algorithm with performance ratio 2 for tree alignment. The algorithm is then extended to a polynomial-time approximation scheme. The construction actually works for Steiner trees in any metric space, and thus implies a polynomial-time approximation scheme for planar Steiner trees under a given topology (with any constant degree). To our knowledge, this is the first polynomial-time approximation scheme in the fields of computational biology and Steiner trees. The approximation algorithms may be useful in evolutionary genetics practice as they can provide a good initial alignment for the iterative method in [23].Supported in part by NSERC Operating Grant OGP0046613.Supported in part by NSERC Operating Grant OGP0046613 and a Canadian Genome Analysis and Technology Research Grant.Supported in part by US Department of Energy Grant DE-FG03-90ER6099.     

基于物元理论的任意功能树相似扩展方法

功能模型是概念设计的核心处理对象,功能树是一种典型的、应用广泛的 功能模型。使用现有相似度计算方法计算任意功能树的相似度存在困难。因此,基于布尔代 数提出了析取范式树的概念,以及两种求解析取范式树的方法,并描述了任意功能树的物元 相似度计算方法。拓展了功能树相似扩展方法的应用范围,扩大了设计解空间,增加了获得 创新解的可能性,最后给出实例验证了方法的有效性。     

Pairwise Matching of 3D Fragments Using Cluster Trees

We propose a novel and efficient surface matching approach for reassembling broken solids as well as for matching assembly components using cluster trees of oriented points. The method rapidly scans through the space of all possible contact poses of the fragments to be (re)assembled using a tree search strategy, which neither relies on any surface features nor requires an initial solution. The new method first decomposes each point set into a binary tree structure using a hierarchical clustering algorithm. Subsequently the fragments are matched pairwise by descending the cluster trees simultaneously in a depth-first fashion. In contrast to the reassemblage of pottery and thin walled artifacts, this paper addresses the problem of matching broken 3D solids on the basis of their 2.5D fracture surfaces, which are assumed to be reasonable large. Our proposed contact area maximization is a powerful common basis for most surface matching tasks, which can be adapted to numerous special applications. The suggested approach is very robust and offers an outstanding efficiency.     

基于自适应布告板的三维树木表达方法

植被、地形以及人工建构筑物是三维虚拟地理场景可视化表达的基本内容,树木是植被的主要组成部分.由于树木自然形态的复杂性,其真实感表达非常困难.基于几何模型的树木表达可以产生逼真的细节,但场景实时渲染具有巨大的计算负担,而基于纹理的简化模型在真实感表达上有所欠缺,但具有更好的渲染性能.如何兼顾场景渲染效率与视觉真实感受一直是树木三维可视化表达的研究热点.本文提出一种基于自适应布告板的三维树木表达方法,该方法在通常的平面布告板方法基础上,根据视点与布告板的相对位置关系,从预先获得的多张树木影像中选取最符合视点与树木相对位置关系的影像作为树木纹理渲染于该布告板上,实现了布告板纹理的动态调整,使得不同视点下的树木渲染效果尽量接近真实,同时也具有布告板的渲染性能优势.本文基于WebGL在浏览器中构建了一个三维场景,其中包含若干树木模型.实验结果表明本方法在表达树林时,在浏览器这样的低渲染计算能力环境下也能取得可接受的渲染性能与表达效果.     

3D Z-string: A new knowledge structure to represent spatio-temporal relations between objects in a video

In this paper, we propose a new knowledge structure called 3D Z-string, extended from the 2D Z-string, to represent the spatial and temporal relations between objects in a video and to keep track of the motions and size changes of the objects. Since there are no cuttings between objects in the 3D Z-string, the integrity of objects is preserved. The string generation and video reconstruction algorithms for the 3D Z-string representation of video objects are also developed. The string generated by the string generation algorithm is unique for a given video and the video reconstructed from a given 3D Z-string is unique too. The experimental results show that the 3D Z-string is more compact and efficient than the 3D C-string in terms of storage space and execution time.     

自动驾驶汽车虚拟测试中的树木点云生成方法

自动驾驶汽车虚拟测试已成为自动驾驶或车路协同测试评价的一个重要手段,三维激光雷达数据模拟生成是自动驾驶汽车虚拟测试中的重要任务之一,目前多采用基于飞行时间原理的几何模型方法生成激光雷达三维点云数据,该方法生成点云实时性较差。布告牌是虚拟场景中常采用的树木建模方法,由于布告牌仅由两个矩形面片即八个三角形面片组成,直接采用布告牌方法生成的三维点云数据难以反映树木的真实空间信息。针对上述问题,提出了一种基于布告牌空间变换的快速树木三维点云生成方法。以布告牌的纹理图像为依据,根据纹理透明度获取树木二维平面点云分布,经二维树木点云的轮廓提取,结合树木结构的先验知识进行旋转、随机偏移和尺度变换,以更少的三角形面片数和更小的计算代价获得树木的三维点云数据。提出了一种空间直方图三维点云相似度评价方法,将三维点云空间量化为若干个子空间,获得三维点云的投影空间直方图,采用巴氏系数计算投影空间直方图相似度,以投影空间直方图加权相似度作为点云相似度评价值。实验结果表明,基于布告牌空间变换方法和几何模型方法生成的云杉等三种树木的三维点云数据的平均相似度在90%以上,且该方法生成树木点云的时间仅是几何模型法的1%,因此布告牌空间变换树木三维点云生成方法快速且准确,可以满足自动驾驶汽车虚拟测试的性能要求。     

Statistical Modeling of the 3D Geometry and Topology of Botanical Trees

We propose a framework for statistical modeling of the 3D geometry and topology of botanical trees. We treat botanical trees as points in a tree‐shape space equipped with a proper metric that captures the geometric and the topological differences between trees. Geodesics in the tree‐shape space correspond to the optimal sequence of deformations, i.e. bending, stretching, and topological changes, which align one tree onto another. In this way, the 3D tree modeling and synthesis problem becomes a problem of exploring the tree‐shape space either in a controlled fashion, using statistical regression, or randomly by sampling from probability distributions fitted to populations in the tree‐shape space. We show how to use this framework for (1) computing statistical summaries, e.g. the mean and modes of variations, of a population of botanical trees, (2) synthesizing random instances of botanical trees from probability distributions fitted to a population of botanical trees, and (3) modeling, interactively, 3D botanical trees using a simple sketching interface. The approach is fast and only requires as input 3D botanical tree models with a known upright orientation.     

Decision forest: Twenty years of research

A decision tree is a predictive model that recursively partitions the covariate’s space into subspaces such that each subspace constitutes a basis for a different prediction function. Decision trees can be used for various learning tasks including classification, regression and survival analysis. Due to their unique benefits, decision trees have become one of the most powerful and popular approaches in data science. Decision forest aims to improve the predictive performance of a single decision tree by training multiple trees and combining their predictions. This paper provides an introduction to the subject by explaining how a decision forest can be created and when it is most valuable. In addition, we are reviewing some popular methods for generating the forest, fusion the individual trees’ outputs and thinning large decision forests.