Images géométriques de genre arbitraire dans le domaine sphérique

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

基于几何的网格模型编辑处理的研究

在计算机动画、 计算机辅助设计、 计算机视觉等领域，几何模型通常用三角网格来表示。 为了能够快速真实地 绘制几何体，规则且细节丰富的几何模型有利于使用GPU进行加速。本文基于网格模型，在模型的重采样、变体，以及图像变形方面进行了针对性的研究。 论文的贡献主要体现在以下几个方面: 第一， 将现有的差分坐标的概念扩展到图像上，首次提出差分几何图像的概念， 将几何模型的差分坐标信息封装在与几何图像(geometry images或GIM)类似的结构中。由于差分坐标反映了几何模型的局部特性，于是差分几何图像也就将局部信息封装到了图像中。 第二，我们展示了使用差分几何图像作为限定条件来适应不同的应用。对于网格重建来说，传统使用GIM重建的方法需要记录采样顶点的法向信息以用于绘制模型， 因为使用对角线连接的固定连接方式导致了局部信息的丢失，使得采样后按顶点位置计算的真实法向和曲率与记录的法向信息不能精确一致。即使记录了法向信息，模型在一些广泛应用的软件如3D Exploration等里面仍然不能正确显示， 因为这些软件是按顶点的位置来自动计算法向而不是根据模型文件记录的法向对模型进行绘制的。使用我们的方法， 模型的局部形状可以正确地保持，从而模型可以正确地显示， 无需再记录法向信息。 对于变体来说，由于局部形状（包括法向和曲率）被正确地保持，并且使用我们的重建算法， 所有的模型有相同的拓扑结构，于是可以利用差分几何图像生成的模型得到正确的变体模型。另外，由于参数化方式的统一性，我们可以在GPU上动态绘制层次细节(Level Of Detail或LOD)几何模型。 第三， 改进了现有的使用形状空间进行变形的算法 。 在形状空间中，由三角形网格构成的模型可视为空间中的一个点，可以借助黎曼度量对形状空间进行操作， 从而实现对模型的变换。本文改进了已有的操纵形状空间的方法，根据输入模型顶点的位置变化判断是否需要利用黎曼度量计算插值位置，从而降低了形状空间的维数， 提高了运算速度。 实验结果显示，混合线性插值方式而生成的模型具有良好的效果。 第四， 对使用笼体进行图像变形的方法进行了对比分析， 并作了改进，在GPU上加速以达到快速实时变形。本文将现有的使用笼体进行变形的坐标诸如均值坐标、调和坐标、格林坐标等统一成类似的形式，对2D图像进行变形。笼体通过针对ROI(Region of Interest)区域进行交互式生成。我们设计了一种简单的方法保证图像在变形过程中整体上基本保持不变。与此同时，构建了使用GPU加速笼体坐标变形图像的框架。 结果显示，这种直观的交互方式和实时的绘制速度便于应用到2D图像的动画设计中，其动画通过设定笼体顶点的运动速度来实现。

M-deformations of A-simple germs from R(n) to R(n+1)

All A-simple corank-1 germs from R(n) to R(n+1), where n not equal 4, have an M-deformation, that is a deformation in which the maximal numbers of isolated stable singular points are simultaneously present in the image.

Wind-vector estimation for RADARSAT-1 SAR images: Validation of wind-direction estimates based upon geometry diversity

In this letter, a new wind-vector algorithm is presented that uses radar backscatter sigma(0) measurements at two adjacent subscenes of RADARSAT-1 synthetic aperture radar (SAR) images, with each subscene having slightly different geometry. Resultant wind vectors are validated using in situ buoy measurements and compared with wind vectors determined from a hybrid wind-retrieval model using wind directions determined by spectral analysis of wind-induced image streaks and observed by colocated QuikSCAT measurements. The hybrid wind-retrieval model consists of CMOD-IFR2 [applicable to C-band vertical-vertical (W) polarization] and a C-band copolarization ratio according to Kirchhoff scattering. The new algorithm displays improved skill in wind-vector estimation for RADARSAT-1 SAR data when compared to conventional wind-retrieval methodology. In addition, unlike conventional methods, the present method is applicable to RADARSAT-1 images both with and without visible streaks. However, this method requires ancillary data such as buoy measurements to resolve the ambiguity in retrieved wind direction.

Automatically Recovering Geometry and Texture from Large Sets of Calibrated Images

Three-dimensional models which contain both geometry and texture have numerous applications such as urban planning, physical simulation, and virtual environments. A major focus of computer vision (and recently graphics) research is the automatic recovery of three-dimensional models from two-dimensional images. After many years of research this goal is yet to be achieved. Most practical modeling systems require substantial human input and unlike automatic systems are not scalable. This thesis presents a novel method for automatically recovering dense surface patches using large sets (1000's) of calibrated images taken from arbitrary positions within the scene. Physical instruments, such as Global Positioning System (GPS), inertial sensors, and inclinometers, are used to estimate the position and orientation of each image. Essentially, the problem is to find corresponding points in each of the images. Once a correspondence has been established, calculating its three-dimensional position is simply a matter of geometry. Long baseline images improve the accuracy. Short baseline images and the large number of images greatly simplifies the correspondence problem. The initial stage of the algorithm is completely local and scales linearly with the number of images. Subsequent stages are global in nature, exploit geometric constraints, and scale quadratically with the complexity of the underlying scene. We describe techniques for: 1) detecting and localizing surface patches; 2) refining camera calibration estimates and rejecting false positive surfels; and 3) grouping surface patches into surfaces and growing the surface along a two-dimensional manifold. We also discuss a method for producing high quality, textured three-dimensional models from these surfaces. Some of the most important characteristics of this approach are that it: 1) uses and refines noisy calibration estimates; 2) compensates for large variations in illumination; 3) tolerates significant soft occlusion (e.g. tree branches); and 4) associates, at a fundamental level, an estimated normal (i.e. no frontal-planar assumption) and texture with each surface patch.

Sensitivity of proximal femoral stiffness and areal bone mineral density to changes in bone geometry and density

Areal bone mineral density (aBMD) is the most common surrogate measurement for assessing the bone strength of the proximal femur associated with osteoporosis. Additional factors, however, contribute to the overall strength of the proximal femur, primarily the anatomical geometry. Finite element analysis (FEA) is an effective and widely used computerbased simulation technique for modeling mechanical loading of various engineering structures, providing predictions of displacement and induced stress distribution due to the applied load. FEA is therefore inherently dependent upon both density and anatomical geometry. FEA may be performed on both three-dimensional and two-dimensional models of the proximal femur derived from radiographic images, from which the mechanical stiffness may be redicted. It is examined whether the outcome measures of two-dimensional FEA, two-dimensional, finite element analysis of X-ray images (FEXI), and three-dimensional FEA computed stiffness of the proximal femur were more sensitive than aBMD to changes in trabecular bone density and femur geometry. It is assumed that if an outcome measure follows known trends with changes in density and geometric parameters, then an increased sensitivity will be indicative of an improved prediction of bone strength. All three outcome measures increased non-linearly with trabecular bone density, increased linearly with cortical shell thickness and neck width, decreased linearly with neck length, and were relatively insensitive to neck-shaft angle. For femoral head radius, aBMD was relatively insensitive, with two-dimensional FEXI and threedimensional FEA demonstrating a non-linear increase and decrease in sensitivity, respectively. For neck anteversion, aBMD decreased non-linearly, whereas both two-dimensional FEXI and three dimensional FEA demonstrated a parabolic-type relationship, with maximum stiffness achieved at an angle of approximately 15o. Multi-parameter analysis showed that all three outcome measures demonstrated their highest sensitivity to a change in cortical thickness. When changes in all input parameters were considered simultaneously, three and twodimensional FEA had statistically equal sensitivities (0.41±0.20 and 0.42±0.16 respectively, p = ns) that were significantly higher than the sensitivity of aBMD (0.24±0.07; p = 0.014 and 0.002 for three-dimensional and two-dimensional FEA respectively). This simulation study suggests that since mechanical integrity and FEA are inherently dependent upon anatomical geometry, FEXI stiffness, being derived from conventional two-dimensional radiographic images, may provide an improvement in the prediction of bone strength of the proximal femur than currently provided by aBMD.

Geometry vs appearance for discriminating between posed and spontaneous emotions

Spontaneous facial expressions differ from posed ones in appearance, timing and accompanying head movements. Still images cannot provide timing or head movement information directly. However, indirectly the distances between key points on a face extracted from a still image using active shape models can capture some movement and pose changes. This information is superposed on information about non-rigid facial movement that is also part of the expression. Does geometric information improve the discrimination between spontaneous and posed facial expressions arising from discrete emotions? We investigate the performance of a machine vision system for discrimination between posed and spontaneous versions of six basic emotions that uses SIFT appearance based features and FAP geometric features. Experimental results on the NVIE database demonstrate that fusion of geometric information leads only to marginal improvement over appearance features. Using fusion features, surprise is the easiest emotion (83.4% accuracy) to be distinguished, while disgust is the most difficult (76.1%). Our results find different important facial regions between discriminating posed versus spontaneous version of one emotion and classifying the same emotion versus other emotions. The distribution of the selected SIFT features shows that mouth is more important for sadness, while nose is more important for surprise, however, both the nose and mouth are important for disgust, fear, and happiness. Eyebrows, eyes, nose and mouth are important for anger.

The unfinished landscape fractal geometry and the aesthetics of ecological design

During the late 20th century it was proposed that a design aesthetic reflecting current ecological concerns was required within the overall domain of the built environment and specifically within landscape design. To address this, some authors suggested various theoretical frameworks upon which such an aesthetic could be based. Within these frameworks there was an underlying theme that the patterns and processes of Nature may have the potential to form this aesthetic — an aesthetic based on fractal rather than Euclidean geometry. In order to understand how fractal geometry, described as the geometry of Nature, could become the referent for a design aesthetic, this research examines the mathematical concepts of fractal Geometry, and the underlying philosophical concepts behind the terms ‘Nature’ and ‘aesthetics’. The findings of this initial research meant that a new definition of Nature was required in order to overcome the barrier presented by the western philosophical Nature¯culture duality. This new definition of Nature is based on the type and use of energy. Similarly, it became clear that current usage of the term aesthetics has more in common with the term ‘style’ than with its correct philosophical meaning. The aesthetic philosophy of both art and the environment recognises different aesthetic criteria related to either the subject or the object, such as: aesthetic experience; aesthetic attitude; aesthetic value; aesthetic object; and aesthetic properties. Given these criteria, and the fact that the concept of aesthetics is still an active and ongoing philosophical discussion, this work focuses on the criteria of aesthetic properties and the aesthetic experience or response they engender. The examination of fractal geometry revealed that it is a geometry based on scale rather than on the location of a point within a three-dimensional space. This enables fractal geometry to describe the complex forms and patterns created through the processes of Wild Nature. Although fractal geometry has been used to analyse the patterns of built environments from a plan perspective, it became clear from the initial review of the literature that there was a total knowledge vacuum about the fractal properties of environments experienced every day by people as they move through them. To overcome this, 21 different landscapes that ranged from highly developed city centres to relatively untouched landscapes of Wild Nature have been analysed. Although this work shows that the fractal dimension can be used to differentiate between overall landscape forms, it also shows that by itself it cannot differentiate between all images analysed. To overcome this two further parameters based on the underlying structural geometry embedded within the landscape are discussed. These parameters are the Power Spectrum Median Amplitude and the Level of Isotropy within the Fourier Power Spectrum. Based on the detailed analysis of these parameters a greater understanding of the structural properties of landscapes has been gained. With this understanding, this research has moved the field of landscape design a step close to being able to articulate a new aesthetic for ecological design.

Object tracking via non-Euclidean geometry : a Grassmann approach

A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single image. In this paper, we first propose a tracking approach based on affine subspaces (constructed from several images) which are able to accommodate the abovementioned variations. We use affine subspaces not only to represent the object, but also the candidate areas that the object may occupy. We furthermore propose a novel approach to measure affine subspace-to-subspace distance via the use of non-Euclidean geometry of Grassmann manifolds. The tracking problem is then considered as an inference task in a Markov Chain Monte Carlo framework via particle filtering. Quantitative evaluation on challenging video sequences indicates that the proposed approach obtains considerably better performance than several recent state-of-the-art methods such as Tracking-Learning-Detection and MILtrack.

Towards robust automatic affective classification of images using facial expressions for practical applications

Affect is an important feature of multimedia content and conveys valuable information for multimedia indexing and retrieval. Most existing studies for affective content analysis are limited to low-level features or mid-level representations, and are generally criticized for their incapacity to address the gap between low-level features and high-level human affective perception. The facial expressions of subjects in images carry important semantic information that can substantially influence human affective perception, but have been seldom investigated for affective classification of facial images towards practical applications. This paper presents an automatic image emotion detector (IED) for affective classification of practical (or non-laboratory) data using facial expressions, where a lot of “real-world” challenges are present, including pose, illumination, and size variations etc. The proposed method is novel, with its framework designed specifically to overcome these challenges using multi-view versions of face and fiducial point detectors, and a combination of point-based texture and geometry. Performance comparisons of several key parameters of relevant algorithms are conducted to explore the optimum parameters for high accuracy and fast computation speed. A comprehensive set of experiments with existing and new datasets, shows that the method is effective despite pose variations, fast, and appropriate for large-scale data, and as accurate as the method with state-of-the-art performance on laboratory-based data. The proposed method was also applied to affective classification of images from the British Broadcast Corporation (BBC) in a task typical for a practical application providing some valuable insights.

The equilibrium geometry and electronic structure of Bi nanolines on clean and hydrogenated Si(001) surfaces

The equilibrium geometry, electronic structure and energetic stability of Bi nanolines on clean and hydrogenated Si(001) surfaces have been examined by means of ab initio total energy calculations and scanning tunnelling microscopy. For the Bi nanolines on a clean Si surface the two most plausible structural models, the Miki or M model (Miki et al 1999 Phys. Rev. B 59 14868) and the Haiku or H model (Owen et al 2002 Phys. Rev. Lett. 88 226104), have been examined in detail. The results of the total energy calculations support the stability of the H model over the M model, in agreement with previous theoretical results. For Bi nanolines on the hydrogenated Si(001) surface, we find that an atomic configuration derived from the H model is also more stable than an atomic configuration derived from the M model. However, the energetically less stable (M) model exhibits better agreement with experimental measurements for equilibrium geometry. The electronic structures of the H and M models are very similar. Both models exhibit a semiconducting character, with the highest occupied Bi-derived bands lying at ~0.5 eV below the valence band maximum. Simulated and experimental STM images confirm that at a low negative bias the Bi lines exhibit an 'antiwire' property for both structural models.

The geometry of Bi nanolines on Si(0 0 1)

A study of the Bi nanoline geometry on Si(0 0 1) has been performed using a combination of ab initio theoretical technique and scanning tunnelling microscopy (STM). Our calculations demonstrate decisively that the recently proposed Haiku geometry is a lower energy configuration than any of the previously proposed line geometries. Furthermore, we have made comparisons between STM constant-current topographs of the lines and Tersoff–Haman STM simulations. Although the Haiku and the Miki geometries both reproduce the main features of the constant-current topographs, the simulated STM images of the Miki geometry have a dark stripe between the dimer rows that does not correspond well with experiment.

Study of tracheal collapsibility, compliance and stress by considering its asymmetric geometry

The shape of tracheal cartilage has been widely treated as symmetric in analytical and numerical models. However, according to both histological images and in vivo medical image, tracheal cartilage is of highly asymmetric shape. Taking the cartilage as symmetric structure will induce bias in calculation of the collapse behavior, as well as compliance and muscular stress. However, this has been rarely discussed. In this paper, tracheal collapse is represented by considering its asymmetric shape. For comparison, the symmetric shape, which is reconstructed by half of the cartilage, is also presented. A comparison of cross-sectional area, compliance of airway and stress in the muscular membrane, determined by asymmetric shape and symmetric shape is made. The result indicates that the symmetric assumption brings a small error, around 5% in predicting the cross-sectional area under loading conditions. The relative error of compliance is more than 10%. Particularly when the pressure is close to zero, the error could be more than 50%. The model considering the symmetric shape results in a significant difference in predicting stress in muscular membrane by either under- or over-estimating it. In conclusion, tracheal cartilage should not be treated as a symmetric structure. The results obtained in this study are helpful in evaluating the error induced by the assumption in geometry.