Geometric modeling of non-rigid 3D shapes : theory and application to object recognition.

One of the major goals of computer vision is the development of flexible and efficient methods for shape representation. This is true, especially for non-rigid 3D shapes where a great variety of shapes are produced as a result of deformations of a non-rigid object. Modeling these non-rigid shapes is a very challenging problem. Being able to analyze the properties of such shapes and describe their behavior is the key issue in research. Also, considering photometric features can play an important role in many shape analysis applications, such as shape matching and correspondence because it contains rich information about the visual appearance of real objects. This new information (contained in photometric features) and its important applications add another, new dimension to the problem\u27s difficulty. Two main approaches have been adopted in the literature for shape modeling for the matching and retrieval problem, local and global approaches. Local matching is performed between sparse points or regions of the shape, while the global shape approaches similarity is measured among entire models. These methods have an underlying assumption that shapes are rigidly transformed. And Most descriptors proposed so far are confined to shape, that is, they analyze only geometric and/or topological properties of 3D models. A shape descriptor or model should be isometry invariant, scale invariant, be able to capture the fine details of the shape, computationally efficient, and have many other good properties. A shape descriptor or model is needed. This shape descriptor should be: able to deal with the non-rigid shape deformation, able to handle the scale variation problem with less sensitivity to noise, able to match shapes related to the same class even if these shapes have missing parts, and able to encode both the photometric, and geometric information in one descriptor. This dissertation will address the problem of 3D non-rigid shape representation and textured 3D non-rigid shapes based on local features. Two approaches will be proposed for non-rigid shape matching and retrieval based on Heat Kernel (HK), and Scale-Invariant Heat Kernel (SI-HK) and one approach for modeling textured 3D non-rigid shapes based on scale-invariant Weighted Heat Kernel Signature (WHKS). For the first approach, the Laplace-Beltrami eigenfunctions is used to detect a small number of critical points on the shape surface. Then a shape descriptor is formed based on the heat kernels at the detected critical points for different scales. Sparse representation is used to reduce the dimensionality of the calculated descriptor. The proposed descriptor is used for classification via the Collaborative Representation-based Classification with a Regularized Least Square (CRC-RLS) algorithm. The experimental results have shown that the proposed descriptor can achieve state-of-the-art results on two benchmark data sets. For the second approach, an improved method to introduce scale-invariance has been also proposed to avoid noise-sensitive operations in the original transformation method. Then a new 3D shape descriptor is formed based on the histograms of the scale-invariant HK for a number of critical points on the shape at different time scales. A Collaborative Classification (CC) scheme is then employed for object classification. The experimental results have shown that the proposed descriptor can achieve high performance on the two benchmark data sets. An important observation from the experiments is that the proposed approach is more able to handle data under several distortion scenarios (noise, shot-noise, scale, and under missing parts) than the well-known approaches. For modeling textured 3D non-rigid shapes, this dissertation introduces, for the first time, a mathematical framework for the diffusion geometry on textured shapes. This dissertation presents an approach for shape matching and retrieval based on a weighted heat kernel signature. It shows how to include photometric information as a weight over the shape manifold, and it also propose a novel formulation for heat diffusion over weighted manifolds. Then this dissertation presents a new discretization method for the weighted heat kernel induced by the linear FEM weights. Finally, the weighted heat kernel signature is used as a shape descriptor. The proposed descriptor encodes both the photometric, and geometric information based on the solution of one equation. Finally, this dissertation proposes an approach for 3D face recognition based on the front contours of heat propagation over the face surface. The front contours are extracted automatically as heat is propagating starting from a detected set of landmarks. The propagation contours are used to successfully discriminate the various faces. The proposed approach is evaluated on the largest publicly available database of 3D facial images and successfully compared to the state-of-the-art approaches in the literature. This work can be extended to the problem of dense correspondence between non-rigid shapes. The proposed approaches with the properties of the Laplace-Beltrami eigenfunction can be utilized for 3D mesh segmentation. Another possible application of the proposed approach is the view point selection for 3D objects by selecting the most informative views that collectively provide the most descriptive presentation of the surface

Nonrigid reconstruction of 3D breast surfaces with a low-cost RGBD camera for surgical planning and aesthetic evaluation

Accounting for 26% of all new cancer cases worldwide, breast cancer remains the most common form of cancer in women. Although early breast cancer has a favourable long-term prognosis, roughly a third of patients suffer from a suboptimal aesthetic outcome despite breast conserving cancer treatment. Clinical-quality 3D modelling of the breast surface therefore assumes an increasingly important role in advancing treatment planning, prediction and evaluation of breast cosmesis. Yet, existing 3D torso scanners are expensive and either infrastructure-heavy or subject to motion artefacts. In this paper we employ a single consumer-grade RGBD camera with an ICP-based registration approach to jointly align all points from a sequence of depth images non-rigidly. Subtle body deformation due to postural sway and respiration is successfully mitigated leading to a higher geometric accuracy through regularised locally affine transformations. We present results from 6 clinical cases where our method compares well with the gold standard and outperforms a previous approach. We show that our method produces better reconstructions qualitatively by visual assessment and quantitatively by consistently obtaining lower landmark error scores and yielding more accurate breast volume estimates

Analysis of rolling contact spall life in 440 C steel bearing rims

The results of a two year study of the mechanisms of spall failure in the HPOTP bearings are described. The objective was to build a foundation for detailed analyses of the contact life in terms of: cyclic plasticity, contact mechanics, spall nucleation, and spall growth. Since the laboratory rolling contact testing is carried out in the 3 ball/rod contact fatigue testing machine, the analysis of the contacts and contact lives produced in this machine received attention. The results from the experimentally observed growth lives are compared with calculated predictions derived from the fracture mechanics calculations

Bifurcations and dynamics in convection with temperature-dependent viscosity in the presence of the O(2) symmetry

We focus the study of a convection problem in a 2D setup in the presence of the O(2) symmetry. The viscosity in the fluid depends on the temperature as it changes its value abruptly in an interval around a temperature of transition. The influence of the viscosity law on the morphology of the plumes is examined for several parameter settings, and a variety of shapes ranging from spout to mushroom shaped is found. We explore the impact of the symmetry on the time evolution of this type of fluid, and find solutions which are greatly influenced by its presence: at a large aspect ratio and high Rayleigh numbers, traveling waves, heteroclinic connections and chaotic regimes are found. These solutions, which are due to the symmetry presence, have not been previously described in the context of temperature dependent viscosities. However, similarities are found with solutions described in other contexts such as flame propagation problems or convection problems with constant viscosity also under the presence of the O(2) symmetry, thus confirming the determining role of the symmetry in the dynamics.Comment: 21 pages, 10 figure

Novel Correspondence-based Approach for Consistent Human Skeleton Extraction

This paper presents a novel base-points-driven shape correspondence (BSC) approach to extract skeletons of articulated objects from 3D mesh shapes. The skeleton extraction based on BSC approach is more accurate than the traditional direct skeleton extraction methods. Since 3D shapes provide more geometric information, BSC offers the consistent information between the source shape and the target shapes. In this paper, we first extract the skeleton from a template shape such as the source shape automatically. Then, the skeletons of the target shapes of different poses are generated based on the correspondence relationship with source shape. The accuracy of the proposed method is demonstrated by presenting a comprehensive performance evaluation on multiple benchmark datasets. The results of the proposed approach can be applied to various applications such as skeleton-driven animation, shape segmentation and human motion analysis

Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure

A Computational Study of the Inertial Collapse of Gas Bubbles Near a Rigid Surface

Cavitation research is essential to a variety of applications ranging from naval hydrodynamics to medicine and energy sciences. Vapor cavities can grow from sub-micron-sized nuclei to millimeter-sized bubbles, and collapse violently in an inertial fashion. This implosion, which concentrates energy into a small volume, can produce high pressures and temperatures, generate strong shock waves, and even emit visible light. One of the main consequences of cavitation is structural damage to neighboring surfaces due to bubble collapse. The propagation of shock and rarefaction waves in a multiphase medium results in a complicated multiscale and multiphysics problem. Laboratory experiments of such flows are challenging due to the wide range of spatial and temporal scales, difficult optical access, and limitations of measurement devices. To better understand these flows, we use highly resolved numerical simulations of the inertial collapse of individual vapor bubbles near a rigid surface. For this purpose, we developed a novel numerical multiphase model combined with high-performance computing techniques to perform accurate and efficient simulations of the three-dimensional compressible Navier-Stokes equations for a binary, gas-liquid system. We present the detailed dynamics of the Rayleigh collapse of a single vapor bubble near a rigid wall for different geometrical configurations and driving pressures. We explain that the presence of a rigid boundary breaks the symmetry of the collapse and hinders the energy concentration. As a result, a liquid re-entrant jet directed toward the wall forms, ultimately giving rise to lower pressure and temperatures produced upon collapse. We characterize the collapse non-sphericity, and show that this quantity, which strongly depends on the initial stand-off distance of the bubble from the wall, significantly affects the overall dynamics. We further show that bubbles initially close to the wall or attached to the surface are responsible not only for the high pressure loads along the wall, but also the elevated temperatures on the solid surface. In fact, for certain soft materials, instantaneous temperatures greater than the melting point may be achieved on the surface, thus confirming that thermal damage is a potential threat to such materials exposed to cavitating flows. Furthermore, the development of scalings for important collapse properties (jet velocity, shock pressure, wall pressures/temperatures), in terms of the initial stand-off distance and driving pressure, not only illustrates universality of non-spherical bubble dynamics but also provides means to predict these phenomena. Since real flows involve many bubbles, we also investigate the inertial collapse of a pair of vapor bubbles near a rigid surface. We explain that the presence of a second bubble in the vicinity of the original (primary) bubble leads to far more complicated dynamics and completely changes the single-bubble scalings. Strong interactions between the bubbles and the boundary drastically increase the collapse non-sphericity and amplify/hinder the pressures and temperatures produced by the collapse. Our simulations show that the re-entrant jets in both bubbles form at distorted angles, and for certain configurations, ``double jetting'', occurs, in which two jets penetrate the primary bubble. The results indicate that bubble-bubble interactions and their effects on collapse dynamics near a wall are non-negligible. Furthermore, given the complexity of even this simple problem and the large number of parameters, the value of extending such high-resolution simulations to develop scalings for the collapse of many bubbles is debatable at the present time; it may be worth considering alternative modeling approaches.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144079/1/alahyari_1.pd

Design and optimization of joints to mitigate shock in military vehicles under blast and impact loaDing

Shock from a blast loading may risk the lives of the occupants of a military vehicle and damage the sensitive electronic components within it. The objective of this work is to develop an approach to mitigate shocks due to mine blast loading and impact loading by proper design of joint(s) in the military vehicles. Two types of vehicle configurations are studied for this purpose. The first vehicle is studied to examine ways to mitigate shock due to mine blast while the second vehicle is studied to mitigate shock due to projectile impact load. The proposed research includes design of joints in a way to disrupt/reflect/absorb the incident shock loading due to these transient events. The overall purpose of the study is to determine optimal types and configurations of joints that dissipate energy and incorporate the advantageous joint designs