The human visual system has the ability o utilize motion information to infer the shapes of surfaces. More specifically, we are able to derive descriptions of rigidly rotating smooth surfaces entirely from the orthographic projection of the motions of their surface markings. A computational analysis of this ability is proposed based on "shape from motion" proposition. This proposition states that given the first spatial derivatives of the orthographically projected velocity and the acceleration fields of a rigidly rotating regular surface, then the angular velocity and the surface normal at each visible point on that surface are uniquely determined up to a reflection.

Yes / Bezier curves and surfaces are two very useful tools in Geometric Modeling, with many applications. In this paper, we will offer a new method to provide approximations of regular curves and surfaces by Bezier ones, with the corresponding examples.

This dissertation proposes an approach for 3D micro-scale shape reconstruction using photometric stereo (PS) with surface normal integration (SNI). Based on the proposed approach, a portable cost-effective stationary system is developed to capture 3D shapes in the order of micrometer scale. The PS with SNI technique is adopted to reconstruct 3D microtopology since this technique is highlighted for its capability to reproduce fine surface details at pixel resolution. Furthermore, since the primary hardware components are merely a camera and several typical LEDs, the system based on PS with SNI can be made portable at low cost. The principal contributions are three folds. First, a PS method based on dichromatic reflectance model (DRM) using color input images is proposed to generalize PS applicable to a wider range of surfaces with non-Lambertian reflectances. The proposed method not only estimates surface orientations from diffuse reflection but also exploits information from specularities owing to the proposed diffuse-specular separation algorithm. Using the proposed PS method, material-dependent features can be simultaneously extracted in addition to surface orientations, which offers much richer information in understanding the 3D scene and poses more potential functionalities, such as specular removal, intrinsic image decomposition, digital relighting, material-based segmentation, material transfer and material classification. The second contribution is the development of an SNI method dealing with perspective distortion. The proposed SNI is performed on the image plane instead of on the target surface as did by orthographic SNI owing to the newly derived representation of surface normals. The motivation behind the representation is from the observation that spatially uniform image points are simpler for integration than the non-uniform distribution of surface points under perspective projection. The new representation is then manipulated to the so-called log gradient space in analogy to the gradient space in orthographic SNI. With this analogy, the proposed method can inherit most past algorithms developed for orthographic SNI. By applying the proposed SNI, perspective distortion can be efficiently tackled with for smooth surfaces. In addition, the method is PS-independent, which can keep the image irradiance equation in a simple form during PS. The third contribution is the design and calibration of a 3D micro-scale shape reconstruction system using the derived PS and SNI methods. This system is originally designed for on-site measurement of pavement microtexture, while its applicability can be generalized to a wider range of surfaces. Optimal illumination was investigated in theory and through numerical simulations. Five different calibrations regarding various aspects of the system were either newly proposed or modified from existing methods. The performances of these calibrations were individually evaluated. Efficacy of the developed system was finally demonstrated through comprehensive comparative studies with existing systems. Its capability for on-site measurement was also confirmed. / Ph. D.

This work deals with the matter of powertrain vibration reduction, focusing on the transmission. These units, depending on the purpose of utilization, consist of a high number of dimensionally complex components. These need to possess features, selected already in the design phase, which would guarantee smooth and quiet operation. A properly designed tooth profile and the related specified accuracy of manufacturing are one of the most important features. The basic function and the purpose of transmissions application indicate a relatively wide range of operating speeds and transmitted loads. Moreover, combination of both loading with improperly designed string’s parameter can cause a number of various problems. The vibration initiation with related noise from gear mesh belong to the most significant sources of issues. There are multiple mechanisms of oscillation initiation. Even when using the latest trends in the development of teeth, when their shape is upgraded and developed to meet specifically given load range, the above mentioned irregularity of transferred torque cannot be completely eliminated. Therefore, it is necessary, already in the design phase, to eliminate the transmission paths by which are vibrations transmitting to other components. People perceive this action in the form of vibration, noise, or temperature change in the surroundings. With the increasing comfort levels and number of produced vehicles the reduction of vibration and noise of machinery parts becomes stricter, including gears. The experimental approach is primarily used to assess the accuracy of designed gearboxes, but it is a very expensive and a time consuming method. Therefore, it is necessary to develop a process that utilizes both numerical simulation and experimental approach but also combines the advantages of both, particularly time and cost savings and comparability of results. For this purpose, the experimental gearbox is designed and manufactured including the single-stage gear enabling variable configurations in terms of the ratio change. The gearbox is subjected to numerical simulation of different complexity levels, as well as technical experiment. Furthermore, the universal virtual prototype in Multi-Body System ADAMS is created, which reflects the impact of several key parameters for proper functionality, such as axial distance, backlash, gear mesh stiffness, shaft mounting stiffness (bearings) and modal properties of the shafts and gearbox housing. Last but not least, the impact of imbalance or irregularity of input shaft speed is incorporated. The last part focuses on a brief description of the application of the presented methodology – modelling of vibrations on the tractor gearbox.

Space-based telescopes are limit by the payload requirements of existing launch vehicles. Thus, despite distinct advantages the resolution of terrestrial telescopes exceeds space-based telescopes due to larger size and powerful adaptive optics. To overcome payload limitations, a primary mirror technology that is lighter in weight, but no less effective, is required. As this will result in new structural conditions, new approaches to maintaining the optical shape (figure) of the mirror will also be required. This thesis culminates work at the Georgia Institute of Technology in modelling a hexagonal thin-shell deformation mirror manipulated by an adaptive truss. This research specifically examines the feasibility of a surface parallel actuated (SPA) thin-shell CuZr deformable mirror (DM) as an alternative to a typical surface normal actuated (SNA) based mirror. It is believed that by using a thin-shell mirror (100 m or less in thickness) with a light weight substrate, such as a truss, that a significant weight-savings will occur, thus enabling larger space based telescopes. This thesis advances the SPA DM concept by 1) creating a representative model, 2) developing design evaluation methods, 3) evaluating the FEA simulated response of the deformable mirror over Zernike error modes, 4) evaluating the FEA simulated response to select thermal loads, and 5) evaluating the ability of the DM to remove thermal error, and the forces required to do so. Finally, it is concluded that overall the SPA DM concept is feasible.

In this study, a computer code is developed in MATLAB&reg / to compute the Radar Cross Section (RCS) of arbitrary shaped complex targets by using Physical Optics (PO) and Modified PO. To increase the computational efficiency of the code, a novel fast integration procedure for oscillatory integrals, called Levin&rsquo / s integration, is applied to PO integrals. In order to improve the performance of PO near grazing angles and to model diffraction effects, a method called PO with Modified Surface Normal Vectors is implemented. In this method, new surface normals are defined to model the diffraction mechanism. Secondary scattering mechanisms like multiple scattering and shadowing algorithms are also included into the code to obtain a complete RCS prediction tool. For this purpose, an iterative version of PO is used to account for multiple scattering effects. Indeed, accounting for multiple scattering effects automatically solves the shadowing problem with a minor modification. Therefore, a special code for shadowing problem is not developed. In addition to frequency domain solutions of scattering problems, a waveform analysis of scattered fields in time domain is also comprised into this thesis. Instead of direct time domain methods like Time Domain Physical Optics, a Fourier domain approach is preferred to obtain the time domain expressions of the scattered fields. Frequency and time domain solutions are obtained for some simple shapes and for a complex tank model for differently polarized incident fields. Furthermore, a statistical analysis for the scattered field from the tank model is conducted.

In this thesis, the expression variation problem in two-dimensional (2D) and three-dimensional (3D) face recognition is tackled. While discriminant analysis (DA) methods are effective solutions for recognizing expression-variant 2D face images, they are not directly applicable when only a single sample image per subject is available. This problem is addressed in this thesis by introducing expression subspaces which can be used for synthesizing new expression images from subjects with only one sample image. It is proposed that by augmenting a generic training set with the gallery and their synthesized new expression images, and then training DA methods using this new set, the face recognition performance can be significantly improved. An important advantage of the proposed method is its simplicity; the expression of an image is transformed simply by projecting it into another subspace. The above proposed solution can also be used in general pattern recognition applications. The above method can also be used in 3D face recognition where expression variation is a more serious issue. However, DA methods cannot be readily applied to 3D faces because of the lack of a proper alignment method for 3D faces. To solve this issue, a method is proposed for sampling the points of the face that correspond to the same facial features across all faces, denoted as the closest-normal points (CNPs). It is shown that the performance of the linear discriminant analysis (LDA) method, applied to such an aligned representation of 3D faces, is significantly better than the performance of the state-of-the-art methods which, rely on one-by-one registration of the probe faces to every gallery face. Furthermore, as an important finding, it is shown that the surface normal vectors of the face provide a higher level of discriminatory information rather than the coordinates of the points. In addition, the expression subspace approach is used for the recognition of 3D faces from single sample. By constructing expression subspaces from the surface normal vectors at the CNPs, the surface normal vectors of a 3D face with single sample can be synthesized under other expressions. As a result, by improving the estimation of the within-class scatter matrix using the synthesized samples, a significant improvement in the recognition performance is achieved.

In this thesis, the expression variation problem in two-dimensional (2D) and three-dimensional (3D) face recognition is tackled. While discriminant analysis (DA) methods are effective solutions for recognizing expression-variant 2D face images, they are not directly applicable when only a single sample image per subject is available. This problem is addressed in this thesis by introducing expression subspaces which can be used for synthesizing new expression images from subjects with only one sample image. It is proposed that by augmenting a generic training set with the gallery and their synthesized new expression images, and then training DA methods using this new set, the face recognition performance can be significantly improved. An important advantage of the proposed method is its simplicity; the expression of an image is transformed simply by projecting it into another subspace. The above proposed solution can also be used in general pattern recognition applications. The above method can also be used in 3D face recognition where expression variation is a more serious issue. However, DA methods cannot be readily applied to 3D faces because of the lack of a proper alignment method for 3D faces. To solve this issue, a method is proposed for sampling the points of the face that correspond to the same facial features across all faces, denoted as the closest-normal points (CNPs). It is shown that the performance of the linear discriminant analysis (LDA) method, applied to such an aligned representation of 3D faces, is significantly better than the performance of the state-of-the-art methods which, rely on one-by-one registration of the probe faces to every gallery face. Furthermore, as an important finding, it is shown that the surface normal vectors of the face provide a higher level of discriminatory information rather than the coordinates of the points. In addition, the expression subspace approach is used for the recognition of 3D faces from single sample. By constructing expression subspaces from the surface normal vectors at the CNPs, the surface normal vectors of a 3D face with single sample can be synthesized under other expressions. As a result, by improving the estimation of the within-class scatter matrix using the synthesized samples, a significant improvement in the recognition performance is achieved.