Gradient-Based Surface Reconstruction and the Application to Wind Waves

New gradient-based surface reconstruction techniques are presented: regularized least absolute deviations based methods using common discrete differential operators, and spline based methods. All new methods are formulated in the same mathematical framework as convex optimization problems and can handle non-rectangular domains. For the spline based methods, either common P-splines or P1-splines can be used. Extensive reconstruction error analysis shows that the new P1-spline based method is superior to conventional methods in the case of gradient fields corrupted with outliers. In the analysis, both spline based methods provide the lowest reconstruction errors for reconstructions from incomplete gradient fields. Furthermore, the pre-processing of gradient fields is investigated. Median filter pre-processing offers a computationally efficient method that is robust to outliers. After the reconstruction error analysis, selected reconstruction methods are applied to imaging slope gauge data measured in the wind-wave facility Aeolotron in Heidelberg. Using newly developed segmentation methods, it is possible to detect different coordinate system orientations of gradient field data and reconstruction algorithms. In addition, the use of a zero slope correction for reconstructions from the provided imaging slope gauge data is justified. The impact of light refracting bubbles on reconstructions from this data is part of this thesis as well. Finally, some water surface reconstructions for measurement conditions with different fetch lengths at the same wind speed in the Aeolotron are shown

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

The Watershed Transformation Applied to Image Segmentation

Image segmentation by mathematical morphology is a methodology based upon the notions of watershed and homotopy modification.This paper aims at introducing this methodology through various examples of segmentation in materials sciences, electron microscopy and scene analysis. First, we defined our basic tool, the watershed transform. We showed that this transformation can be built by implementing a flooding process on a greytone image. This flooding process can be performed by using elementary morphological operations such as geodesic skeleton and reconstruction. Other algorithms are also briefly presented (arrows representation). Then, the use of this transformation for image segmentation purposes is discussed. The application of the watershed transform to gradient images and the problems raised by over-segmentation are emphasized. This leads, into the third part, to the introduction of a general methodology for segmentation, based on the definition of markers and on a transformation called homotopy modification. This complex tool is defined in detail and various types of implementations are given. Many examples of segmentation are presented. These examples are taken from various fields: transmission electron microscopy, scanning electron microscopy (SEM), 3D holographic pictures, radiography, non destructive control and so on. The final part of this paper is devoted to the use of the watershed transformation for hierarchical segmentation. This tool is particularly efficient for defining different levels of segmentation starting from a graph representation of the images based on the mosaic image transform. This approach will be explained by means of examples in industrial vision and scene analysis

Inverse rendering for scene reconstruction in general environments

Demand for high-quality 3D content has been exploding recently, owing to the advances in 3D displays and 3D printing. However, due to insufficient 3D content, the potential of 3D display and printing technology has not been realized to its full extent. Techniques for capturing the real world, which are able to generate 3D models from captured images or videos, are a hot research topic in computer graphics and computer vision. Despite significant progress, many methods are still highly constrained and require lots of prerequisites to succeed. Marker-less performance capture is one such dynamic scene reconstruction technique that is still confined to studio environments. The requirements involved, such as the need for a multi-view camera setup, specially engineered lighting or green-screen backgrounds, prevent these methods from being widely used by the film industry or even by ordinary consumers. In the area of scene reconstruction from images or videos, this thesis proposes new techniques that succeed in general environments, even using as few as two cameras. Contributions are made in terms of reducing the constraints of marker-less performance capture on lighting, background and the required number of cameras. The primary theoretical contribution lies in the investigation of light transport mechanisms for high-quality 3D reconstruction in general environments. Several steps are taken to approach the goal of scene reconstruction in general environments. At first, the concept of employing inverse rendering for scene reconstruction is demonstrated on static scenes, where a high-quality multi-view 3D reconstruction method under general unknown illumination is developed. Then, this concept is extended to dynamic scene reconstruction from multi-view video, where detailed 3D models of dynamic scenes can be captured under general and even varying lighting, and in front of a general scene background without a green screen. Finally, efforts are made to reduce the number of cameras employed. New performance capture methods using as few as two cameras are proposed to capture high-quality 3D geometry in general environments, even outdoors.Die Nachfrage nach qualitativ hochwertigen 3D Modellen ist in letzter Zeit, bedingt durch den technologischen Fortschritt bei 3D-Wieder-gabegeräten und -Druckern, stark angestiegen. Allerdings konnten diese Technologien wegen mangelnder Inhalte nicht ihr volles Potential entwickeln. Methoden zur Erfassung der realen Welt, welche 3D-Modelle aus Bildern oder Videos generieren, sind daher ein brandaktuelles Forschungsthema im Bereich Computergrafik und Bildverstehen. Trotz erheblichen Fortschritts in dieser Richtung sind viele Methoden noch stark eingeschränkt und benötigen viele Voraussetzungen um erfolgreich zu sein. Markerloses Performance Capturing ist ein solches Verfahren, das dynamische Szenen rekonstruiert, aber noch auf Studio-Umgebungen beschränkt ist. Die spezifischen Anforderung solcher Verfahren, wie zum Beispiel einen Mehrkameraaufbau, maßgeschneiderte, kontrollierte Beleuchtung oder Greenscreen-Hintergründe verhindern die Verbreitung dieser Verfahren in der Filmindustrie und besonders bei Endbenutzern. Im Bereich der Szenenrekonstruktion aus Bildern oder Videos schlägt diese Dissertation neue Methoden vor, welche in beliebigen Umgebungen und auch mit nur wenigen (zwei) Kameras funktionieren. Dazu werden Schritte unternommen, um die Einschränkungen bisheriger Verfahren des markerlosen Performance Capturings im Hinblick auf Beleuchtung, Hintergründe und die erforderliche Anzahl von Kameras zu verringern. Der wichtigste theoretische Beitrag liegt in der Untersuchung von Licht-Transportmechanismen für hochwertige 3D-Rekonstruktionen in beliebigen Umgebungen. Dabei werden mehrere Schritte unternommen, um das Ziel der Szenenrekonstruktion in beliebigen Umgebungen anzugehen. Zunächst wird die Anwendung von inversem Rendering auf die Rekonstruktion von statischen Szenen dargelegt, indem ein hochwertiges 3D-Rekonstruktionsverfahren aus Mehransichtsaufnahmen unter beliebiger, unbekannter Beleuchtung entwickelt wird. Dann wird dieses Konzept auf die dynamische Szenenrekonstruktion basierend auf Mehransichtsvideos erweitert, wobei detaillierte 3D-Modelle von dynamischen Szenen unter beliebiger und auch veränderlicher Beleuchtung vor einem allgemeinen Hintergrund ohne Greenscreen erfasst werden. Schließlich werden Anstrengungen unternommen die Anzahl der eingesetzten Kameras zu reduzieren. Dazu werden neue Verfahren des Performance Capturings, unter Verwendung von lediglich zwei Kameras vorgeschlagen, um hochwertige 3D-Geometrie im beliebigen Umgebungen, sowie im Freien, zu erfassen

3D freeform surface measurement on coordinate measuring machine using photometric stereo method

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonSurface metrology has been widely used in manufacturing for many years. There has been a wide range of techniques applied for measuring surface topography. A photometric stereo technique is one of the best ways for the analysis of three-dimensional (3D) surface textural patterns. Many published works are concerned the developed approach for recovering the 3D profiles from surface normal. This research not only presents a methodology used to retrieve the profiles of surface roughness standards but also investigates the uncertainty estimation of textural measurement determined by the photometric stereo method. Various input quantities have been studied such as pixel error from recovered 3D surface textural patterns, the power of light source which involved with surface roughness average (Ra) value and the effect of room temperature. The surface roughness standards were utilized as the reference value. In term of increasing accuracy of the reference value, a contact method (stylus instrument) was used to calibrate them. Illumination angles of light source had some influence on the measurement results. A coordinate measuring machine (CMM) was used for holding the light source in order to study the effects of tilt and slant angles. The effect of tilt and slant angles were investigated. The results of these experiments successfully indicated that the angle used in photometric stereo method played an important role to the accuracy level of the roughness measurement results. The surface roughness specimen manufactured by a Computer Numerical Control (CNC) was applied to validate the capability of the photometric stereo system.The royal Thai government, ministry of sciences and technology and national institute of metrology Thailand (NIMT