Wavefront reconstruction of discontinuous phase objects from optical deflectometry

One of the challenges in phase measuring deflectometry is to retrieve the wavefront from objects that present discontinuities or non-differentiable gradient fields. Here, we propose the integration of such gradients fields based on an Lp-norm minimization problem. The solution of this problem results in a nonlinear partial differential equation, which can be solved with a fast and well-known numerical methods and doesn't depend on external parameters. Numerical reconstructions on both synthetic and experimental data are presented that demonstrate the capability of the proposed method

Three-Dimensional Shape Measurements of Specular Objects Using Phase-Measuring Deflectometry

The fast development in the fields of integrated circuits, photovoltaics, the automobile industry, advanced manufacturing, and astronomy have led to the importance and necessity of quickly and accurately obtaining three-dimensional (3D) shape data of specular surfaces for quality control and function evaluation. Owing to the advantages of a large dynamic range, non-contact operation, full-field and fast acquisition, high accuracy, and automatic data processing, phase-measuring deflectometry (PMD, also called fringe reflection profilometry) has been widely studied and applied in many fields. Phase information coded in the reflected fringe patterns relates to the local slope and height of the measured specular objects. The 3D shape is obtained by integrating the local gradient data or directly calculating the depth data from the phase information. We present a review of the relevant techniques regarding classical PMD. The improved PMD technique is then used to measure specular objects having discontinuous and/or isolated surfaces. Some influential factors on the measured results are presented. The challenges and future research directions are discussed to further advance PMD techniques. Finally, the application fields of PMD are briefly introduce

Geometric Numerical Integration (hybrid meeting)

The topics of the workshop included interactions between geometric numerical integration and numerical partial differential equations; geometric aspects of stochastic differential equations; interaction with optimisation and machine learning; new applications of geometric integration in physics; problems of discrete geometry, integrability, and algebraic aspects

Efficient Techniques for High Resolution Stereo

The purpose of stereo is extracting 3-dimensional (3D) information from 2-dimensional (2D) images, which is a fundamental problem in computer vision. In general, given a known imaging geometry the position of any 3D point observed by two or more different views can be recovered by triangulation, so 3D reconstruction task relies on figuring out the pixel’s correspondence between the reference and matching images. In general computational complexity of stereo algorithms is proportional to the image resolution (the total number of pixels) and the search space (the number of depth candidates). Hence, high resolution stereo tasks are not tractable for many existing stereo algorithms whose computational costs (including the processing time and the storage space) increase drastically with higher image resolution. The aim of this dissertation is to explore techniques aimed at improving the efficiency of high resolution stereo without any accuracy loss. The efficiency of stereo is the first focus of this dissertation. We utilize the implicit smoothness property of the local image patches and propose a general framework to reduce the search space of stereo. The accumulated matching costs (measured by the pixel similarity) are investigated to estimate the representative depths of the local patch. Then, a statistical analysis model for the search space reduction based on sequential probability ratio test is provided, and an optimal sampling scheme is proposed to find a complete and compact candidate depth set according to the structure of local regions. By integrating our optimal sampling schemes as a pre-processing stage, the performance of most existing stereo algorithms can be significantly improved. The accuracy of stereo algorithms is the second focus. We present a plane-based approach for the local geometry estimation combining with a parallel structure propagation algorithm, which outperforms most state-of-the-art stereo algorithms. To obtain precise local structures, we also address the problem of utilizing surface normals, and provide a framework to integrate color and normal information for high quality scene reconstruction.Doctor of Philosoph

A PDE approach to Shape from Shading via Photometric Stereo

We present a new analytic and numerical approach to the shape from shading using photometric stereo technique. That is, we solve the problem to find the 3D surface of an object starting from its several 2D pictures taken from the same point of view, but changing, for every image, the direction of the light source

Reconstruction of interfaces from the elastic farfield measurements using CGO solutions

In this work, we are concerned with the inverse scattering by interfaces for the linearized and isotropic elastic model at a fixed frequency. First, we derive complex geometrical optic solutions with linear or spherical phases having a computable dominant part and an $H^\alpha$-decaying remainder term with $\alpha <3$, where $H^{\alpha}$ is the classical Sobolev space. Second, based on these properties, we estimate the convex hull as well as non convex parts of the interface using the farfields of only one of the two reflected body waves (pressure waves or shear waves) as measurements. The results are given for both the impenetrable obstacles, with traction boundary conditions, and the penetrable obstacles. In the analysis, we require the surfaces of the obstacles to be Lipschitz regular and, for the penetrable obstacles, the Lam\'e coefficients to be measurable and bounded with the usual jump conditions across the interface.Comment: 32 page