Review of phase measuring deflectometry

Dynamic full-field three-dimensional sensing of specular reflective surfaces can be conveniently implemented with fringe reflection technique. A monoscopic fringe reflectometric system can be adopted as a simple measuring setup. With the assistance of the windowed Fourier ridges method as an advanced fringe demodulation technique, only one cross grating is needed to reconstruct the three-dimensional surface shape changes. A suitable calibration enables determination of the actual three-dimensional surface profile. Experimental results of water wave variations are shown to demonstrate the feasibility of the proposed approach.

Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry.

We study the tensor structure of two operations: the transformation of a given multidimensional vector into a multilevel Toeplitz matrix and the convolution of two given multidimensional vectors. We show that the low-rank tensor structure of the input is preserved in the output and propose efficient algorithms for these operations in the newly introduced quantized tensor train (QTT) format. Consider a $d$-dimensional $2n \times\cdots\times 2n$-vector $\boldsymbol{x}$. If it is represented elementwise, the number of parameters is $(2n)^{d}$. However, if we assume that $\boldsymbol{x}$ is given in a QTT representation with ranks bounded by $p$, the number of parameters is reduced to $\mathcal{O}\left(dp^{2} \log n\right)$. Under this assumption we show how the multilevel Toeplitz matrix generated by $\boldsymbol{x}$ can be obtained in the QTT format with ranks bounded by $2p$ in $\mathcal{O}\left(dp^{2} \log n\right)$ operations. We also describe how the convolution $\boldsymbol{x}\star\boldsymbol{y}$ of $\...

/pdf/multilevel-toeplitz-matrices-generated-by-tensor-structured-3xcblpqa8k.pdf

Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity

Mixed reality-based user interface for quality control inspection of car body surfaces

Detecting dings and dents on specular car body surfaces based on optical flow

The inspection of specular surfaces differs significantly from the case of non-specular surfaces. In contrast to the non-specular case, the appearance of a specular surface is dominated by the reflections of the environment that are visible in it. The transfer of this observation into automated visual inspection is called deflectometry. The main principle of deflectometric surface acquisition is to use a highly controllable environment, where a screen on which a well-defined pattern is presented is observed via the specular reflecting surface. Knowing that pattern, it is possible to inspect the surface qualitatively and - at least with certain additional knowledge - to reconstruct the surface under test. In this paper, we introduce the theoretical background of deflectometry. After presenting some properties of the deflectometric inspection itself, we describe the qualitative and quantitative evaluation of the deflectometric observation in detail. We will show that an inspection of specular and partially specular objects is feasible in an industrially applicable inspection system. For complexly formed and/or large objects, we propose a robot-based inspection setup.

/pdf/inspection-of-specular-and-partially-specular-surfaces-1v09cvc960.pdf

Inspection of specular and partially specular surfaces

Utilizing separation to decompose a local filter mask is a well-known technique to accelerate its convolution with discrete two-dimensional signals such as images. However, many modern days' applications involve higher-dimensional, discrete data that needs to be processed but whose inherent spatial complexity would render immediate/naive convolutions computationally infeasible. In this paper, we show how separability of general higher-order tensors can be leveraged to reduce the computational effort for discrete convolutions from super-polynomial to polynomial (in both the filter mask's tensor order and spatial expansion). Thus, where applicable, our method compares favorably to current tensor convolution methods and, it renders linear filtering applicable to signal domains whose spatial complexity would otherwise have been prohibitively high. In addition to our theoretical guarantees, we experimentally illustrate our approach to be highly beneficial not only in theory but also in practice.

On the computational benefit of tensor separation for high-dimensional discrete convolutions

Along with the boom of computer vision- and other signal processing-based applications, the question of fast local operator application has become increasingly important over the past decade. For two-dimensional signals, such as images, local operator separation has proven to ameliorate the computational effort incurred by prominent operators such as mean filter, binomial filter or Sobel filter [1]. However, many modern days' applications involve higher-dimensional input signals including tomography, functional magnetic resonance imaging (fMRI), selective plane illumination microscopy (SPIM), confocal laser scanning microscopy (CLSM), special image fusion.

On generalized separation and the speedup of local operators on multi-dimensional signals

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Inspection of specular and partially specular surfaces

On the computational benefit of tensor separation for high-dimensional discrete convolutions

On generalized separation and the speedup of local operators on multi-dimensional signals