Shape reconstruction from gradient data.
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TLDR
A generalized method for reconstructing the shape of an object from measured gradient data based on an approximation employing radial basis functions that can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.Abstract:
We present a generalized method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object but rather its local slope. These sensors display several advantages, including high information efficiency, sensitivity, and robustness. For many applications, however, it is necessary to acquire the shape, which must be calculated from the slopes by numerical integration. Existing integration techniques show drawbacks that render them unusable in many cases. Our method is based on an approximation employing radial basis functions. It can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.read more
Citations
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Time-of-flight PET data determine the attenuation sinogram up to a constant.
TL;DR: It is shown that in time-of-flight PET, the attenuation sinogram is determined by the emission data except for a constant and that its gradient can be estimated efficiently using a simple analytic algorithm.
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Review of phase measuring deflectometry
TL;DR: The fundamental principle and the basic concepts of PMD technique are introduced and followed by a brief overview of its key developments since it was first proposed to provide some suggestions for potential future investigations.
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Principles of Shape from Specular Reflection
Jonathan Balzer,Stefan Werling +1 more
TL;DR: In this article, the authors present a comprehensive survey of the state of the art in the field of shape from reflection, including all known forward models of the reflection process, as well as numerical methods related to Shape from Specular Reflection.
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Comparison of two-dimensional integration methods for shape reconstruction from gradient data
TL;DR: In this work, three types of two-dimensional integration methods are compared under various conditions to provide suggestions in selection of a proper integration method for a particular application.
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Normal Integration: A Survey
TL;DR: In this article, the authors present a survey of the most important properties that one may expect from a normal integration method, based on a thorough study of two pioneering works by Horn and rooks (Comput Vis Graph Image Process 33(2): 174−208, 1986) and Frankot and Chellappa (IEEE Trans Pattern Anal Mach Intell 10(4): 439-451, 1988).
References
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Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
TL;DR: A new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support is constructed, it is proved that they are of minimal degree and unique up to a constant factor.
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Martin D. Buhmann,M. D. Buhmann +1 more
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A method for enforcing integrability in shape from shading algorithms
Robert T. Frankot,Rama Chellappa +1 more
TL;DR: An approach for enforcing integrability, a particular implementation of the approach, an example of its application to extending an existing shape-from-shading algorithm, and experimental results showing the improvement that results from enforcingIntegrability are presented.
Journal ArticleDOI
Wave-front estimation from wave-front slope measurements
TL;DR: In this paper, the problem of wavefront estimation from wave-front slope measurements has been examined from a least-squares curve fitting model point of view, and a new zonal phase gradient model is introduced and its error propagator, which relates the mean square wavefront error to the noisy slope measurements, has been compared with two previously used models.
Proceedings ArticleDOI
Phase measuring deflectometry: a new approach to measure specular free-form surfaces
TL;DR: In this paper, a stereo-based enhancement of phase measuring deflectometry (PMD) is proposed to measure the height and the slope of specular free-form surfaces within seconds.