We propose a generalized equation to represent a continuum of surface reconstruction solutions of a given non-integrable gradient field. We show that common approaches such as Poisson solver and Frankot-Chellappa algorithm are special cases of this generalized equation. For a N x N pixel grid, the subspace of all integrable gradient fields is of dimension N 2 - 1. Our framework can be applied to derive a range of meaningful surface reconstructions from this high dimensional space. The key observation is that the range of solutions is related to the degree of anisotropy in applying weights to the gradients in the integration process. While common approaches use isotropic weights, we show that by using a progression of spatially varying anisotropic weights, we can achieve significant improvement in reconstructions. We propose (a) α-surfaces using binary weights, where the parameter a allows trade off between smoothness and robustness, (b) M-estimators and edge preserving regularization using continuous weights and (c) Diffusion using affine transformation of gradients. We provide results on photometric stereo, compare with previous approaches and show that anisotropic treatment discounts noise while recovering salient features in reconstructions.

What Is the Range of Surface Reconstructions from a Gradient Field

農林水産省経営局長賞 尿石症により尿道閉塞した雄子牛に対するバルーンカテーテルを用いた膀胱-皮膚フィステル装着による治療法の考案 (平成26年度家畜診療等技術全国研究集会・入賞論文)

IT is not often that a reissue of the collected papers of an outstanding scientific man has been called for. Some of the papers cannot fail to have historical value because of the part which their original publication played in the development of science; but that value alone would not be sufficient to secure the demand. The work involved must be of present-day importance. Therefore its consequences must still be in process of development; and it follows that if, as in the present case, the republication follows the first publication after an interval of half a century, the main papers involved must have been of very epoch-making type. The condition of present value is a sufficient test; but the most essential condition is that of permanent value. Present value persisting after the lapse of fifty years suggests permanence, and at least points to some enduring quality—the direct impress of the distinctive personality of the man. The Scientific Papers of James Clerk Maxwell. Edited By W. D. Niven. (Photographic Reprint by arrangement with the Cambridge University Press.) Vol. 1. Pp. xxxii + 607. Vol. 2. Pp. viii + 806. (Paris: J. Hermann, 1927.) 3 livres 6.

The Scientific Papers of James Clerk Maxwell

(1992). Matrices: Methods and Applications. Journal of the Operational Research Society: Vol. 43, No. 12, pp. 1185-1185.

/pdf/matrices-methods-and-applications-3mhi2vv26h.pdf

Matrices: Methods and Applications

Computer Vision Technology for Food Quality Evaluation

A parallel paper [Berujon, Cojocaru, Piault, Celestre, Roth, Barrett & Ziegler (2020), J. Synchrotron Rad. 27, 284–292] reviewed theoretically some of the available processing schemes for X-ray wavefront sensing based on random modulation. Shown here are experimental applications of the technique for characterizing both refractive and reflective optical components. These fast and accurate X-ray at-wavelength metrology methods can assist the manufacture of X-ray optics that transport X-ray beams with a minimum amount of wavefront distortion. It is also recalled how such methods can facilitate online optimization of active optics.

X-ray optics and beam characterization using random modulation: experiments.

We consider different approaches to simulate a modern X-ray beamline. Several methodologies with increasing complexity are applied to discuss the relevant parameters that quantify the beamline performance. Parameters such as flux, dimensions and intensity distribution of the focused beam and coherence properties are obtained from simple analytical calculations to sophisticated computer simulations using ray-tracing and wave optics techniques. A latest-generation X-ray nanofocusing beamline for coherent applications (ID16A at the ESRF) has been chosen to study in detail the issues related to highly demagnifying synchrotron sources and exploiting the beam coherence. The performance of the beamline is studied for two storage rings: the old ESRF-1 (emittance 4000~pm) and the new ESRF-EBS (emittance 150~pm). In addition to traditional results in terms of flux and beam sizes, an innovative study on the partial coherence properties based on the propagation of coherent modes is presented. The different algorithms and methodologies are implemented in the software suite OASYS. Those are discussed with emphasis placed upon the their benefits and limitations of each.

/pdf/a-hierarchical-approach-for-modelling-x-ray-beamlines-2m8fpvtd9o.pdf

A hierarchical approach for modelling X-ray beamlines. Application to a coherent beamline

After the big impact of optical 3D-imaging processing, multi- and hyperspectral imaging solutions will be the next technological innovation in image processing for industrial application. This work presents a clever and affordable solution for multispectral imaging: a smart imager for measurements spanning 400 nm to 950 nm in a 50 nm step with 50 nm bandwidth. With a combination of industrial interface technology (GigE-Vision), new CMOS-imaging sensors as well as new approaches for the active compensation of chromatic aberration novel applications are possible. The core idea of the smart multispectral sensor is to support of such features, while giving the user a friendly interface. This manuscript is organised as follows: firstly, a compact overview on history, spectral imaging and smart cameras is presented. The introduction is shortly followed by a brief description of the state of the art. The system is meticulously presented in the four subsequent sections. System evaluation shows some specific applications and a conclusion closes this work.

Smart multispectral imager for industrial applications

In a previous paper, we reviewed theoretically some of the available processing schemes for X-ray wavefront sensing based on random modulation. We here show experimental applications of the technique for characterising both refractive and reflective optical components. These fast and accurate X-ray at-wavelength metrology methods can assist the manufacture of X-ray optics that transport X-ray beams with minimum amount of wavefront distortion. We also recall how such methods can facilitate online optimization of active optics.

X-ray optics and beam characterisation using random modulation: Experiments.

X-ray near-field speckle-based phase-sensing approaches provide efficient means of characterizing optical elements. Presented here is a theoretical review of several of these speckle methods within the framework of optical characterization, and a generalization of the concept is provided. As is also demonstrated experimentally in a parallel paper [Berujon, Cojocaru, Piault, Celestre, Roth, Barrett & Ziegler (2020), J. Synchrotron Rad. 27, (this issue)], the methods theoretically developed here can be applied to different beams and optics and within a variety of situations where at-wavelength metrology is desired. By understanding the differences between the various processing methods, it is possible to find and implement the most suitable approach for each metrology scenario.

Rafael Celestre

Papers

X-ray optics and beam characterization using random modulation: experiments.

A hierarchical approach for modelling X-ray beamlines. Application to a coherent beamline

Smart multispectral imager for industrial applications

X-ray optics and beam characterisation using random modulation: Experiments.

X-ray optics and beam characterization using random modulation: theory.