Normal Map Research Articles

Reproducing Gloss Unevenness on Printed Paper Based on the Measurement and Analysis of Mesoscopic Facets

In this article, the authors reproduce gloss unevenness on a paper surface by expanding the Torrance‐Sparrow model, which is based on the measurement and analysis of mesoscopic facets on paper. As the conventional Torrance‐Sparrow model only considers macroscopic and microscopic facets, the authors expand the model to be able to consider mesoscopic facets. The normal vectors of mesoscopic facets on a paper surface were measured by using a collimator lens system with a small pinhole aperture, and the authors obtained the normal vector map by moving the stage for the paper. Gloss unevenness was reproduced by generating the same probability distribution as the measured distribution of the normal vectors. As a result, the authors succeeded in reproducing gloss unevenness using an expanded Torrance‐Sparrow model.

On Stability of M-stationary Points in MPCCs

We consider parameterized Mathematical Programs with Complementarity Constraints arising, e.g., in modeling of deregulated electricity markets. Using the standard rules of the generalized differential calculus we analyze qualitative stability of solutions to the respective M-stationarity conditions. In particular, we provide characterizations and criteria for the isolated calmness and the Aubin properties of the stationarity map. To this end, we introduce the second-order limiting coderivative of mappings and provide formulas for this notion and for the graphical derivative of the limiting coderivative in the case of the normal cone mapping to \(\mathbb {R}^{n}_{+}\).

Modeling of Pixelated Detector in SPECT Pinhole Reconstruction.

A challenge for the pixelated detector is that the detector response of a gamma-ray photon varies with the incident angle and the incident location within a crystal. The normalization map obtained by measuring the flood of a point-source at a large distance can lead to artifacts in reconstructed images. In this work, we investigated a method of generating normalization maps by ray-tracing through the pixelated detector based on the imaging geometry and the photo-peak energy for the specific isotope. The normalization is defined for each pinhole as the normalized detector response for a point-source placed at the focal point of the pinhole. Ray-tracing is used to generate the ideal flood image for a point-source. Each crystal pitch area on the back of the detector is divided into 60 × 60 sub-pixels. Lines are obtained by connecting between a point-source and the centers of sub-pixels inside each crystal pitch area. For each line ray-tracing starts from the entrance point at the detector face and ends at the center of a sub-pixel on the back of the detector. Only the attenuation by NaI(Tl) crystals along each ray is assumed to contribute directly to the flood image. The attenuation by the silica (SiO2) reflector is also included in the ray-tracing. To calculate the normalization for a pinhole, we need to calculate the ideal flood for a point-source at 360 mm distance (where the point-source was placed for the regular flood measurement) and the ideal flood image for the point-source at the pinhole focal point, together with the flood measurement at 360 mm distance. The normalizations are incorporated in the iterative OSEM reconstruction as a component of the projection matrix. Applications to single-pinhole and multi-pinhole imaging showed that this method greatly reduced the reconstruction artifacts.

(99m)Tc-hexamethyl propyleneamine oxime brain perfusion single photon emission computed tomography in characterization of dementia: an initial experience in Indian clinical practice.

There is a growing health burden in developing countries due to recent trends of increasing incidence of neurodegenerative diseases. To reduce the healthcare cost and effective management of dementia illness, early diagnosis, accurate differentiation and their progression assessment is becoming crucially important. We are utilizing 99mTc-d, l-hexamethyl propyleneamine oxime (HMPAO) brain perfusion single photon emission computed tomography (SPECT) to characterize dementia on the basis of perfusion patterns and observed significant improvement in their management. Eleven patients (median age of 60 years range of 53-83 years) with clinical suspicion of dementia underwent 99mTc-HMPAO brain perfusion SPECT. SPECT-computed tomography acquisition done, data are reconstructed, reviewed in three view and further processed in “neurogam” to get voxel based analysis and the comparison with age based normal database and surface mapping. Final diagnosis was done with clinical correlation. Four patients are diagnosed as Alzheimer's disease, two as frontotemporal dementia, one as dementia of Lewy bodies, two as vascular dementia and two as pseudodementia. All imaging findings are well-correlated with clinical background. Brain perfusion SPECT with HMPAO was very helpful to us in characterizing the patients of dementia by its perfusion pattern.

Integrated topographic, photometric and spectral analysis of the lunar surface: Application to impact melt flows and ponds

This study provides an analysis of the impact melt deposits (melt flows and ponds) associated with eight lunar craters with diameters between 9 and 96km in terms of their topographic, photometric and spectral properties. Our analysis is based on an integrated method for construction of digital elevation models (DEM) of high lateral resolution, pixel-wise photometric modelling, construction of topographically corrected normalised reflectance maps, extraction of spectral parameters and estimation of elemental abundances based on Moon Mineralogy Mapper (M3) hyperspectral data and data of the Lunar Prospector Gamma Ray Spectrometer instrument. Most of the examined geologically fresh impact melt flows are characterised by lower albedos than the surrounding surface and tend to originate from topographically low parts of the source crater rim. As an exception, we find that the impact melt deposits northeast of crater Aristillus lack any optical signature and are not visible in monochrome images, but can only be observed by their anomalously smooth surface inferred from the DEM. Some impact melt flows and ponds exhibit photometric anomalies in terms of the asymmetries in the single-particle scattering function and the slope of that parameter with respect to wavelength. These photometric anomalies may be due to impact melt specific anomalies of the surface structure, e.g. consolidated rock rather than regolith, or anomalies in size or shape of the geometric surface elements (e.g. individual grains or their aggregates) on submillimetre spatial scales. The strength of the hydroxyl absorption displays a negative anomaly with respect to the surrounding surface for the majority of the examined impact melt flows. As an impact melt specific spectral behaviour, we find a decrease in the absorption band depth around 2000nm and (in several cases) a simultaneous increase of the absorption band depth near 1000nm. These observations are consistent with the laboratory analyses by Tompkins et al. (Tompkins, S., Pieters, C.M. [2010]. Meteorit. Planet. Sci. 45 (7), 1152–1169) of chemically uniformly composed mixtures between crystalline and glass material. For several impact melt flows, their data allow to roughly estimate the fraction of glass material based on our spectral analysis.

Stripe-rearing changes multiple aspects of the structure of primary visual cortex

An important example of brain plasticity is the change in the structure of the orientation map in mammalian primary visual cortex in response to a visual environment consisting of stripes of one orientation. In principle there are many different ways in which the structure of a normal map could change to accommodate increased preference for one orientation. However, until now these changes have been characterised only by the relative sizes of the areas of primary visual cortex representing different orientations. Here we extend to the stripe-reared case a recently proposed Bayesian method for reconstructing orientation maps from intrinsic signal optical imaging data. We first formulated a suitable prior for the stripe-reared case, and developed an efficient method for maximising the marginal likelihood of the model in order to determine the optimal parameters. We then applied this to a set of orientation maps from normal and stripe-reared cats. This analysis revealed that several parameters of overall map structure, specifically the difference between wavelength, scaling and mean of the two vector components of maps, changed in response to stripe-rearing, which together give a more nuanced assessment of the effect of rearing condition on map structure than previous measures. Overall this work expands our understanding of the effects of the environment on brain structure.

Taut submanifolds and foliations

We give an equivalent description of taut submanifolds of complete Riemannian manifolds as exactly those submanifolds whose normal exponential map has the property that every preimage of a point is a union of submanifolds. It turns out that every taut submanifold is also $\mathbb{Z}_2$-taut. We explicitly construct generalized Bott-Samelson cycles for the critical points of the energy functionals on the path spaces of a taut submanifold that, generically, represent a basis for the $\mathbb{Z}_2$-cohomology. We also consider singular Riemannian foliations all of whose leaves are taut. Using our characterization of taut submanifolds, we are able to show that tautness of a singular Riemannian foliation is actually a property of the quotient.

Comments on: Farkas’ lemma: three decades of generalizations for mathematical optimization

In these comments on the excellent survey by Dinh and Jeyakumar, we briefly discuss some recently developed topics and results on applications of extended Farkas’ lemma(s) and related qualification conditions to problems of variational analysis and optimization, which are not fully reflected in the survey. They mainly concern: Lipschitzian stability of feasible solution maps for parameterized semi-infinite and infinite programs with linear and convex inequality constraints indexed by arbitrary sets; optimality conditions for nonsmooth problems involving such constraints; evaluating various subdifferentials of optimal value functions in DC and bilevel infinite programs with applications to Lipschitz continuity of value functions and optimality conditions; calculating and estimating normal cones to feasible solution sets for nonlinear smooth as well as nonsmooth semi-infinite, infinite, and conic programs with deriving necessary optimality conditions for them; calculating coderivatives of normal cone mappings for convex polyhedra in finite and infinite dimensions with applications to robust stability of parameterized variational inequalities. We also give some historical comments on the original Farkas’ papers.

Normal map recovery using bundle adjustment

Although modern reconstruction methods have advanced considerably, their ability to retrieve fine details, small features of a surface is limited. Applying texture can be used to conceal lack of geometry to some extent, but it becomes apparent when lighting varies. A more sophisticated solution is to map normal vectors to the surface of the model in order to alter the way it is rendered under different illuminations in accordance with the properties of the real object. The principle of photometric stereo is to reconstruct normals from a series of images. By illuminating the object with different directional light sources local surface orientation can be inferred. The contribution of this study is that the authors successfully applied the widely used bundle adjustment algorithm to photometric stereo problems when non‐parallel light rays illuminate the objects.

A Class of Linear Generalized Equations

Solution stability of a class of linear generalized equations in finite dimensional Euclidean spaces is investigated by means of generalized differentiation. Exact formulas for the Frechet and the Mordukhovich coderivatives of the normal cone mappings of perturbed Euclidean balls are obtained. Necessary and sufficient conditions for the local Lipschitz-like property of the solution maps of such linear generalized equations are derived from these coderivative formulas. Since the trust-region subproblems in nonlinear programming can be regarded as linear generalized equations, these conditions lead to new results on stability of the parametric trust-region subproblems.

Geometric Subdivision Based on the Mosaic View Related PN-Patch for Multifunctional Materials

To the problem of memory consumption caused by the method based on GPU geometric segments, this paper used the new features of DX11 inlaid the PN-Patch geometric segmentation to resolve. Mixed triangular and quadrilateral mesh, combined with displacement maps and normal maps to get rich surface details with reasonable viewpoint mosaic factor calculation method.

Symmetric Confidence Regions and Confidence Intervals for Normal Map Formulations of Stochastic Variational Inequalities

Stochastic variational inequalities (SVIs) model a large class of equilibrium problems subject to data uncertainty and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method for building asymptotically exact confidence regions and confidence intervals for the solution of the normal map formulation, based on the asymptotic distribution of SAA solutions. The confidence regions are single ellipsoids with high probability. We also discuss the computation of simultaneous and individual confidence intervals.

Photometric stereo-based single time-of-flight camera

We present a method to enhance depth quality of a time-of-flight (ToF) camera without additional devices or hardware modifications. By controlling the turn-off patterns of the LEDs of the camera, we obtain depth and normal maps simultaneously. Sixteen subphase images are acquired with variations in gate-pulse timing and light emission pattern of the camera. The subphase images allow us to obtain a normal map, which are combined with depth maps for improved depth details. These details typically cannot be captured by conventional ToF cameras. By the proposed method, the average of absolute differences between the measured and laser-scanned depth maps has decreased from 4.57 to 3.77 mm.

Mapping Alberta's surface water resources for the period 1971–2000

AbstractAlthough the sustainability and wealth of Alberta is closely linked to the quantity, quality, and management of its water resources, the province lacks watershed‐based inventories of its water supplies. The mean annual water yield for 287 gauged watersheds across Alberta was calculated for the period 1971–2000 by relating available streamflow records with the respective watershed areas. The percent contribution of each watershed relative to the outlet of each of the 16 major river basins located in Alberta was computed, which enabled the identification of the most important water‐producing regions. The integration of high‐resolution precipitation normal maps, available for the same period, enabled the calculation of mean annual runoff coefficients and the determination of mean annual regional water balances. These analyses resulted in important water resources baseline data, against which impacts of environmental and climate change can be compared. All data are available online in the form of spreadsheets and shapefiles.

The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature

In this paper we are concerned with the image of the normal Gauss map of a minimal surface immersed in ℝ3 with finite total curvature. We give a different proof of the following theorem of R. Osserman: The normal Gauss map of a minimal surface immersed in ℝ3 with finite total curvature, which is not a plane, omits at most three points of��2 Moreover, under an additional hypothesis on the type of ends, we prove that this number is exactly 2.

A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima

Images of an object under different illumination are known to provide strong cues about the object surface. A mathematical formalization of how to recover the normal map of such a surface leads to the so-called uncalibrated photometric stereo problem. In the simplest instance, this problem can be reduced to the task of identifying only three parameters: the so-called generalized bas-relief (GBR) ambiguity. The challenge is to find additional general assumptions about the object, that identify these parameters uniquely. Current approaches are not consistent, i.e., they provide different solutions when run multiple times on the same data. To address this limitation, we propose exploiting local diffuse reflectance (LDR) maxima, i.e., points in the scene where the normal vector is parallel to the illumination direction (see Fig. 1). We demonstrate several noteworthy properties of these maxima: a closed-form solution, computational efficiency and GBR consistency. An LDR maximum yields a simple closed-form solution corresponding to a semi-circle in the GBR parameters space (see Fig. 2); because as few as two diffuse maxima in different images identify a unique solution, the identification of the GBR parameters can be achieved very efficiently; finally, the algorithm is consistent as it always returns the same solution given the same data. Our algorithm is also remarkably robust: It can obtain an accurate estimate of the GBR parameters even with extremely high levels of outliers in the detected maxima (up to 80 % of the observations). The method is validated on real data and achieves state-of-the-art results.

Describing 3-paths in normal plane maps

We prove that every normal plane map, as well as every 3-polytope, has a path on three vertices whose degrees are bounded from above by one of the following triplets: (3,3,∞), (3,4,11), (3,7,5), (3,10,4), (3,15,3), (4,4,9), (6,4,8), (7,4,7), and (6,5,6). No parameter of this description can be improved, as shown by appropriate 3-polytopes.

A Super-Resolution Framework for High-Accuracy Multiview Reconstruction

We present a variational framework to estimate super-resolved texture maps on a 3D geometry model of a surface from multiple images. Given the calibrated images and the reconstructed geometry, the proposed functional is convex in the super-resolution texture. Using a conformal atlas of the surface, we transform the model from the curved geometry to the flat charts and solve it using state-of-the-art and provably convergent primal–dual algorithms. In order to improve image alignment and quality of the texture, we extend the functional to also optimize for a normal displacement map on the surface as well as the camera calibration parameters. Since the sub-problems for displacement and camera parameters are non-convex, we revert to relaxation schemes in order to robustly estimate a minimizer via sequential convex programming. Experimental results confirm that the proposed super-resolution framework allows to recover textured models with significantly higher level-of-detail than the individual input images.

Stability for trust-region methods via generalized differentiation

We obtain necessary and sufficient conditions for local Lipschitz-like property and sufficient conditions for local metric regularity in Robinson's sense of Karush---Kuhn---Tucker point set maps of trust-region subproblems in trust-region methods. The main tools being used in our investigation are dual criteria for fundamental properties of implicit multifunctions which are established on the basis of generalized differentiation of normal cone mappings.

Rapid Reflective Facet Characterization Using Fringe Reflection Techniques

Reflective mirror facets for concentrating solar power (CSP) systems have stringent requirements on the surface slope accuracy in order to provide adequate system performance. This paper presents a tool that can fully characterize facets quickly enough for 100% inspection on a production line. A facet for a CSP system, specifically a dish concentrator has a parabolic design shape. This shape will concentrate near-parallel rays from the sun to a point (or a line for trough systems). Deviations of surface slope from the design shape impact the performance of the system, either losing power that misses the target or increasing peak fluxes to undesirable levels. During development or production, accurate knowledge of facet defects can lead to improvements to lower cost or improve performance. The reported characterization system, SOFAST (Sandia Optical Fringe Analysis Slope Tool), has a computer-connected camera that images the reflective surface, which is positioned so that it reflects an active target, such as an LCD screen, to the camera. A series of fringe patterns are displayed on the screen while images are captured. Using the captured information, the reflected target location of each pixel of mirror viewed can be determined, and thus through a mathematical transformation, a surface normal map can be developed. This is then fitted to the selected model equation, and the errors from design are characterized. While similar approaches have been explored, several key developments are presented here. The combination of the display, capture, and data reduction in one system allows rapid characterization. An “electronic boresight” approach is utilized to accommodate physical equipment positioning deviations, making the system insensitive to setup errors. Up to 1.5 × 106 points are characterized on each facet. Finally, while prior automotive industry commercial systems resolve the data to shape determination, SOFAST concentrates on slope characterization and reporting, which is tailored to solar applications. SOFAST can be used for facet analysis during development. However, the real payoff is in production, where complete analysis is performed in about 10 s. With optimized coding, this could be further reduced.