18,937 research outputs found
Designing Illumination Lenses and Mirrors by the Numerical Solution of Monge-Amp\`ere Equations
We consider the inverse refractor and the inverse reflector problem. The task
is to design a free-form lens or a free-form mirror that, when illuminated by a
point light source, produces a given illumination pattern on a target. Both
problems can be modeled by strongly nonlinear second-order partial differential
equations of Monge-Amp\`ere type. In [Math. Models Methods Appl. Sci. 25
(2015), pp. 803--837, DOI: 10.1142/S0218202515500190] the authors have proposed
a B-spline collocation method which has been applied to the inverse reflector
problem. Now this approach is extended to the inverse refractor problem. We
explain in depth the collocation method and how to handle boundary conditions
and constraints. The paper concludes with numerical results of refracting and
reflecting optical surfaces and their verification via ray tracing.Comment: 16 pages, 6 figures, 2 tables; Keywords: Inverse refractor problem,
inverse reflector problem, elliptic Monge-Amp\`ere equation, B-spline
collocation method, Picard-type iteration; OCIS: 000.4430, 080.1753,
080.4225, 080.4228, 080.4298, 100.3190. Minor revision: two typos have been
corrected and copyright note has been adde
Flux-Limited Diffusion for Multiple Scattering in Participating Media
For the rendering of multiple scattering effects in participating media,
methods based on the diffusion approximation are an extremely efficient
alternative to Monte Carlo path tracing. However, in sufficiently transparent
regions, classical diffusion approximation suffers from non-physical radiative
fluxes which leads to a poor match to correct light transport. In particular,
this prevents the application of classical diffusion approximation to
heterogeneous media, where opaque material is embedded within transparent
regions. To address this limitation, we introduce flux-limited diffusion, a
technique from the astrophysics domain. This method provides a better
approximation to light transport than classical diffusion approximation,
particularly when applied to heterogeneous media, and hence broadens the
applicability of diffusion-based techniques. We provide an algorithm for
flux-limited diffusion, which is validated using the transport theory for a
point light source in an infinite homogeneous medium. We further demonstrate
that our implementation of flux-limited diffusion produces more accurate
renderings of multiple scattering in various heterogeneous datasets than
classical diffusion approximation, by comparing both methods to ground truth
renderings obtained via volumetric path tracing.Comment: Accepted in Computer Graphics Foru
On Algorithms Based on Joint Estimation of Currents and Contrast in Microwave Tomography
This paper deals with improvements to the contrast source inversion method
which is widely used in microwave tomography. First, the method is reviewed and
weaknesses of both the criterion form and the optimization strategy are
underlined. Then, two new algorithms are proposed. Both of them are based on
the same criterion, similar but more robust than the one used in contrast
source inversion. The first technique keeps the main characteristics of the
contrast source inversion optimization scheme but is based on a better
exploitation of the conjugate gradient algorithm. The second technique is based
on a preconditioned conjugate gradient algorithm and performs simultaneous
updates of sets of unknowns that are normally processed sequentially. Both
techniques are shown to be more efficient than original contrast source
inversion.Comment: 12 pages, 12 figures, 5 table
3D differential phase contrast microscopy
We demonstrate 3D phase and absorption recovery from partially coherent intensity images captured with a programmable LED array source. Images are captured through-focus with four different illumination patterns. Using first Born and weak object approximations (WOA), a linear 3D differential phase contrast (DPC) model is derived. The partially coherent transfer functions relate the sample's complex refractive index distribution to intensity measurements at varying defocus. Volumetric reconstruction is achieved by a global FFT-based method, without an intermediate 2D phase retrieval step. Because the illumination is spatially partially coherent, the transverse resolution of the reconstructed field achieves twice the NA of coherent systems and improved axial resolution
A Novel Framework for Highlight Reflectance Transformation Imaging
We propose a novel pipeline and related software tools for processing the multi-light image collections (MLICs) acquired in different application contexts to obtain shape and appearance information of captured surfaces, as well as to derive compact relightable representations of them. Our pipeline extends the popular Highlight Reflectance Transformation Imaging (H-RTI) framework, which is widely used in the Cultural Heritage domain. We support, in particular, perspective camera modeling, per-pixel interpolated light direction estimation, as well as light normalization correcting vignetting and uneven non-directional illumination. Furthermore, we propose two novel easy-to-use software tools to simplify all processing steps. The tools, in addition to support easy processing and encoding of pixel data, implement a variety of visualizations, as well as multiple reflectance-model-fitting options. Experimental tests on synthetic and real-world MLICs demonstrate the usefulness of the novel algorithmic framework and the potential benefits of the proposed tools for end-user applications.Terms: "European Union (EU)" & "Horizon 2020" / Action: H2020-EU.3.6.3. - Reflective societies - cultural heritage and European identity / Acronym: Scan4Reco / Grant number: 665091DSURF project (PRIN 2015) funded by the Italian Ministry of University and ResearchSardinian Regional Authorities under projects VIGEC and Vis&VideoLa
Graph-based classification of multiple observation sets
We consider the problem of classification of an object given multiple
observations that possibly include different transformations. The possible
transformations of the object generally span a low-dimensional manifold in the
original signal space. We propose to take advantage of this manifold structure
for the effective classification of the object represented by the observation
set. In particular, we design a low complexity solution that is able to exploit
the properties of the data manifolds with a graph-based algorithm. Hence, we
formulate the computation of the unknown label matrix as a smoothing process on
the manifold under the constraint that all observations represent an object of
one single class. It results into a discrete optimization problem, which can be
solved by an efficient and low complexity algorithm. We demonstrate the
performance of the proposed graph-based algorithm in the classification of sets
of multiple images. Moreover, we show its high potential in video-based face
recognition, where it outperforms state-of-the-art solutions that fall short of
exploiting the manifold structure of the face image data sets.Comment: New content adde
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