956 research outputs found
Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves
Given a real valued function f(X,Y), a box region B_0 in R^2 and a positive
epsilon, we want to compute an epsilon-isotopic polygonal approximation to the
restriction of the curve S=f^{-1}(0)={p in R^2: f(p)=0} to B_0. We focus on
subdivision algorithms because of their adaptive complexity and ease of
implementation. Plantinga and Vegter gave a numerical subdivision algorithm
that is exact when the curve S is bounded and non-singular. They used a
computational model that relied only on function evaluation and interval
arithmetic. We generalize their algorithm to any bounded (but possibly
non-simply connected) region that does not contain singularities of S. With
this generalization as a subroutine, we provide a method to detect isolated
algebraic singularities and their branching degree. This appears to be the
first complete purely numerical method to compute isotopic approximations of
algebraic curves with isolated singularities
Quadtrees as an Abstract Domain
Quadtrees have proved popular in computer graphics and spatial databases as a way of representing regions in two dimensional space. This hierarchical data-structure is flexible enough to support non-convex and even disconnected regions, therefore it is natural to ask whether this datastructure can form the basis of an abstract domain. This paper explores this question and suggests that quadtrees offer a new approach to weakly relational domains whilst their hierarchical structure naturally lends itself to representation with boolean functions
Discrete denoising of heterogenous two-dimensional data
We consider discrete denoising of two-dimensional data with characteristics
that may be varying abruptly between regions.
Using a quadtree decomposition technique and space-filling curves, we extend
the recently developed S-DUDE (Shifting Discrete Universal DEnoiser), which was
tailored to one-dimensional data, to the two-dimensional case. Our scheme
competes with a genie that has access, in addition to the noisy data, also to
the underlying noiseless data, and can employ different two-dimensional
sliding window denoisers along distinct regions obtained by a quadtree
decomposition with leaves, in a way that minimizes the overall loss. We
show that, regardless of what the underlying noiseless data may be, the
two-dimensional S-DUDE performs essentially as well as this genie, provided
that the number of distinct regions satisfies , where is the total
size of the data. The resulting algorithm complexity is still linear in both
and , as in the one-dimensional case. Our experimental results show that
the two-dimensional S-DUDE can be effective when the characteristics of the
underlying clean image vary across different regions in the data.Comment: 16 pages, submitted to IEEE Transactions on Information Theor
Simultaneous multi-band detection of Low Surface Brightness galaxies with Markovian modelling
We present an algorithm for the detection of Low Surface Brightness (LSB)
galaxies in images, called MARSIAA (MARkovian Software for Image Analysis in
Astronomy), which is based on multi-scale Markovian modeling. MARSIAA can be
applied simultaneously to different bands. It segments an image into a
user-defined number of classes, according to their surface brightness and
surroundings - typically, one or two classes contain the LSB structures. We
have developed an algorithm, called DetectLSB, which allows the efficient
identification of LSB galaxies from among the candidate sources selected by
MARSIAA. To assess the robustness of our method, the method was applied to a
set of 18 B and I band images (covering 1.3 square degrees in total) of the
Virgo cluster. To further assess the completeness of the results of our method,
both MARSIAA, SExtractor, and DetectLSB were applied to search for (i) mock
Virgo LSB galaxies inserted into a set of deep Next Generation Virgo Survey
(NGVS) gri-band subimages and (ii) Virgo LSB galaxies identified by eye in a
full set of NGVS square degree gri images. MARSIAA/DetectLSB recovered ~20%
more mock LSB galaxies and ~40% more LSB galaxies identified by eye than
SExtractor/DetectLSB. With a 90% fraction of false positives from an entirely
unsupervised pipeline, a completeness of 90% is reached for sources with r_e >
3" at a mean surface brightness level of mu_g=27.7 mag/arcsec^2 and a central
surface brightness of mu^0 g=26.7 mag/arcsec^2. About 10% of the false
positives are artifacts, the rest being background galaxies. We have found our
method to be complementary to the application of matched filters and an
optimized use of SExtractor, and to have the following advantages: it is
scale-free, can be applied simultaneously to several bands, and is well adapted
for crowded regions on the sky.Comment: 39 pages, 18 figures, accepted for publication in A
Measuring Visual Consistency in 3D Rendering Systems
One of the major challenges facing a present day game development company is the removal of bugs from such complex virtual environments. This work presents an approach for measuring the correctness of synthetic scenes generated by a rendering system of a 3D application, such as a computer game. Our approach builds a database of labelled point clouds representing the spatiotemporal colour distribution for the objects present in a sequence of bug-free frames. This is done by converting the position that the pixels take over time into the 3D equivalent points with associated colours. Once the space of labelled points is built, each new image produced from the same game by any rendering system can be analysed by measuring its visual inconsistency in terms of distance from the database. Objects within the scene can be relocated (manually or by the application engine); yet the algorithm is able to perform the image analysis in terms of the 3D structure and colour distribution of samples on the surface of the object. We applied our framework to the publicly available game RacingGame developed for Microsoft(R) Xna(R). Preliminary results show how this approach can be used to detect a variety of visual artifacts generated by the rendering system in a professional quality game engine
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