43,620 research outputs found
Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D
We propose an efficient approach for the grouping of local orientations
(points on vessels) via nilpotent approximations of sub-Riemannian distances in
the 2D and 3D roto-translation groups and . In our distance
approximations we consider homogeneous norms on nilpotent groups that locally
approximate , and which are obtained via the exponential and logarithmic
map on . In a qualitative validation we show that the norms provide
accurate approximations of the true sub-Riemannian distances, and we discuss
their relations to the fundamental solution of the sub-Laplacian on .
The quantitative experiments further confirm the accuracy of the
approximations. Quantitative results are obtained by evaluating perceptual
grouping performance of retinal blood vessels in 2D images and curves in
challenging 3D synthetic volumes. The results show that 1) sub-Riemannian
geometry is essential in achieving top performance and 2) that grouping via the
fast analytic approximations performs almost equally, or better, than
data-adaptive fast marching approaches on and .Comment: 18 pages, 9 figures, 3 tables, in review at JMI
From Multiview Image Curves to 3D Drawings
Reconstructing 3D scenes from multiple views has made impressive strides in
recent years, chiefly by correlating isolated feature points, intensity
patterns, or curvilinear structures. In the general setting - without
controlled acquisition, abundant texture, curves and surfaces following
specific models or limiting scene complexity - most methods produce unorganized
point clouds, meshes, or voxel representations, with some exceptions producing
unorganized clouds of 3D curve fragments. Ideally, many applications require
structured representations of curves, surfaces and their spatial relationships.
This paper presents a step in this direction by formulating an approach that
combines 2D image curves into a collection of 3D curves, with topological
connectivity between them represented as a 3D graph. This results in a 3D
drawing, which is complementary to surface representations in the same sense as
a 3D scaffold complements a tent taut over it. We evaluate our results against
truth on synthetic and real datasets.Comment: Expanded ECCV 2016 version with tweaked figures and including an
overview of the supplementary material available at
multiview-3d-drawing.sourceforge.ne
Classification of Hungarian medieval silver coins using x-ray fluorescent spectroscopy and multivariate data analysis
A set of silver coins from the collection of Déri Museum Debrecen (Hungary) was examined by X-ray
fluorescent elemental analysis with the aim to assign the coins to different groups with the best possible precision
based on the acquired chemical information and to build models, which arrange the coins according to their
historical periods.
Results: Principal component analysis, linear discriminant analysis, partial least squares discriminant analysis,
classification and regression trees and multivariate curve resolution with alternating least squares were applied to
reveal dominant pattern in the data and classify the coins into several groups. We also identified those chemical
components, which are present in small percentages, but are useful for the classification of the coins. With the
coins divided into two groups according to adequate historical periods, we have obtained a correct classification
(76-78%) based on the chemical compositions.
Conclusions: X-ray fluorescent elemental analysis together with multivariate data analysis methods is suitable to
group medieval coins according to historical periods.
Keywords: X-ray fluorescence spectroscopy, Multivariate techniques, Coin, Silver, Middle age
Environmental modeling and recognition for an autonomous land vehicle
An architecture for object modeling and recognition for an autonomous land vehicle is presented. Examples of objects of interest include terrain features, fields, roads, horizon features, trees, etc. The architecture is organized around a set of data bases for generic object models and perceptual structures, temporary memory for the instantiation of object and relational hypotheses, and a long term memory for storing stable hypotheses that are affixed to the terrain representation. Multiple inference processes operate over these databases. Researchers describe these particular components: the perceptual structure database, the grouping processes that operate over this, schemas, and the long term terrain database. A processing example that matches predictions from the long term terrain model to imagery, extracts significant perceptual structures for consideration as potential landmarks, and extracts a relational structure to update the long term terrain database is given
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