19,862 research outputs found
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
A local Gaussian filter and adaptive morphology as tools for completing partially discontinuous curves
This paper presents a method for extraction and analysis of curve--type
structures which consist of disconnected components. Such structures are found
in electron--microscopy (EM) images of metal nanograins, which are widely used
in the field of nanosensor technology.
The topography of metal nanograins in compound nanomaterials is crucial to
nanosensor characteristics. The method of completing such templates consists of
three steps. In the first step, a local Gaussian filter is used with different
weights for each neighborhood. In the second step, an adaptive morphology
operation is applied to detect the endpoints of curve segments and connect
them. In the last step, pruning is employed to extract a curve which optimally
fits the template
Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification
We present an efficient method for classifying the morphology of the
intersection curve of two quadrics (QSIC) in PR3, 3D real projective space;
here, the term morphology is used in a broad sense to mean the shape,
topological, and algebraic properties of a QSIC, including singularity,
reducibility, the number of connected components, and the degree of each
irreducible component, etc. There are in total 35 different QSIC morphologies
with non-degenerate quadric pencils. For each of these 35 QSIC morphologies,
through a detailed study of the eigenvalue curve and the index function jump we
establish a characterizing algebraic condition expressed in terms of the Segre
characteristics and the signature sequence of a quadric pencil. We show how to
compute a signature sequence with rational arithmetic so as to determine the
morphology of the intersection curve of any two given quadrics. Two immediate
applications of our results are the robust topological classification of QSIC
in computing B-rep surface representation in solid modeling and the derivation
of algebraic conditions for collision detection of quadric primitives
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