2,332 research outputs found
Estimating Multidimensional Persistent Homology through a Finite Sampling
An exact computation of the persistent Betti numbers of a submanifold of
a Euclidean space is possible only in a theoretical setting. In practical
situations, only a finite sample of is available. We show that, under
suitable density conditions, it is possible to estimate the multidimensional
persistent Betti numbers of from the ones of a union of balls centered on
the sample points; this even yields the exact value in restricted areas of the
domain.
Using these inequalities we improve a previous lower bound for the natural
pseudodistance to assess dissimilarity between the shapes of two objects from a
sampling of them.
Similar inequalities are proved for the multidimensional persistent Betti
numbers of the ball union and the one of a combinatorial description of it
Real-time monitoring of apples (Malus domestica var. Gala) during hot-air drying using NIR spectroscopy
Among commercial fruits, apple shows a growing trend to its worldwide consumption, where dried apple plays a major part in food industry as raw material to produce snacks, integral breakfast foods, chips, etc., which have become popular in the diet of modern consumers in parallel with the human consumption of organic products. Despite apple tissue exhibits extensive and non-homogeneous discoloration during drying, it is nowadays often dried by conventional methods which, however, are usually uncontrolled and then prone to product quality deterioration. However, because no all conventional drying treatments are allowed by the European Organic Regulation (i.e. EC No. 834/2007 and EC No. 889/2008), drying of organic apples should be carefully optimized to obtain comparable results to conventional methods. Therefore, the main objective of the proposed study was to investigate the feasibility of near-infrared (NIR) spectroscopy as smart drying technology to proactively and non-destructively detect and monitor quality change in organic apple wedges during hot-air drying
Beyond topological persistence: Starting from networks
Persistent homology enables fast and computable comparison of topological
objects. However, it is naturally limited to the analysis of topological
spaces. We extend the theory of persistence, by guaranteeing robustness and
computability to significant data types as simple graphs and quivers. We focus
on categorical persistence functions that allow us to study in full generality
strong kinds of connectedness such as clique communities, -vertex and
-edge connectedness directly on simple graphs and monic coherent categories.Comment: arXiv admin note: text overlap with arXiv:1707.0967
Size Functions for the Morphological Analysis of Melanocytic Lesions
Size Functions and Support Vector Machines are used to implement a new automatic classifier of melanocytic lesions. This is mainly based on a qualitative assessment of asymmetry, performed by halving images by several lines through the center of mass, and comparing the two halves in terms of color, mass distribution, and boundary. The program is used, at clinical level, with two thresholds, so that comparison of the two outputs produces a report of low-middle-high risk. Experimental results on 977 images, with cross-validation, are reported
Multidimensional persistent homology is stable
Multidimensional persistence studies topological features of shapes by
analyzing the lower level sets of vector-valued functions. The rank invariant
completely determines the multidimensional analogue of persistent homology
groups. We prove that multidimensional rank invariants are stable with respect
to function perturbations. More precisely, we construct a distance between rank
invariants such that small changes of the function imply only small changes of
the rank invariant. This result can be obtained by assuming the function to be
just continuous. Multidimensional stability opens the way to a stable shape
comparison methodology based on multidimensional persistence.Comment: 14 pages, 3 figure
Estimating multidimensional persistent homology through a finite sampling
An exact computation of the persistent Betti numbers of a submanifold X of a Euclidean space is possible only in a theoretical setting. In practical situations, only a finite sample of X is available. We show that, under suitable density conditions, it is possible to estimate the multidimensional persistent Betti numbers of X from the ones of a union of balls centered on the sample points;
this even yields the exact value in restricted areas of the domain.
Similar inequalities are proved for the multidimensional persistent Betti numbers of the ball union and the one of a combinatorial description of it
Local Triangle Choice for Impact Computation in the Tactile Exploration of a Virtual Surface
Evaluating the intersection of the trajectory of the exploring finger, with the virtual surface representing the scene, is
a key problem in the VIDET project of an aid for the visually
impaired. A substitute for Delaunay triangulation, which permits
of local computation for that goal, is proposed
Steady and ranging sets in graph persistence
Generalised persistence functions (gp-functions) are defined on -indexed diagrams in a given category. A sufficient condition for
stability is also introduced. In the category of graphs, a standard way of
producing gp-functions is proposed: steady and ranging sets for a given
feature. The example of steady and ranging hubs is studied in depth; their
meaning is investigated in three concrete networks
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