Geometrical redundancy of street patterns based on threshold of isoperimetric ratio

2014 ◽  
pp. 101-110
Keyword(s):  
Isoperimetric Ratio

On submanifolds of highly negatively curved spaces

2014 ◽  
Vol 25 (06) ◽  
pp. 1450055
Author(s):  
G. Pacelli Bessa ◽  
Stefano Pigola ◽  
Alberto G. Setti
Keyword(s):  
Mean Curvature ◽  
Curved Spaces ◽  
Negatively Curved ◽  
Curvature Estimates ◽  
Isoperimetric Ratio

We prove spectral, stochastic and mean curvature estimates for complete m-submanifolds φ : M → N of n-manifolds with a pole N in terms of the comparison isoperimetric ratio Im and the extrinsic radius rφ ≤ ∞. Our proof holds for the bounded case rφ < ∞, recovering the known results, as well as for the unbounded case rφ = ∞. In both cases, the fundamental ingredient in these estimates is the integrability over (0, rφ) of the inverse [Formula: see text] of the comparison isoperimetric radius. When rφ = ∞, this condition is guaranteed if N is highly negatively curved.

An Improved Segmentation Algorithm for Infrared Imaging Object

2011 ◽  
Vol 467-469 ◽  
pp. 1770-1775
Author(s):  
Jin Liu ◽  
Mian Li ◽  
Hong Bing Ji
Keyword(s):  
Infrared Imaging ◽  
Sparse Matrix ◽  
Segmentation Algorithm ◽  
Experimental Results ◽  
Weight Matrix ◽  
Infrared Images ◽  
Traditional Methods ◽  
Threshold Segmentation ◽  
Isoperimetric Ratio ◽  
Optimum Threshold

In this paper, an improved threshold segmentation algorithm based on isoperimetric ratio for infrared imaging object is proposed. The segmentation weight matrix is constructed by computing the similarity among the pixies with 4 adjoining points and stored in a sparse matrix. The isoperimetric ratio is obtained after the indicator vectors are formed with 255 gray levels. The proposed algorithm selects the minimum isoperimetric ratio confined in conditions as the best partition criterion instead of the traditional minimum isoperimetric ratio. By analyzing the variation of isoperimetric ratio with the gray levels, the proposed method can find the optimum threshold to segment infrared imaging object. Experimental results show that compared with the traditional methods, the proposed algorithm can reach a higher segmentation rate and is more robust in different kinds of infrared images.

scholarly journals Polytopal approximation of elongated convex bodies

2018 ◽  
Vol 18 (1) ◽  
pp. 105-114
Author(s):  
Gilles Bonnet
Keyword(s):  
Convex Body ◽  
Best Approximation ◽  
Convex Set ◽  
Hausdorff Metric ◽  
Convex Bodies ◽  
The Best Approximation ◽  
Polytopal Approximation ◽  
Isoperimetric Ratio

AbstractThis paper presents bounds for the best approximation, with respect to the Hausdorff metric, of a convex bodyKby a circumscribed polytopePwith a given number of facets. These bounds are of particular interest ifKis elongated. To measure the elongation of the convex set, its isoperimetric ratioVj(K)1/jVi(K)−1/iis used.

scholarly journals An existence theorem on the isoperimetric ratio over scalar-flat conformal classes

2020 ◽  
Vol 269 (5) ◽  
pp. 4116-4136
Author(s):  
Xuezhang Chen ◽  
Tianling Jin ◽  
Yuping Ruan
Keyword(s):  
Existence Theorem ◽  
Isoperimetric Ratio
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