scholarly journals Object Partitioning Using Local Convexity

2014 ◽  
Author(s):  
Simon Christoph Stein ◽  
Markus Schoeler ◽  
Jeremie Papon ◽  
Florentin Worgotter
Keyword(s):  
Local Convexity ◽  
Object Partitioning

scholarly journals Reduced statistical fluctuations of the position of an object partitioning in two its environment

2011 ◽  
Author(s):  
Eugenio DelRe ◽  
Paolo Di Porto ◽  
Stefano Di Sabatino ◽  
Bruno Crosignani ◽  
Daniel P. Sheehan
Keyword(s):  
Statistical Fluctuations ◽  
Object Partitioning

scholarly journals Local Convexity-PreservingC2Rational Cubic Spline for Convex Data

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammad Abbas ◽  
Ahmad Abd Majid ◽  
Jamaludin Md. Ali
Keyword(s):  
Shape Parameter ◽  
Cubic Spline ◽  
Convex Curve ◽  
Shape Feature ◽  
Local Convexity ◽  
Shape Parameters ◽  
Numerical Examples ◽  
2D Data ◽  
Industrial Demand ◽  
Made In

We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data usingC2rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing.

scholarly journals ULTRAMETRIC AND NON-LOCALLY CONVEX ANALOGUES OF THE GENERAL CURVE LEMMA OF CONVENIENT DIFFERENTIAL CALCULUS

2008 ◽  
Vol 50 (2) ◽  
pp. 271-288
Author(s):  
HELGE GLÖCKNER
Keyword(s):  
Differential Calculus ◽  
Vector Spaces ◽  
Local Convexity ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
General Curve ◽  
Infinite Dimensional Analysis ◽  
Locally Convex ◽  
Differentiability Properties ◽  
Made In

AbstractThe General Curve Lemma is a tool of Infinite-Dimensional Analysis that enables refined studies of differentiability properties of maps between real locally convex spaces to be made. In this article, we generalize the General Curve Lemma in two ways. First, we remove the condition of local convexity in the real case. Second, we adapt the lemma to the case of curves in topological vector spaces over ultrametric fields.

scholarly journals Scattered Point Cloud Data Reconstruction Algorithm Based on Local Convexity

2020 ◽  
Author(s):  
Sorush Niknamian
Keyword(s):  
Point Cloud ◽  
Reconstruction Algorithm ◽  
Large Error ◽  
Small Error ◽  
Data Reconstruction ◽  
Point Cloud Data ◽  
Local Convexity ◽  
Cloud Data ◽  
Time Consumption ◽  
Local Connection

Point cloud data reconstruction is the basis of point cloud data processing. The reconstruction effect has a great impact on application. For the problems of low precision, large error, and high time consumption of the current scattered point cloud data reconstruction algorithm, a new algorithm of scattered point cloud data reconstruction based on local convexity is proposed in this paper. Firstly, according to surface variation based on local outlier factor (SVLOF), the noise points of point cloud data are divided into near outlier and far outlier, and filtered for point cloud data preprocessing. Based on this, the algorithm based on local convexity is improved. The method of constructing local connection point set is used to replace triangulation to analyze the relationship of neighbor points. The connection part identification method is used for data reconstruction. Experimental results show that, the proposed method can reconstruct the scattered point cloud data accurately, with high precision, small error and low time consumption.

Improved local convexity algorithm of segmentation for 3D point cloud

2017 ◽  
Vol 10 (3) ◽  
pp. 348-354 ◽  
Author(s):  
王雅男 WANG Ya-nan ◽  
王挺峰 WANG Ting-feng ◽  
田玉珍 TIAN Yu-zhen ◽  
孙涛 SUN Tao
Keyword(s):  
Point Cloud ◽  
3D Point Cloud ◽  
Local Convexity

An n + 1 Member Decomposition for Sets Whose Lnc Points Form n Convex Sets

1975 ◽  
Vol 27 (6) ◽  
pp. 1378-1383 ◽  
Author(s):  
Marilyn Breen
Keyword(s):  
Convex Sets ◽  
Local Convexity ◽  
Locally Convex

Let S be a subset of Rd. A point x in 5 is a point of local convexity of S if and only if there is some neighborhood N of x such that, if y, z ∈ N ᑎ 5, then [y, z] ⊆ S. If S fails to be locally convex at some point q in S then q is called a point of local nonconvexity (lnc point) of S.

scholarly journals The Goldilocks Zone: Towards Better Understanding of Neural Network Loss Landscapes

2019 ◽  
Vol 33 ◽  
pp. 3574-3581
Author(s):  
Stanislav Fort ◽  
Adam Scherlis
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Configuration Space ◽  
Loss Function ◽  
Positive Curvature ◽  
Local Convexity ◽  
Convolutional Networks ◽  
Hollow Spherical Shell ◽  
Low Dimensional ◽  
Fully Connected

We explore the loss landscape of fully-connected and convolutional neural networks using random, low-dimensional hyperplanes and hyperspheres. Evaluating the Hessian, H, of the loss function on these hypersurfaces, we observe 1) an unusual excess of the number of positive eigenvalues of H, and 2) a large value of Tr(H)/||H|| at a well defined range of configuration space radii, corresponding to a thick, hollow, spherical shell we refer to as the Goldilocks zone. We observe this effect for fully-connected neural networks over a range of network widths and depths on MNIST and CIFAR-10 datasets with the ReLU and tanh non-linearities, and a similar effect for convolutional networks. Using our observations, we demonstrate a close connection between the Goldilocks zone, measures of local convexity/prevalence of positive curvature, and the suitability of a network initialization. We show that the high and stable accuracy reached when optimizing on random, low-dimensional hypersurfaces is directly related to the overlap between the hypersurface and the Goldilocks zone, and as a corollary demonstrate that the notion of intrinsic dimension is initialization-dependent. We note that common initialization techniques initialize neural networks in this particular region of unusually high convexity/prevalence of positive curvature, and offer a geometric intuition for their success. Furthermore, we demonstrate that initializing a neural network at a number of points and selecting for high measures of local convexity such as Tr(H)/||H||, number of positive eigenvalues of H, or low initial loss, leads to statistically significantly faster training on MNIST. Based on our observations, we hypothesize that the Goldilocks zone contains an unusually high density of suitable initialization configurations.

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