1,701,990 research outputs found
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
We introduce a new framework for learning dense correspondence between
deformable 3D shapes. Existing learning based approaches model shape
correspondence as a labelling problem, where each point of a query shape
receives a label identifying a point on some reference domain; the
correspondence is then constructed a posteriori by composing the label
predictions of two input shapes. We propose a paradigm shift and design a
structured prediction model in the space of functional maps, linear operators
that provide a compact representation of the correspondence. We model the
learning process via a deep residual network which takes dense descriptor
fields defined on two shapes as input, and outputs a soft map between the two
given objects. The resulting correspondence is shown to be accurate on several
challenging benchmarks comprising multiple categories, synthetic models, real
scans with acquisition artifacts, topological noise, and partiality.Comment: Accepted for publication at ICCV 201
Deep Optical Flow Estimation Via Multi-Scale Correspondence Structure Learning
As an important and challenging problem in computer vision, learning based
optical flow estimation aims to discover the intrinsic correspondence structure
between two adjacent video frames through statistical learning. Therefore, a
key issue to solve in this area is how to effectively model the multi-scale
correspondence structure properties in an adaptive end-to-end learning fashion.
Motivated by this observation, we propose an end-to-end multi-scale
correspondence structure learning (MSCSL) approach for optical flow estimation.
In principle, the proposed MSCSL approach is capable of effectively capturing
the multi-scale inter-image-correlation correspondence structures within a
multi-level feature space from deep learning. Moreover, the proposed MSCSL
approach builds a spatial Conv-GRU neural network model to adaptively model the
intrinsic dependency relationships among these multi-scale correspondence
structures. Finally, the above procedures for correspondence structure learning
and multi-scale dependency modeling are implemented in a unified end-to-end
deep learning framework. Experimental results on several benchmark datasets
demonstrate the effectiveness of the proposed approach.Comment: 7 pages, 3 figures, 2 table
Reconstructing interacting new agegraphic polytropic gas model in non-flat FRW universe
We study the correspondence between the interacting new agegraphic dark
energy and the polytropic gas model of dark energy in the non-flat FRW
universe. This correspondence allows to reconstruct the potential and the
dynamics for the scalar field of the polytropic model, which describe
accelerated expansion of the universe.Comment: 9 page
Multiple Correspondence Analysis & the Multilogit Bilinear Model
Multiple Correspondence Analysis (MCA) is a dimension reduction method which
plays a large role in the analysis of tables with categorical nominal variables
such as survey data. Though it is usually motivated and derived using geometric
considerations, in fact we prove that it amounts to a single proximal Newtown
step of a natural bilinear exponential family model for categorical data the
multinomial logit bilinear model. We compare and contrast the behavior of MCA
with that of the model on simulations and discuss new insights on the
properties of both exploratory multivariate methods and their cognate models.
One main conclusion is that we could recommend to approximate the multilogit
model parameters using MCA. Indeed, estimating the parameters of the model is
not a trivial task whereas MCA has the great advantage of being easily solved
by singular value decomposition and scalable to large data
-opers, the -Langlands correspondence, and quantum/classical duality
A special case of the geometric Langlands correspondence is given by the
relationship between solutions of the Bethe ansatz equations for the Gaudin
model and opers - connections on the projective line with extra structure. In
this paper, we describe a deformation of this correspondence for . We
introduce a difference equation version of opers called -opers and prove a
-Langlands correspondence between nondegenerate solutions of the Bethe
ansatz equations for the XXZ model and nondegenerate twisted -opers with
regular singularities on the projective line. We show that the
quantum/classical duality between the XXZ spin chain and the trigonometric
Ruijsenaars-Schneider model may be viewed as a special case of the
-Langlands correspondence. We also describe an application of -opers to
the equivariant quantum -theory of the cotangent bundles to partial flag
varieties.Comment: v3: 32 pages, 2 figures; minor revisions, to appear in Commun. Math.
Phy
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