77 research outputs found
Learned Vertex Descent: A New Direction for 3D Human Model Fitting
We propose a novel optimization-based paradigm for 3D human model fitting on
images and scans. In contrast to existing approaches that directly regress the
parameters of a low-dimensional statistical body model (e.g. SMPL) from input
images, we train an ensemble of per-vertex neural fields network. The network
predicts, in a distributed manner, the vertex descent direction towards the
ground truth, based on neural features extracted at the current vertex
projection. At inference, we employ this network, dubbed LVD, within a
gradient-descent optimization pipeline until its convergence, which typically
occurs in a fraction of a second even when initializing all vertices into a
single point. An exhaustive evaluation demonstrates that our approach is able
to capture the underlying body of clothed people with very different body
shapes, achieving a significant improvement compared to state-of-the-art. LVD
is also applicable to 3D model fitting of humans and hands, for which we show a
significant improvement to the SOTA with a much simpler and faster method.Comment: Project page: https://www.iri.upc.edu/people/ecorona/lvd
Generalized beta models and population growth: so many routes to chaos
Logistic and Gompertz growth equations are the usual choice to model sustainable growth and immoderate growth causing depletion of resources, respectively. Observing that the logistic distribution is geo-max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, we investigate other models proportional to either geo-max-stable distributions (log-logistic and backward log-logistic) or to other max-stable distributions (Fréchet or max-Weibull). We show that the former arise when in the hyper-logistic Blumberg equation, connected to the Beta (Formula presented.) function, we use fractional exponents (Formula presented.) and (Formula presented.), and the latter when in the hyper-Gompertz-Turner equation, the exponents of the logarithmic factor are real and eventually fractional. The use of a BetaBoop function establishes interesting connections to Probability Theory, Riemann–Liouville’s fractional integrals, higher-order monotonicity and convexity and generalized unimodality, and the logistic map paradigm inspires the investigation of the dynamics of the hyper-logistic and hyper-Gompertz maps.info:eu-repo/semantics/publishedVersio
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Relating relative entropy, optimal transport and Fisher information: a quantum HWI inequality
Quantum Markov semigroups characterize the time evolution of an important
class of open quantum systems. Studying convergence properties of such a
semigroup, and determining concentration properties of its invariant state,
have been the focus of much research. Quantum versions of functional
inequalities (like the modified logarithmic Sobolev and Poincar\'{e}
inequalities) and the so-called transportation cost inequalities, have proved
to be essential for this purpose. Classical functional and transportation cost
inequalities are seen to arise from a single geometric inequality, called the
Ricci lower bound, via an inequality which interpolates between them. The
latter is called the HWI-inequality, where the letters I, W and H are,
respectively, acronyms for the Fisher information (arising in the modified
logarithmic Sobolev inequality), the so-called Wasserstein distance (arising in
the transportation cost inequality) and the relative entropy (or Boltzmann H
function) arising in both. Hence, classically, all the above inequalities and
the implications between them form a remarkable picture which relates elements
from diverse mathematical fields, such as Riemannian geometry, information
theory, optimal transport theory, Markov processes, concentration of measure,
and convexity theory. Here we consider a quantum version of the Ricci lower
bound introduced by Carlen and Maas, and prove that it implies a quantum HWI
inequality from which the quantum functional and transportation cost
inequalities follow. Our results hence establish that the unifying picture of
the classical setting carries over to the quantum one
The Generalized Multiplicative Gradient Method and Its Convergence Rate Analysis
Multiplicative gradient method is a classical and effective method for
solving the positron emission tomography (PET) problem. In this work, we
propose a generalization of this method on a broad class of problems, which
includes the PET problem as a special case. We show that this generalized
method converges with rate .Comment: 20 page
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