1,044 research outputs found
Integral Geometric Dual Distributions of Multilinear Models
We propose an integral geometric approach for computing dual distributions
for the parameter distributions of multilinear models. The dual distributions
can be computed from, for example, the parameter distributions of conics,
multiple view tensors, homographies, or as simple entities as points, lines,
and planes. The dual distributions have analytical forms that follow from the
asymptotic normality property of the maximum likelihood estimator and an
application of integral transforms, fundamentally the generalised Radon
transforms, on the probability density of the parameters. The approach allows
us, for instance, to look at the uncertainty distributions in feature
distributions, which are essentially tied to the distribution of training data,
and helps us to derive conditional distributions for interesting variables and
characterise confidence intervals of the estimates
Uncalibrated Non-Rigid Factorisation by Independent Subspace Analysis
We propose a general, prior-free approach for the uncalibrated non-rigid
structure-from-motion problem for modelling and analysis of non-rigid objects
such as human faces. The word general refers to an approach that recovers the
non-rigid affine structure and motion from 2D point correspondences by assuming
that (1) the non-rigid shapes are generated by a linear combination of rigid 3D
basis shapes, (2) that the non-rigid shapes are affine in nature, i.e., they
can be modelled as deviations from the mean, rigid shape, (3) and that the
basis shapes are statistically independent. In contrast to the majority of
existing works, no prior information is assumed for the structure and motion
apart from the assumption the that underlying basis shapes are statistically
independent. The independent 3D shape bases are recovered by independent
subspace analysis (ISA). Likewise, in contrast to the most previous approaches,
no calibration information is assumed for affine cameras; the reconstruction is
solved up to a global affine ambiguity that makes our approach simple but
efficient. In the experiments, we evaluated the method with several standard
data sets including a real face expression data set of 7200 faces with 2D point
correspondences and unknown 3D structure and motion for which we obtained
promising results
Theorems and algorithms for multiple view geometry with applications to electron tomography
The thesis considers both theory and algorithms for geometric computer vision. The framework of the work is built around the application of autonomous transmission electron microscope image registration.
The theoretical part of the thesis first develops a consistent robust estimator that is evaluated in estimating two view geometry with both affine and projective camera models. The uncertainty of the fundamental matrix is similarly estimated robustly, and the previous observation whether the covariance matrix of the fundamental matrix contains disparity information of the scene is explained and its utilization in matching is discussed. For point tracking purposes, a reliable wavelet-based matching technique and two EM algorithms for the maximum likelihood affine reconstruction under missing data are proposed. The thesis additionally discusses identification of degeneracy as well as affine bundle adjustment.
The application part of the thesis considers transmission electron microscope image registration, first with fiducial gold markers and thereafter without markers. Both methods utilize the techniques proposed in the theoretical part of the thesis and, in addition, a graph matching method is proposed for matching gold markers. Conversely, alignment without markers is disposed by tracking interest points of the intensity surface of the images. At the present level of development, the former method is more accurate but the latter is appropriate for situations where fiducial markers cannot be used.
Perhaps the most significant result of the thesis is the proposed robust estimator because of consistence proof and its many application areas, which are not limited to the computer vision field. The other algorithms could be found useful in multiple view applications in computer vision that have to deal with uncertainty, matching, tracking, and reconstruction. From the viewpoint of image registration, the thesis further achieved its aims since two accurate image alignment methods are suggested for obtaining the most exact reconstructions in electron tomography.reviewe
Tensor-based Subspace Factorization for StyleGAN
In this paper, we propose GAN a tensor-based method for modeling the
latent space of generative models. The objective is to identify semantic
directions in latent space. To this end, we propose to fit a multilinear tensor
model on a structured facial expression database, which is initially embedded
into latent space. We validate our approach on StyleGAN trained on FFHQ using
BU-3DFE as a structured facial expression database. We show how the parameters
of the multilinear tensor model can be approximated by Alternating Least
Squares. Further, we introduce a tacked style-separated tensor model, defined
as an ensemble of style-specific models to integrate our approach with the
extended latent space of StyleGAN. We show that taking the individual styles of
the extended latent space into account leads to higher model flexibility and
lower reconstruction error. Finally, we do several experiments comparing our
approach to former work on both GANs and multilinear models. Concretely, we
analyze the expression subspace and find that the expression trajectories meet
at an apathetic face that is consistent with earlier work. We also show that by
changing the pose of a person, the generated image from our approach is closer
to the ground truth than results from two competing approaches.Comment: Accepted for FG202
On the Probabilistic Epipolar Geometry
In this paper, we are going to answer the following question: assuming that we have estimates for the epipolar geometry and its uncertainty between two views, how probable it is that a new, independent point pair will satisfy the true epipolar geometry and be, in this sense, a feasible candidate correspon-dence pair? If we knew the true fundamental matrix, the answer would be trivial but in reality it is not because of estimation errors. So, as a point in the first view is given, we will show that we may compute a probability density for the feasible correspondence locations in the second view that describes the current level of knowledge of the epipolar geometry between the views. We will thus have a point–probability-density relation which can be under-stood as a probabilistic form of the epipolar constraint; it also approaches the true point–line relation as the number of training correspondences tends to in-finity. We will also show that the eigenvectors of the epipolar line covariance matrix have certain interpretations on the image plane, of which one is the previously observed, narrowest point of the epipolar envelope. The results of this paper are novel and important since the uncertainty of the epipolar constraint can be now taken into account in a sound way in applications.
Science Frontiers In Galaxy Evolution: Deep-Wide Surveys
Astro2010: The Astronomy and Astrophysics Decadal Survey : Science White Papers no 79. Available online : http://www8.nationalacademies.org/astro2010/DetailFileDisplay.aspx?id=24
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