1,416 research outputs found
Relaxed 2-D Principal Component Analysis by Norm for Face Recognition
A relaxed two dimensional principal component analysis (R2DPCA) approach is
proposed for face recognition. Different to the 2DPCA, 2DPCA- and G2DPCA,
the R2DPCA utilizes the label information (if known) of training samples to
calculate a relaxation vector and presents a weight to each subset of training
data. A new relaxed scatter matrix is defined and the computed projection axes
are able to increase the accuracy of face recognition. The optimal -norms
are selected in a reasonable range. Numerical experiments on practical face
databased indicate that the R2DPCA has high generalization ability and can
achieve a higher recognition rate than state-of-the-art methods.Comment: 19 pages, 11 figure
Surface Networks
We study data-driven representations for three-dimensional triangle meshes,
which are one of the prevalent objects used to represent 3D geometry. Recent
works have developed models that exploit the intrinsic geometry of manifolds
and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants,
which learn from the local metric tensor via the Laplacian operator. Despite
offering excellent sample complexity and built-in invariances, intrinsic
geometry alone is invariant to isometric deformations, making it unsuitable for
many applications. To overcome this limitation, we propose several upgrades to
GNNs to leverage extrinsic differential geometry properties of
three-dimensional surfaces, increasing its modeling power.
In particular, we propose to exploit the Dirac operator, whose spectrum
detects principal curvature directions --- this is in stark contrast with the
classical Laplace operator, which directly measures mean curvature. We coin the
resulting models \emph{Surface Networks (SN)}. We prove that these models
define shape representations that are stable to deformation and to
discretization, and we demonstrate the efficiency and versatility of SNs on two
challenging tasks: temporal prediction of mesh deformations under non-linear
dynamics and generative models using a variational autoencoder framework with
encoders/decoders given by SNs
Color Image Analysis by Quaternion-Type Moments
International audienceIn this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. appears to be an optimal choice
Generalized Two-Dimensional Quaternion Principal Component Analysis with Weighting for Color Image Recognition
A generalized two-dimensional quaternion principal component analysis
(G2DQPCA) approach with weighting is presented for color image analysis. As a
general framework of 2DQPCA, G2DQPCA is flexible to adapt different constraints
or requirements by imposing norms both on the constraint function and
the objective function. The gradient operator of quaternion vector functions is
redefined by the structure-preserving gradient operator of real vector
function. Under the framework of minorization-maximization (MM), an iterative
algorithm is developed to obtain the optimal closed-form solution of G2DQPCA.
The projection vectors generated by the deflating scheme are required to be
orthogonal to each other. A weighting matrix is defined to magnify the effect
of main features. The weighted projection bases remain the accuracy of face
recognition unchanged or moving in a tight range as the number of features
increases. The numerical results based on the real face databases validate that
the newly proposed method performs better than the state-of-the-art algorithms.Comment: 15 pages, 15 figure
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