247 research outputs found
On the Subspace of Image Gradient Orientations
We introduce the notion of Principal Component Analysis (PCA) of image
gradient orientations. As image data is typically noisy, but noise is
substantially different from Gaussian, traditional PCA of pixel intensities
very often fails to estimate reliably the low-dimensional subspace of a given
data population. We show that replacing intensities with gradient orientations
and the norm with a cosine-based distance measure offers, to some
extend, a remedy to this problem. Our scheme requires the eigen-decomposition
of a covariance matrix and is as computationally efficient as standard
PCA. We demonstrate some of its favorable properties on robust subspace
estimation
MAGMA: Multi-level accelerated gradient mirror descent algorithm for large-scale convex composite minimization
Composite convex optimization models arise in several applications, and are
especially prevalent in inverse problems with a sparsity inducing norm and in
general convex optimization with simple constraints. The most widely used
algorithms for convex composite models are accelerated first order methods,
however they can take a large number of iterations to compute an acceptable
solution for large-scale problems. In this paper we propose to speed up first
order methods by taking advantage of the structure present in many applications
and in image processing in particular. Our method is based on multi-level
optimization methods and exploits the fact that many applications that give
rise to large scale models can be modelled using varying degrees of fidelity.
We use Nesterov's acceleration techniques together with the multi-level
approach to achieve convergence rate, where
denotes the desired accuracy. The proposed method has a better
convergence rate than any other existing multi-level method for convex
problems, and in addition has the same rate as accelerated methods, which is
known to be optimal for first-order methods. Moreover, as our numerical
experiments show, on large-scale face recognition problems our algorithm is
several times faster than the state of the art
A Unified Framework for Compositional Fitting of Active Appearance Models
Active Appearance Models (AAMs) are one of the most popular and
well-established techniques for modeling deformable objects in computer vision.
In this paper, we study the problem of fitting AAMs using Compositional
Gradient Descent (CGD) algorithms. We present a unified and complete view of
these algorithms and classify them with respect to three main characteristics:
i) cost function; ii) type of composition; and iii) optimization method.
Furthermore, we extend the previous view by: a) proposing a novel Bayesian cost
function that can be interpreted as a general probabilistic formulation of the
well-known project-out loss; b) introducing two new types of composition,
asymmetric and bidirectional, that combine the gradients of both image and
appearance model to derive better conver- gent and more robust CGD algorithms;
and c) providing new valuable insights into existent CGD algorithms by
reinterpreting them as direct applications of the Schur complement and the
Wiberg method. Finally, in order to encourage open research and facilitate
future comparisons with our work, we make the implementa- tion of the
algorithms studied in this paper publicly available as part of the Menpo
Project.Comment: 39 page
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