1,838 research outputs found
Automatic vehicle tracking and recognition from aerial image sequences
This paper addresses the problem of automated vehicle tracking and
recognition from aerial image sequences. Motivated by its successes in the
existing literature focus on the use of linear appearance subspaces to describe
multi-view object appearance and highlight the challenges involved in their
application as a part of a practical system. A working solution which includes
steps for data extraction and normalization is described. In experiments on
real-world data the proposed methodology achieved promising results with a high
correct recognition rate and few, meaningful errors (type II errors whereby
genuinely similar targets are sometimes being confused with one another).
Directions for future research and possible improvements of the proposed method
are discussed
A semidiscrete version of the Citti-Petitot-Sarti model as a plausible model for anthropomorphic image reconstruction and pattern recognition
In his beautiful book [66], Jean Petitot proposes a sub-Riemannian model for
the primary visual cortex of mammals. This model is neurophysiologically
justified. Further developments of this theory lead to efficient algorithms for
image reconstruction, based upon the consideration of an associated
hypoelliptic diffusion. The sub-Riemannian model of Petitot and Citti-Sarti (or
certain of its improvements) is a left-invariant structure over the group
of rototranslations of the plane. Here, we propose a semi-discrete
version of this theory, leading to a left-invariant structure over the group
, restricting to a finite number of rotations. This apparently very
simple group is in fact quite atypical: it is maximally almost periodic, which
leads to much simpler harmonic analysis compared to Based upon this
semi-discrete model, we improve on previous image-reconstruction algorithms and
we develop a pattern-recognition theory that leads also to very efficient
algorithms in practice.Comment: 123 pages, revised versio
Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems
In this paper we develop new techniques for revealing geometrical structures
in phase space that are valid for aperiodically time dependent dynamical
systems, which we refer to as Lagrangian descriptors. These quantities are
based on the integration, for a finite time, along trajectories of an intrinsic
bounded, positive geometrical and/or physical property of the trajectory
itself. We discuss a general methodology for constructing Lagrangian
descriptors, and we discuss a "heuristic argument" that explains why this
method is successful for revealing geometrical structures in the phase space of
a dynamical system. We support this argument by explicit calculations on a
benchmark problem having a hyperbolic fixed point with stable and unstable
manifolds that are known analytically. Several other benchmark examples are
considered that allow us the assess the performance of Lagrangian descriptors
in revealing invariant tori and regions of shear. Throughout the paper
"side-by-side" comparisons of the performance of Lagrangian descriptors with
both finite time Lyapunov exponents (FTLEs) and finite time averages of certain
components of the vector field ("time averages") are carried out and discussed.
In all cases Lagrangian descriptors are shown to be both more accurate and
computationally efficient than these methods. We also perform computations for
an explicitly three dimensional, aperiodically time-dependent vector field and
an aperiodically time dependent vector field defined as a data set. Comparisons
with FTLEs and time averages for these examples are also carried out, with
similar conclusions as for the benchmark examples.Comment: 52 pages, 25 figure
Statistical Models and Optimization Algorithms for High-Dimensional Computer Vision Problems
Data-driven and computational approaches are showing significant promise in solving several challenging problems in various fields such as bioinformatics, finance and many branches of engineering. In this dissertation, we explore the potential of these approaches, specifically statistical data models and optimization algorithms, for solving several challenging problems in computer vision. In doing so, we contribute to the literatures of both statistical data models and computer vision. In the context of statistical data models, we propose principled approaches for solving robust regression problems, both linear and kernel, and missing data matrix factorization problem. In computer vision, we propose statistically optimal and efficient algorithms for solving the remote face recognition and structure from motion (SfM) problems.
The goal of robust regression is to estimate the functional relation between two variables from a given data set which might be contaminated with outliers. Under the reasonable assumption that there are fewer outliers than inliers in a data set, we formulate the robust linear regression problem as a sparse learning problem, which can be solved using efficient polynomial-time algorithms. We also provide sufficient conditions under which the proposed algorithms correctly solve the robust regression problem. We then extend our robust formulation to the case of kernel regression, specifically to propose a robust version for relevance vector machine (RVM) regression.
Matrix factorization is used for finding a low-dimensional representation for data embedded in a high-dimensional space. Singular value decomposition is the standard algorithm for solving this problem. However, when the matrix has many missing elements this is a hard problem to solve. We formulate the missing data matrix factorization problem as a low-rank semidefinite programming problem (essentially a rank constrained SDP), which allows us to find accurate and efficient solutions for large-scale factorization problems.
Face recognition from remotely acquired images is a challenging problem because of variations due to blur and illumination. Using the convolution model for blur, we show that the set of all images obtained by blurring a given image forms a convex set. We then use convex optimization techniques to find the distances between a given blurred (probe) image and the gallery images to find the best match. Further, using a low-dimensional linear subspace model for illumination variations, we extend our theory in a similar fashion to recognize blurred and poorly illuminated faces.
Bundle adjustment is the final optimization step of the SfM problem where the goal is to obtain the 3-D structure of the observed scene and the camera parameters from multiple images of the scene. The traditional bundle adjustment algorithm, based on minimizing the l_2 norm of the image re-projection error, has cubic complexity in the number of unknowns. We propose an algorithm, based on minimizing the l_infinity norm of the re-projection error, that has quadratic complexity in the number of unknowns. This is achieved by reducing the large-scale optimization problem into many small scale sub-problems each of which can be solved using second-order cone programming
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