3,043 research outputs found
On the Design and Analysis of Multiple View Descriptors
We propose an extension of popular descriptors based on gradient orientation
histograms (HOG, computed in a single image) to multiple views. It hinges on
interpreting HOG as a conditional density in the space of sampled images, where
the effects of nuisance factors such as viewpoint and illumination are
marginalized. However, such marginalization is performed with respect to a very
coarse approximation of the underlying distribution. Our extension leverages on
the fact that multiple views of the same scene allow separating intrinsic from
nuisance variability, and thus afford better marginalization of the latter. The
result is a descriptor that has the same complexity of single-view HOG, and can
be compared in the same manner, but exploits multiple views to better trade off
insensitivity to nuisance variability with specificity to intrinsic
variability. We also introduce a novel multi-view wide-baseline matching
dataset, consisting of a mixture of real and synthetic objects with ground
truthed camera motion and dense three-dimensional geometry
On Unlimited Sampling
Shannon's sampling theorem provides a link between the continuous and the
discrete realms stating that bandlimited signals are uniquely determined by its
values on a discrete set. This theorem is realized in practice using so called
analog--to--digital converters (ADCs). Unlike Shannon's sampling theorem, the
ADCs are limited in dynamic range. Whenever a signal exceeds some preset
threshold, the ADC saturates, resulting in aliasing due to clipping. The goal
of this paper is to analyze an alternative approach that does not suffer from
these problems. Our work is based on recent developments in ADC design, which
allow for ADCs that reset rather than to saturate, thus producing modulo
samples. An open problem that remains is: Given such modulo samples of a
bandlimited function as well as the dynamic range of the ADC, how can the
original signal be recovered and what are the sufficient conditions that
guarantee perfect recovery? In this paper, we prove such sufficiency conditions
and complement them with a stable recovery algorithm. Our results are not
limited to certain amplitude ranges, in fact even the same circuit architecture
allows for the recovery of arbitrary large amplitudes as long as some estimate
of the signal norm is available when recovering. Numerical experiments that
corroborate our theory indeed show that it is possible to perfectly recover
function that takes values that are orders of magnitude higher than the ADC's
threshold.Comment: 11 pages, 4 figures, copy of initial version to appear in Proceedings
of 12th International Conference on Sampling Theory and Applications (SampTA
Visual Representations: Defining Properties and Deep Approximations
Visual representations are defined in terms of minimal sufficient statistics
of visual data, for a class of tasks, that are also invariant to nuisance
variability. Minimal sufficiency guarantees that we can store a representation
in lieu of raw data with smallest complexity and no performance loss on the
task at hand. Invariance guarantees that the statistic is constant with respect
to uninformative transformations of the data. We derive analytical expressions
for such representations and show they are related to feature descriptors
commonly used in computer vision, as well as to convolutional neural networks.
This link highlights the assumptions and approximations tacitly assumed by
these methods and explains empirical practices such as clamping, pooling and
joint normalization.Comment: UCLA CSD TR140023, Nov. 12, 2014, revised April 13, 2015, November
13, 2015, February 28, 201
Changing Views on Curves and Surfaces
Visual events in computer vision are studied from the perspective of
algebraic geometry. Given a sufficiently general curve or surface in 3-space,
we consider the image or contour curve that arises by projecting from a
viewpoint. Qualitative changes in that curve occur when the viewpoint crosses
the visual event surface. We examine the components of this ruled surface, and
observe that these coincide with the iterated singular loci of the coisotropic
hypersurfaces associated with the original curve or surface. We derive
formulas, due to Salmon and Petitjean, for the degrees of these surfaces, and
show how to compute exact representations for all visual event surfaces using
algebraic methods.Comment: 31 page
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