41 research outputs found
A Multiscale Framework for Challenging Discrete Optimization
Current state-of-the-art discrete optimization methods struggle behind when
it comes to challenging contrast-enhancing discrete energies (i.e., favoring
different labels for neighboring variables). This work suggests a multiscale
approach for these challenging problems. Deriving an algebraic representation
allows us to coarsen any pair-wise energy using any interpolation in a
principled algebraic manner. Furthermore, we propose an energy-aware
interpolation operator that efficiently exposes the multiscale landscape of the
energy yielding an effective coarse-to-fine optimization scheme. Results on
challenging contrast-enhancing energies show significant improvement over
state-of-the-art methods.Comment: 5 pages, 1 figure, To appear in NIPS Workshop on Optimization for
Machine Learning (December 2012). Camera-ready version. Fixed typos,
acknowledgements adde
Fast Detection of Curved Edges at Low SNR
Detecting edges is a fundamental problem in computer vision with many
applications, some involving very noisy images. While most edge detection
methods are fast, they perform well only on relatively clean images. Indeed,
edges in such images can be reliably detected using only local filters.
Detecting faint edges under high levels of noise cannot be done locally at the
individual pixel level, and requires more sophisticated global processing.
Unfortunately, existing methods that achieve this goal are quite slow. In this
paper we develop a novel multiscale method to detect curved edges in noisy
images. While our algorithm searches for edges over a huge set of candidate
curves, it does so in a practical runtime, nearly linear in the total number of
image pixels. As we demonstrate experimentally, our algorithm is orders of
magnitude faster than previous methods designed to deal with high noise levels.
Nevertheless, it obtains comparable, if not better, edge detection quality on a
variety of challenging noisy images.Comment: 9 pages, 11 figure
Wide baseline stereo matching with convex bounded-distortion constraints
Finding correspondences in wide baseline setups is a challenging problem.
Existing approaches have focused largely on developing better feature
descriptors for correspondence and on accurate recovery of epipolar line
constraints. This paper focuses on the challenging problem of finding
correspondences once approximate epipolar constraints are given. We introduce a
novel method that integrates a deformation model. Specifically, we formulate
the problem as finding the largest number of corresponding points related by a
bounded distortion map that obeys the given epipolar constraints. We show that,
while the set of bounded distortion maps is not convex, the subset of maps that
obey the epipolar line constraints is convex, allowing us to introduce an
efficient algorithm for matching. We further utilize a robust cost function for
matching and employ majorization-minimization for its optimization. Our
experiments indicate that our method finds significantly more accurate maps
than existing approaches
A Kernel Perspective of Skip Connections in Convolutional Networks
Over-parameterized residual networks (ResNets) are amongst the most
successful convolutional neural architectures for image processing. Here we
study their properties through their Gaussian Process and Neural Tangent
kernels. We derive explicit formulas for these kernels, analyze their spectra,
and provide bounds on their implied condition numbers. Our results indicate
that (1) with ReLU activation, the eigenvalues of these residual kernels decay
polynomially at a similar rate compared to the same kernels when skip
connections are not used, thus maintaining a similar frequency bias; (2)
however, residual kernels are more locally biased. Our analysis further shows
that the matrices obtained by these residual kernels yield favorable condition
numbers at finite depths than those obtained without the skip connections,
enabling therefore faster convergence of training with gradient descent