70,769 research outputs found
CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration
In this paper, we propose a new framework to remove parts of the systematic
errors affecting popular restoration algorithms, with a special focus for image
processing tasks. Generalizing ideas that emerged for regularization,
we develop an approach re-fitting the results of standard methods towards the
input data. Total variation regularizations and non-local means are special
cases of interest. We identify important covariant information that should be
preserved by the re-fitting method, and emphasize the importance of preserving
the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we
provide an approach that has a "twicing" flavor and allows re-fitting the
restored signal by adding back a local affine transformation of the residual
term. We illustrate the benefits of our method on numerical simulations for
image restoration tasks
From Maxout to Channel-Out: Encoding Information on Sparse Pathways
Motivated by an important insight from neural science, we propose a new
framework for understanding the success of the recently proposed "maxout"
networks. The framework is based on encoding information on sparse pathways and
recognizing the correct pathway at inference time. Elaborating further on this
insight, we propose a novel deep network architecture, called "channel-out"
network, which takes a much better advantage of sparse pathway encoding. In
channel-out networks, pathways are not only formed a posteriori, but they are
also actively selected according to the inference outputs from the lower
layers. From a mathematical perspective, channel-out networks can represent a
wider class of piece-wise continuous functions, thereby endowing the network
with more expressive power than that of maxout networks. We test our
channel-out networks on several well-known image classification benchmarks,
setting new state-of-the-art performance on CIFAR-100 and STL-10, which
represent some of the "harder" image classification benchmarks.Comment: 10 pages including the appendix, 9 figure
Alternating Back-Propagation for Generator Network
This paper proposes an alternating back-propagation algorithm for learning
the generator network model. The model is a non-linear generalization of factor
analysis. In this model, the mapping from the continuous latent factors to the
observed signal is parametrized by a convolutional neural network. The
alternating back-propagation algorithm iterates the following two steps: (1)
Inferential back-propagation, which infers the latent factors by Langevin
dynamics or gradient descent. (2) Learning back-propagation, which updates the
parameters given the inferred latent factors by gradient descent. The gradient
computations in both steps are powered by back-propagation, and they share most
of their code in common. We show that the alternating back-propagation
algorithm can learn realistic generator models of natural images, video
sequences, and sounds. Moreover, it can also be used to learn from incomplete
or indirect training data
Application of optimal data-based binning method to spatial analysis of ecological datasets
Investigation of highly structured data sets to unveil statistical
regularities is of major importance in complex system research. The first step
is to choose the scale at which to observe the process, the most informative
scale being the one that includes the important features while disregarding
noisy details in the data. In the investigation of spatial patterns, the
optimal scale defines the optimal bin size of the histogram in which to
visualize the empirical density of the pattern. In this paper we investigate a
method proposed recently by K.~H.~Knuth to find the optimal bin size of an
histogram as a tool for statistical analysis of spatial point processes. We
test it through numerical simulations on various spatial processes which are of
interest in ecology. We show that Knuth optimal bin size rule reducing noisy
fluctuations performs better than standard kernel methods to infer the
intensity of the underlying process. Moreover it can be used to highlight
relevant spatial characteristics of the underlying distribution such as space
anisotropy and clusterization. We apply these findings to analyse cluster-like
structures in plants' arrangement of Barro Colorado Island rainforest.Comment: 49 pages, 25 figure
Identifying prognostic structural features in tissue sections of colon cancer patients using point pattern analysis
Diagnosis and prognosis of cancer is informed by the architecture inherent in cancer patient tissue sections. This architecture is typically identified by pathologists, yet advances in computational image analysis facilitate quantitative assessment of this structure. In this article we develop a spatial point process approach in order to describe patterns in cell distribution within tissue samples taken from colorectal cancer (CRC) patients. In particular, our approach is centered on the Palm intensity function. This leads to taking an approximate-likelihood technique in fitting point processes models. We consider two Neyman-Scott point processes and a void process, fitting these point process models to the CRC patient data. We find that the parameter estimates of these models may be used to quantify the spatial arrangement of cells. Importantly, we observe characteristic differences in the spatial arrangement of cells between patients who died from CRC and those alive at follow-up
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