26 research outputs found
Spanning embeddings of arrangeable graphs with sublinear bandwidth
The Bandwidth Theorem of B\"ottcher, Schacht and Taraz [Mathematische Annalen
343 (1), 175-205] gives minimum degree conditions for the containment of
spanning graphs H with small bandwidth and bounded maximum degree. We
generalise this result to a-arrangeable graphs H with \Delta(H)<sqrt(n)/log(n),
where n is the number of vertices of H.
Our result implies that sufficiently large n-vertex graphs G with minimum
degree at least (3/4+\gamma)n contain almost all planar graphs on n vertices as
subgraphs. Using techniques developed by Allen, Brightwell and Skokan
[Combinatorica, to appear] we can also apply our methods to show that almost
all planar graphs H have Ramsey number at most 12|H|. We obtain corresponding
results for graphs embeddable on different orientable surfaces.Comment: 20 page
Perfect graphs of fixed density: counting and homogenous sets
For c in [0,1] let P_n(c) denote the set of n-vertex perfect graphs with
density c and C_n(c) the set of n-vertex graphs without induced C_5 and with
density c. We show that
log|P_n(c)|/binom{n}{2}=log|C_n(c)|/binom{n}{2}=h(c)+o(1) with h(c)=1/2 if
1/4<c<3/4 and h(c)=H(|2c-1|)/2 otherwise, where H is the binary entropy
function.
Further, we use this result to deduce that almost all graphs in C_n(c) have
homogenous sets of linear size. This answers a question raised by Loebl, Reed,
Scott, Thomason, and Thomass\'e [Almost all H-free graphs have the
Erd\H{o}s-Hajnal property] in the case of forbidden induced C_5.Comment: 19 page
Towards Arbitrary Noise Augmentation - Deep Learning for Sampling from Arbitrary Probability Distributions
Accurate noise modelling is important for training of deep learning
reconstruction algorithms. While noise models are well known for traditional
imaging techniques, the noise distribution of a novel sensor may be difficult
to determine a priori. Therefore, we propose learning arbitrary noise
distributions. To do so, this paper proposes a fully connected neural network
model to map samples from a uniform distribution to samples of any explicitly
known probability density function. During the training, the Jensen-Shannon
divergence between the distribution of the model's output and the target
distribution is minimized. We experimentally demonstrate that our model
converges towards the desired state. It provides an alternative to existing
sampling methods such as inversion sampling, rejection sampling, Gaussian
mixture models and Markov-Chain-Monte-Carlo. Our model has high sampling
efficiency and is easily applied to any probability distribution, without the
need of further analytical or numerical calculations
Precision Learning: Towards Use of Known Operators in Neural Networks
In this paper, we consider the use of prior knowledge within neural networks.
In particular, we investigate the effect of a known transform within the
mapping from input data space to the output domain. We demonstrate that use of
known transforms is able to change maximal error bounds.
In order to explore the effect further, we consider the problem of X-ray
material decomposition as an example to incorporate additional prior knowledge.
We demonstrate that inclusion of a non-linear function known from the physical
properties of the system is able to reduce prediction errors therewith
improving prediction quality from SSIM values of 0.54 to 0.88.
This approach is applicable to a wide set of applications in physics and
signal processing that provide prior knowledge on such transforms. Also maximal
error estimation and network understanding could be facilitated within the
context of precision learning.Comment: accepted on ICPR 201
Projection image-to-image translation in hybrid X-ray/MR imaging
The potential benefit of hybrid X-ray and MR imaging in the interventional
environment is large due to the combination of fast imaging with high contrast
variety. However, a vast amount of existing image enhancement methods requires
the image information of both modalities to be present in the same domain. To
unlock this potential, we present a solution to image-to-image translation from
MR projections to corresponding X-ray projection images. The approach is based
on a state-of-the-art image generator network that is modified to fit the
specific application. Furthermore, we propose the inclusion of a gradient map
in the loss function to allow the network to emphasize high-frequency details
in image generation. Our approach is capable of creating X-ray projection
images with natural appearance. Additionally, our extensions show clear
improvement compared to the baseline method.Comment: In proceedings of SPIE Medical Imaging 201
Projection-to-Projection Translation for Hybrid X-ray and Magnetic Resonance Imaging
Hybrid X-ray and magnetic resonance (MR) imaging promises large potential in interventional medical imaging applications due to the broad variety of contrast of MRI combined with fast imaging of X-ray-based modalities. To fully utilize the potential of the vast amount of existing image enhancement techniques, the corresponding information from both modalities must be present in the same domain. For image-guided interventional procedures, X-ray fluoroscopy has proven to be the modality of choice. Synthesizing one modality from another in this case is an ill-posed problem due to ambiguous signal and overlapping structures in projective geometry. To take on these challenges, we present a learning-based solution to MR to X-ray projection-to-projection translation. We propose an image generator network that focuses on high representation capacity in higher resolution layers to allow for accurate synthesis of fine details in the projection images. Additionally, a weighting scheme in the loss computation that favors high-frequency structures is proposed to focus on the important details and contours in projection imaging. The proposed extensions prove valuable in generating X-ray projection images with natural appearance. Our approach achieves a deviation from the ground truth of only 6% and structural similarity measure of 0.913 ± 0.005. In particular the high frequency weighting assists in generating projection images with sharp appearance and reduces erroneously synthesized fine details