4,793 research outputs found
Networks for Nonlinear Diffusion Problems in Imaging
A multitude of imaging and vision tasks have seen recently a major
transformation by deep learning methods and in particular by the application of
convolutional neural networks. These methods achieve impressive results, even
for applications where it is not apparent that convolutions are suited to
capture the underlying physics.
In this work we develop a network architecture based on nonlinear diffusion
processes, named DiffNet. By design, we obtain a nonlinear network architecture
that is well suited for diffusion related problems in imaging. Furthermore, the
performed updates are explicit, by which we obtain better interpretability and
generalisability compared to classical convolutional neural network
architectures. The performance of DiffNet tested on the inverse problem of
nonlinear diffusion with the Perona-Malik filter on the STL-10 image dataset.
We obtain competitive results to the established U-Net architecture, with a
fraction of parameters and necessary training data
Left-invariant evolutions of wavelet transforms on the Similitude Group
Enhancement of multiple-scale elongated structures in noisy image data is
relevant for many biomedical applications but commonly used PDE-based
enhancement techniques often fail at crossings in an image. To get an overview
of how an image is composed of local multiple-scale elongated structures we
construct a multiple scale orientation score, which is a continuous wavelet
transform on the similitude group, SIM(2). Our unitary transform maps the space
of images onto a reproducing kernel space defined on SIM(2), allowing us to
robustly relate Euclidean (and scaling) invariant operators on images to
left-invariant operators on the corresponding continuous wavelet transform.
Rather than often used wavelet (soft-)thresholding techniques, we employ the
group structure in the wavelet domain to arrive at left-invariant evolutions
and flows (diffusion), for contextual crossing preserving enhancement of
multiple scale elongated structures in noisy images. We present experiments
that display benefits of our work compared to recent PDE techniques acting
directly on the images and to our previous work on left-invariant diffusions on
orientation scores defined on Euclidean motion group.Comment: 40 page
The Local Structure of Space-Variant Images
Local image structure is widely used in theories of both machine and biological vision. The form of the differential operators describing this structure for space-invariant images has been well documented (e.g. Koenderink, 1984). Although space-variant coordinates are universally used in mammalian visual systems, the form of the operators in the space-variant domain has received little attention. In this report we derive the form of the most common differential operators and surface characteristics in the space-variant domain and show examples of their use. The operators include the Laplacian, the gradient and the divergence, as well as the fundamental forms of the image treated as a surface. We illustrate the use of these results by deriving the space-variant form of corner detection and image enhancement algorithms. The latter is shown to have interesting properties in the complex log domain, implicitly encoding a variable grid-size integration of the underlying PDE, allowing rapid enhancement of large scale peripheral features while preserving high spatial frequencies in the fovea.Office of Naval Research (N00014-95-I-0409
Geometrical-based algorithm for variational segmentation and smoothing of vector-valued images
An optimisation method based on a nonlinear functional is considered for segmentation and smoothing of vector-valued images. An edge-based approach is proposed to initially segment the image using geometrical properties such as metric tensor of the linearly smoothed image. The nonlinear functional is then minimised for each segmented region to yield the smoothed image. The functional is characterised with a unique solution in contrast with the MumfordâShah functional for vector-valued images. An operator for edge detection is introduced as a result of this unique solution. This operator is analytically calculated and its detection performance and localisation are then compared with those of the DroGoperator. The implementations are applied on colour images as examples of vector-valued images, and the results demonstrate robust performance in noisy environments
p-Adic Mathematical Physics
A brief review of some selected topics in p-adic mathematical physics is
presented.Comment: 36 page
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