Fast anisotropic Gauss filtering

Abstract. We derive the decomposition of the anisotropic Gaussian in a one dimensional Gauss filter in the x-direction followed by a one dimensional filter in a non-orthogonal direction ϕ. So also the anisotropic Gaussian can be decomposed by dimension. This appears to be extremely efficient from a computing perspective. An implementation scheme for normal convolution and for recursive filtering is proposed. Also directed derivative filters are demonstrated. For the recursive implementation, filtering an 512 × 512 image is performed within 65 msec, independent of the standard deviations and orientation of the filter. Accuracy of the filters is still reasonable when compared to truncation error or recursive approximation error. The anisotropic Gaussian filtering method allows fast calculation of edge and ridge maps, with high spatial and angular accuracy. For tracking applications, the normal anisotropic convolution scheme is more advantageous, with applications in the detection of dashed lines in engineering drawings. The recursive implementation is more attractive in feature detection applications, for instance in affine invariant edge and ridge detection in computer vision. The proposed computational filtering method enables the practical applicability of orientation scale-space analysis

Probing the Interior Environment of Carbon Nano-test-tubes

We report the filling of single walled carbon nanotubes with an electron spin-active fullerene species where a nitroxide radical is functionalized on the fullerene cage. High resolution transmission electron microscopy (HRTEM), optical absorption and electron spin resonance (ESR) are used to determine the rotational behavior of the encapsulated molecules and determine the polar nature of the nanotube interior

On Using Physical Analogies for Feature and Shape Extraction in Computer Vision

There is a rich literature of approaches to image feature extraction in computer vision. Many sophisticated approaches exist for low- and high-level feature extraction but can be complex to implement with parameter choice guided by experimentation, but impeded by speed of computation. We have developed new ways to extract features based on notional use of physical paradigms, with parameterisation that is more familiar to a scientifically-trained user, aiming to make best use of computational resource. We describe how analogies based on gravitational force can be used for low-level analysis, whilst analogies of water flow and heat can be deployed to achieve high-level smooth shape detection. These new approaches to arbitrary shape extraction are compared with standard state-of-art approaches by curve evolution. There is no comparator operator to our use of gravitational force. We also aim to show that the implementation is consistent with the original motivations for these techniques and so contend that the exploration of physical paradigms offers a promising new avenue for new approaches to feature extraction in computer vision

Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks

The mathematical problem for electrical impedance tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features, such as clear organ boundaries. Convolutional neural networks provide a powerful framework for post-processing such convolved direct reconstructions. In this paper, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems