Mapping carbon nanotube orientation by fast fourier transform of scanning electron micrographs

A novel method of applying a two-dimensional Fourier transform (2D-FFT) to SEM was developed to map the CNT orientation in pre-formed arrays. Local 2D-FFTs were integrated azimuthally to determine an orientation distribution function and the associated Herman parameter. This approach provides data rapidly and over a wide range of lengthscales. Although likely to be applicable to a wide range of anisotropic nanoscale structures, the method was specifically developed to study CNT veils, a system in which orientation critically controls mechanical properties. Using this system as a model, key parameters for the 2D-FFT analysis were optimised, including magnification and domain size; a model set of CNT veils were pre-strained to 5%, 10% and 15%, to vary the alignment degree. The algorithm confirmed a narrower orientation distribution function and increasing Herman parameter, with increasing pre-strain. To validate the algorithm, the local orientation was compared to that derived from a common polarised Raman spectroscopy. Orientation maps of the Herman parameter, derived by both methods, showed good agreement. Quantitatively, the mean Herman parameter calculated using the polarised Raman spectroscopy was 0.42 ± 0.004 compared to 0.32 ± 0.002 for the 2D-FFT method, with a correlation coefficient of 0.73. Possible reasons for the modest and systematic discrepancy were discussed

3D Alignment of Projections in Electron Tomography

The goal of this thesis is to analyze the effect of projection angle errors on reconstructing 3D electron tomography. Noise, missing wedge and miss alignment are three main problems in electron tomography. This thesis focuses on how miss alignment affects the 3D reconstruction relative to the noise and missing wedge effects. Fourier-based iterative method (FIRM) is the main reconstruction method in this work. Instead of projecting the volume and back-projecting the tilt series in the image domain, FIRM conducts those operations in Frequency domain. By using non-uniform fast Fourier transform, FIRM avoids interpolation problem. Besides, the conjugate gradient method is used as the iterative reconstruction process to find the optimal solution. With the simulations, the impacts of noise, missing wedge and miss alignment are studied quantitatively. Missing wedge is the most influential factor among those three factors, the lack of enough information causes the reconstruction volume to be highly burred. Miss alignment has a similar effect as Gaussian noise. However, miss alignment also introduces artifacts in the reconstruction. Normalized mean-square error (NMSE) decreases and resolution increases when decreasing the level of miss alignment. After the level of 0.2-degree variance of projection angle error, the results does not show significant differences

Circulant temporal encoding for video retrieval and temporal alignment

We address the problem of specific video event retrieval. Given a query video of a specific event, e.g., a concert of Madonna, the goal is to retrieve other videos of the same event that temporally overlap with the query. Our approach encodes the frame descriptors of a video to jointly represent their appearance and temporal order. It exploits the properties of circulant matrices to efficiently compare the videos in the frequency domain. This offers a significant gain in complexity and accurately localizes the matching parts of videos. The descriptors can be compressed in the frequency domain with a product quantizer adapted to complex numbers. In this case, video retrieval is performed without decompressing the descriptors. We also consider the temporal alignment of a set of videos. We exploit the matching confidence and an estimate of the temporal offset computed for all pairs of videos by our retrieval approach. Our robust algorithm aligns the videos on a global timeline by maximizing the set of temporally consistent matches. The global temporal alignment enables synchronous playback of the videos of a given scene

Fast, Dense Feature SDM on an iPhone

In this paper, we present our method for enabling dense SDM to run at over 90 FPS on a mobile device. Our contributions are two-fold. Drawing inspiration from the FFT, we propose a Sparse Compositional Regression (SCR) framework, which enables a significant speed up over classical dense regressors. Second, we propose a binary approximation to SIFT features. Binary Approximated SIFT (BASIFT) features, which are a computationally efficient approximation to SIFT, a commonly used feature with SDM. We demonstrate the performance of our algorithm on an iPhone 7, and show that we achieve similar accuracy to SDM