48 research outputs found
Improved Orientation Sampling for Indexing Diffraction Patterns of Polycrystalline Materials
Orientation mapping is a widely used technique for revealing the
microstructure of a polycrystalline sample. The crystalline orientation at each
point in the sample is determined by analysis of the diffraction pattern, a
process known as pattern indexing. A recent development in pattern indexing is
the use of a brute-force approach, whereby diffraction patterns are simulated
for a large number of crystalline orientations, and compared against the
experimentally observed diffraction pattern in order to determine the most
likely orientation. Whilst this method can robust identify orientations in the
presence of noise, it has very high computational requirements. In this
article, the computational burden is reduced by developing a method for
nearly-optimal sampling of orientations. By using the quaternion representation
of orientations, it is shown that the optimal sampling problem is equivalent to
that of optimally distributing points on a four-dimensional sphere. In doing
so, the number of orientation samples needed to achieve a indexing desired
accuracy is significantly reduced. Orientation sets at a range of sizes are
generated in this way for all Laue groups, and are made available online for
easy use.Comment: 11 pages, 7 figure
Development of airborne hemispheric spectrometer
A new concept of hyperspectral instrument is presented. Novel design of hyperspectral skydome allows retrieval of atmospheric constituents and properties from a snapshot of spectral solar radiation over entire sky, regardless of platform motion either on ground or aircraft. Design and description of subsystems of the instrument are given followed by preliminary tolerance analysis, whose results are to be added in the retrieval algorithm along with hardware specifications. Extended application of the hyperspectral skydome is being carried out filling in the gap in the imaging spectrometry
Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold
Single image pose estimation is a fundamental problem in many vision and
robotics tasks, and existing deep learning approaches suffer by not completely
modeling and handling: i) uncertainty about the predictions, and ii) symmetric
objects with multiple (sometimes infinite) correct poses. To this end, we
introduce a method to estimate arbitrary, non-parametric distributions on
SO(3). Our key idea is to represent the distributions implicitly, with a neural
network that estimates the probability given the input image and a candidate
pose. Grid sampling or gradient ascent can be used to find the most likely
pose, but it is also possible to evaluate the probability at any pose, enabling
reasoning about symmetries and uncertainty. This is the most general way of
representing distributions on manifolds, and to showcase the rich expressive
power, we introduce a dataset of challenging symmetric and nearly-symmetric
objects. We require no supervision on pose uncertainty -- the model trains only
with a single pose per example. Nonetheless, our implicit model is highly
expressive to handle complex distributions over 3D poses, while still obtaining
accurate pose estimation on standard non-ambiguous environments, achieving
state-of-the-art performance on Pascal3D+ and ModelNet10-SO(3) benchmarks
Reconstructing continuous distributions of 3D protein structure from cryo-EM images
Cryo-electron microscopy (cryo-EM) is a powerful technique for determining
the structure of proteins and other macromolecular complexes at near-atomic
resolution. In single particle cryo-EM, the central problem is to reconstruct
the three-dimensional structure of a macromolecule from noisy and
randomly oriented two-dimensional projections. However, the imaged protein
complexes may exhibit structural variability, which complicates reconstruction
and is typically addressed using discrete clustering approaches that fail to
capture the full range of protein dynamics. Here, we introduce a novel method
for cryo-EM reconstruction that extends naturally to modeling continuous
generative factors of structural heterogeneity. This method encodes structures
in Fourier space using coordinate-based deep neural networks, and trains these
networks from unlabeled 2D cryo-EM images by combining exact inference over
image orientation with variational inference for structural heterogeneity. We
demonstrate that the proposed method, termed cryoDRGN, can perform ab initio
reconstruction of 3D protein complexes from simulated and real 2D cryo-EM image
data. To our knowledge, cryoDRGN is the first neural network-based approach for
cryo-EM reconstruction and the first end-to-end method for directly
reconstructing continuous ensembles of protein structures from cryo-EM images
A novel sampling theorem on the rotation group
We develop a novel sampling theorem for functions defined on the
three-dimensional rotation group SO(3) by connecting the rotation group to the
three-torus through a periodic extension. Our sampling theorem requires
samples to capture all of the information content of a signal band-limited at
, reducing the number of required samples by a factor of two compared to
other equiangular sampling theorems. We present fast algorithms to compute the
associated Fourier transform on the rotation group, the so-called Wigner
transform, which scale as , compared to the naive scaling of .
For the common case of a low directional band-limit , complexity is reduced
to . Our fast algorithms will be of direct use in speeding up the
computation of directional wavelet transforms on the sphere. We make our SO3
code implementing these algorithms publicly available.Comment: 5 pages, 2 figures, minor changes to match version accepted for
publication. Code available at http://www.sothree.or