84 research outputs found
A least-squares functional for joint exit wave reconstruction and image registration
Images generated by a transmission electron microscope (TEM) are blurred by
aberrations from the objective lens and can be difficult to interpret
correctly. One possible solution to this problem is to reconstruct the
so-called exit wave, i.e. the electron wave in the microscope right before it
passes the objective lens, from a series of TEM images acquired with varying
focus. While the forward model of simulating a TEM image from a given exit wave
is known and easy to evaluate, it is in general not possible to reconstruct the
exit wave from a series of images analytically. The corresponding inverse
problem can be formulated as a minimization problem, which is done in the well
known MAL and MIMAP methods. We propose a generalization of these methods by
performing the exit wave reconstruction and the registration of the image
series simultaneously. We show that our objective functional is not convex with
respect to the exit wave, which also carries over to the MAL and MIMAP
functionals. The main result is the existence of minimizers of our objective
functional. These results are based on the properties of a generalization of
the cross-correlation. Finally, the applicability of our method is verified
with a numerical experiment on simulated input data
Joint denoising and distortion correction of atomic scale scanning transmission electron microscopy images
Nowadays, modern electron microscopes deliver images at atomic scale. The
precise atomic structure encodes information about material properties. Thus,
an important ingredient in the image analysis is to locate the centers of the
atoms shown in micrographs as precisely as possible. Here, we consider scanning
transmission electron microscopy (STEM), which acquires data in a rastering
pattern, pixel by pixel. Due to this rastering combined with the magnification
to atomic scale, movements of the specimen even at the nanometer scale lead to
random image distortions that make precise atom localization difficult. Given a
series of STEM images, we derive a Bayesian method that jointly estimates the
distortion in each image and reconstructs the underlying atomic grid of the
material by fitting the atom bumps with suitable bump functions. The resulting
highly non-convex minimization problems are solved numerically with a trust
region approach. Well-posedness of the reconstruction method and the model
behavior for faster and faster rastering are investigated using variational
techniques. The performance of the method is finally evaluated on both
synthetic and real experimental data
Time Discrete Geodesic Paths in the Space of Images
In this paper the space of images is considered as a Riemannian manifold
using the metamorphosis approach, where the underlying Riemannian metric
simultaneously measures the cost of image transport and intensity variation. A
robust and effective variational time discretization of geodesics paths is
proposed. This requires to minimize a discrete path energy consisting of a sum
of consecutive image matching functionals over a set of image intensity maps
and pairwise matching deformations. For square-integrable input images the
existence of discrete, connecting geodesic paths defined as minimizers of this
variational problem is shown. Furthermore, -convergence of the
underlying discrete path energy to the continuous path energy is proved. This
includes a diffeomorphism property for the induced transport and the existence
of a square-integrable weak material derivative in space and time. A spatial
discretization via finite elements combined with an alternating descent scheme
in the set of image intensity maps and the set of matching deformations is
presented to approximate discrete geodesic paths numerically. Computational
results underline the efficiency of the proposed approach and demonstrate
important qualitative properties.Comment: 27 pages, 7 figure
A Posteriori Error Control for the Binary Mumford-Shah Model
The binary Mumford-Shah model is a widespread tool for image segmentation and
can be considered as a basic model in shape optimization with a broad range of
applications in computer vision, ranging from basic segmentation and labeling
to object reconstruction. This paper presents robust a posteriori error
estimates for a natural error quantity, namely the area of the non properly
segmented region. To this end, a suitable strictly convex and non-constrained
relaxation of the originally non-convex functional is investigated and Repin's
functional approach for a posteriori error estimation is used to control the
numerical error for the relaxed problem in the -norm. In combination with
a suitable cut out argument, a fully practical estimate for the area mismatch
is derived. This estimate is incorporated in an adaptive meshing strategy. Two
different adaptive primal-dual finite element schemes, and the most frequently
used finite difference discretization are investigated and compared. Numerical
experiments show qualitative and quantitative properties of the estimates and
demonstrate their usefulness in practical applications.Comment: 18 pages, 7 figures, 1 tabl
Joint methods in imaging based on diffuse image representations
This thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or piecewise constant manner. Especially the numerical treatment of the discontinuities requires additional models that are also outlined in this work. The main part of this thesis is concerned with four different topics. Simultaneous edge detection and registration of two images: The image edges are detected with the Ambrosio-Tortorelli model, an approximation of the Mumford-Shah model that approximates the discontinuity set with a phase field, and the registration is based on these edges. The registration obtained by this model is fully symmetric in the sense that the same matching is obtained if the roles of the two input images are swapped. Detection of grain boundaries from atomic scale images of metals or metal alloys: This is an image processing problem from materials science where atomic scale images are obtained either experimentally for instance by transmission electron microscopy or by numerical simulation tools. Grains are homogenous material regions whose atomic lattice orientation differs from their surroundings. Based on a Mumford-Shah type functional, the grain boundaries are modeled as the discontinuity set of the lattice orientation. In addition to the grain boundaries, the model incorporates the extraction of a global elastic deformation of the atomic lattice. Numerically, the discontinuity set is modeled by a level set function following the approach by Chan and Vese. Joint motion estimation and restoration of motion-blurred video: A variational model for joint object detection, motion estimation and deblurring of consecutive video frames is proposed. For this purpose, a new motion blur model is developed that accurately describes the blur also close to the boundary of a moving object. Here, the video is assumed to consist of an object moving in front of a static background. The segmentation into object and background is handled by a Mumford-Shah type aspect of the proposed model. Convexification of the binary Mumford-Shah segmentation model: After considering the application of Mumford-Shah type models to tackle specific image processing problems in the previous topics, the Mumford-Shah model itself is studied more closely. Inspired by the work of Nikolova, Esedoglu and Chan, a method is developed that allows global minimization of the binary Mumford-Shah segmentation model by solving a convex, unconstrained optimization problem. In an outlook, segmentation of flowfields into piecewise affine regions using this convexification method is briefly discussed
Mesh-to-raster based non-rigid registration of multi-modal images
Region of interest (ROI) alignment in medical images plays a crucial role in
diagnostics, procedure planning, treatment, and follow-up. Frequently, a model
is represented as triangulated mesh while the patient data is provided from CAT
scanners as pixel or voxel data. Previously, we presented a 2D method for
curve-to-pixel registration. This paper contributes (i) a general
mesh-to-raster (M2R) framework to register ROIs in multi-modal images; (ii) a
3D surface-to-voxel application, and (iii) a comprehensive quantitative
evaluation in 2D using ground truth provided by the simultaneous truth and
performance level estimation (STAPLE) method. The registration is formulated as
a minimization problem where the objective consists of a data term, which
involves the signed distance function of the ROI from the reference image, and
a higher order elastic regularizer for the deformation. The evaluation is based
on quantitative light-induced fluoroscopy (QLF) and digital photography (DP) of
decalcified teeth. STAPLE is computed on 150 image pairs from 32 subjects, each
showing one corresponding tooth in both modalities. The ROI in each image is
manually marked by three experts (900 curves in total). In the QLF-DP setting,
our approach significantly outperforms the mutual information-based
registration algorithm implemented with the Insight Segmentation and
Registration Toolkit (ITK) and Elastix
On the structure of defects in the Fe7Mo6 -Phase
Topologically close packed phases, among them the -phase studied here,
are commonly considered as being hard and brittle due to their close packed and
complex structure. Nanoindentation enables plastic deformation and therefore
investigation of the structure of mobile defects in the -phase, which, in
contrast to grown-in defects, has not been examined yet. High resolution
transmission electron microscopy (HR-TEM) performed on samples deformed by
nanoindentation revealed stacking faults which are likely induced by plastic
deformation. These defects were compared to theoretically possible stacking
faults within the -phase building blocks, and in particular Laves phase
layers. The experimentally observed stacking faults were found resulting from
synchroshear assumed to be associated with deformation in the Laves-phase
building blocks
Joint non-rigid image registration and reconstruction for quantitative atomic resolution scanning transmission electron microscopy
Aberration corrected scanning transmission electron microscopes (STEM) enable
to determine local strain fields, composition and bonding states at atomic
resolution. The precision to locate atomic columns is often obstructed by scan
artifacts limiting the quantitative interpretation of STEM datasets. Here, a
novel bias-corrected non-rigid registration approach is presented that
compensates for fast and slow scan artifacts in STEM image series. The
bias-correction is responsible for the correction of the slow scan artifacts
and based on a explicit coupling of the deformations of the individual images
in a series via a minimization of the average deformation. This allows to
reduce fast scan noise in an image series and slow scan distortions
simultaneously. The novel approach is tested on synthetic and experimental
images and its implication on atomic resolution strain and elemental mapping is
discussed
A distribution-dependent Mumford-Shah model for unsupervised hyperspectral image segmentation
Hyperspectral images provide a rich representation of the underlying spectrum
for each pixel, allowing for a pixel-wise classification/segmentation into
different classes. As the acquisition of labeled training data is very
time-consuming, unsupervised methods become crucial in hyperspectral image
analysis. The spectral variability and noise in hyperspectral data make this
task very challenging and define special requirements for such methods.
Here, we present a novel unsupervised hyperspectral segmentation framework.
It starts with a denoising and dimensionality reduction step by the
well-established Minimum Noise Fraction (MNF) transform. Then, the Mumford-Shah
(MS) segmentation functional is applied to segment the data. We equipped the MS
functional with a novel robust distribution-dependent indicator function
designed to handle the characteristic challenges of hyperspectral data. To
optimize our objective function with respect to the parameters for which no
closed form solution is available, we propose an efficient fixed point
iteration scheme. Numerical experiments on four public benchmark datasets show
that our method produces competitive results, which outperform two
state-of-the-art methods substantially on three of these datasets
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