1,034 research outputs found
Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities
Intensity inhomogeneities in images constitute a considerable challenge in
image segmentation. In this paper we propose a novel biconvex variational model
to tackle this task. We combine a total variation approach for multi class
segmentation with a multiplicative model to handle the inhomogeneities. Our
method assumes that the image intensity is the product of a smoothly varying
part and a component which resembles important image structures such as edges.
Therefore, we penalize in addition to the total variation of the label
assignment matrix a quadratic difference term to cope with the smoothly varying
factor. A critical point of our biconvex functional is computed by a modified
proximal alternating linearized minimization method (PALM). We show that the
assumptions for the convergence of the algorithm are fulfilled by our model.
Various numerical examples demonstrate the very good performance of our method.
Particular attention is paid to the segmentation of 3D FIB tomographical images
which was indeed the motivation of our work
Retrospective Illumination Correction of Retinal Images
A method for correction of nonhomogenous illumination based on optimization of parameters of B-spline shading model with respect to Shannon's entropy is presented. The evaluation of Shannon's entropy is based on Parzen windowing method (Mangin, 2000) with the spline-based shading model. This allows us to express the derivatives of the entropy criterion analytically, which enables efficient use of gradient-based optimization algorithms. Seven different gradient- and nongradient-based optimization algorithms were initially tested on a set of 40 simulated retinal images, generated by a model of the respective image acquisition system. Among the tested optimizers, the gradient-based optimizer with varying step has shown to have the fastest convergence while providing the best precision. The final algorithm proved to be able of suppressing approximately 70% of the artificially introduced non-homogenous illumination. To assess the practical utility of the method, it was qualitatively tested on a set of 336 real retinal images; it proved the ability of eliminating the illumination inhomogeneity substantially in most of cases. The application field of this method is especially in preprocessing of retinal images, as preparation for reliable segmentation or registration
A robust similarity measure for volumetric image registration with outliers
Image registration under challenging realistic conditions is a very important area of research. In this paper, we focus on algorithms that seek to densely align two volumetric images according to a global similarity measure. Despite intensive research in this area, there is still a need for similarity measures that are robust to outliers common to many different types of images. For example, medical image data is often corrupted by intensity inhomogeneities and may contain outliers in the form of pathologies. In this paper we propose a global similarity measure that is robust to both intensity inhomogeneities and outliers without requiring prior knowledge of the type of outliers. We combine the normalised gradients of images with the cosine function and show that it is theoretically robust against a very general class of outliers. Experimentally, we verify the robustness of our measures within two distinct algorithms. Firstly, we embed our similarity measures within a proof-of-concept extension of the Lucas–Kanade algorithm for volumetric data. Finally, we embed our measures within a popular non-rigid alignment framework based on free-form deformations and show it to be robust against both simulated tumours and intensity inhomogeneities
Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery
PCA is one of the most widely used dimension reduction techniques. A related
easier problem is "subspace learning" or "subspace estimation". Given
relatively clean data, both are easily solved via singular value decomposition
(SVD). The problem of subspace learning or PCA in the presence of outliers is
called robust subspace learning or robust PCA (RPCA). For long data sequences,
if one tries to use a single lower dimensional subspace to represent the data,
the required subspace dimension may end up being quite large. For such data, a
better model is to assume that it lies in a low-dimensional subspace that can
change over time, albeit gradually. The problem of tracking such data (and the
subspaces) while being robust to outliers is called robust subspace tracking
(RST). This article provides a magazine-style overview of the entire field of
robust subspace learning and tracking. In particular solutions for three
problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition
(S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an
entire data vector is either an outlier or an inlier. The S+LR formulation
instead assumes that outliers occur on only a few data vector indices and hence
are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201
Accelerated High-Resolution Photoacoustic Tomography via Compressed Sensing
Current 3D photoacoustic tomography (PAT) systems offer either high image
quality or high frame rates but are not able to deliver high spatial and
temporal resolution simultaneously, which limits their ability to image dynamic
processes in living tissue. A particular example is the planar Fabry-Perot (FP)
scanner, which yields high-resolution images but takes several minutes to
sequentially map the photoacoustic field on the sensor plane, point-by-point.
However, as the spatio-temporal complexity of many absorbing tissue structures
is rather low, the data recorded in such a conventional, regularly sampled
fashion is often highly redundant. We demonstrate that combining variational
image reconstruction methods using spatial sparsity constraints with the
development of novel PAT acquisition systems capable of sub-sampling the
acoustic wave field can dramatically increase the acquisition speed while
maintaining a good spatial resolution: First, we describe and model two general
spatial sub-sampling schemes. Then, we discuss how to implement them using the
FP scanner and demonstrate the potential of these novel compressed sensing PAT
devices through simulated data from a realistic numerical phantom and through
measured data from a dynamic experimental phantom as well as from in-vivo
experiments. Our results show that images with good spatial resolution and
contrast can be obtained from highly sub-sampled PAT data if variational image
reconstruction methods that describe the tissues structures with suitable
sparsity-constraints are used. In particular, we examine the use of total
variation regularization enhanced by Bregman iterations. These novel
reconstruction strategies offer new opportunities to dramatically increase the
acquisition speed of PAT scanners that employ point-by-point sequential
scanning as well as reducing the channel count of parallelized schemes that use
detector arrays.Comment: submitted to "Physics in Medicine and Biology
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