2,056 research outputs found
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
Light field image processing: an overview
Light field imaging has emerged as a technology allowing to capture richer visual information from our world. As opposed to traditional photography, which captures a 2D projection of the light in the scene integrating the angular domain, light fields collect radiance from rays in all directions, demultiplexing the angular information lost in conventional photography. On the one hand, this higher dimensional representation of visual data offers powerful capabilities for scene understanding, and substantially improves the performance of traditional computer vision problems such as depth sensing, post-capture refocusing, segmentation, video stabilization, material classification, etc. On the other hand, the high-dimensionality of light fields also brings up new challenges in terms of data capture, data compression, content editing, and display. Taking these two elements together, research in light field image processing has become increasingly popular in the computer vision, computer graphics, and signal processing communities. In this paper, we present a comprehensive overview and discussion of research in this field over the past 20 years. We focus on all aspects of light field image processing, including basic light field representation and theory, acquisition, super-resolution, depth estimation, compression, editing, processing algorithms for light field display, and computer vision applications of light field data
Development and Assessment of a Micro-CT Based System for Quantifying Loaded Knee Joint Kinematics and Tissue Mechanics
Although anterior cruciate ligament (ACL) reconstruction is a highly developed surgical procedure, sub-optimal treatment outcomes persist. This can be partially attributed to an incomplete understanding of knee joint kinematics and regional tissue mechanic properties. A system for minimally-invasive investigation of knee joint kinematics and tissue mechanics under clinically relevant joint loads was developed to address this gap in understanding. A five degree-of-freedom knee joint motion simulator capable of dynamically loading intact human cadaveric knee joints to within 1% of user defined multi-axial target loads was developed. This simulator was uniquely designed to apply joint loads to a joint centered within the field of view of a micro-CT scanner. The use of micro-CT imaging and tissue-embedded radiopaque beads demonstrated high-resolution strain measurement, distinguishing differences in inter-bead distances as low as 0.007 mm. Inter-bead strain measurement was highly accurate and repeatable, with no significant error introduced from cyclic joint loading. Finally, regional strain was repeatably measured using radiopaque markers in four intact, human cadaveric knees to within 0.003 strain in response to multi-directional joint loads. This novel combination of dynamic knee joint motion simulation, tissue-embedded radiopaque markers, and micro-CT imaging provides the opportunity to increase our understanding of the kinematics and tissue mechanics of the knee, with the potential to improve ACL reconstruction outcomes
Sparse and Redundant Representations for Inverse Problems and Recognition
Sparse and redundant representation of data enables the
description of signals as linear combinations of a few atoms from
a dictionary. In this dissertation, we study applications of
sparse and redundant representations in inverse problems and
object recognition. Furthermore, we propose two novel imaging
modalities based on the recently introduced theory of Compressed
Sensing (CS).
This dissertation consists of four major parts. In the first part
of the dissertation, we study a new type of deconvolution
algorithm that is based on estimating the image from a shearlet
decomposition. Shearlets provide a multi-directional and
multi-scale decomposition that has been mathematically shown to
represent distributed discontinuities such as edges better than
traditional wavelets. We develop a deconvolution algorithm that
allows for the approximation inversion operator to be controlled
on a multi-scale and multi-directional basis. Furthermore, we
develop a method for the automatic determination of the threshold
values for the noise shrinkage for each scale and direction
without explicit knowledge of the noise variance using a
generalized cross validation method.
In the second part of the dissertation, we study a reconstruction
method that recovers highly undersampled images assumed to have a
sparse representation in a gradient domain by using partial
measurement samples that are collected in the Fourier domain. Our
method makes use of a robust generalized Poisson solver that
greatly aids in achieving a significantly improved performance
over similar proposed methods. We will demonstrate by experiments
that this new technique is more flexible to work with either
random or restricted sampling scenarios better than its
competitors.
In the third part of the dissertation, we introduce a novel
Synthetic Aperture Radar (SAR) imaging modality which can provide
a high resolution map of the spatial distribution of targets and
terrain using a significantly reduced number of needed transmitted
and/or received electromagnetic waveforms. We demonstrate that
this new imaging scheme, requires no new hardware components and
allows the aperture to be compressed. Also, it
presents many new applications and advantages which include strong
resistance to countermesasures and interception, imaging much
wider swaths and reduced on-board storage requirements.
The last part of the dissertation deals with object recognition
based on learning dictionaries for simultaneous sparse signal
approximations and feature extraction. A dictionary is learned
for each object class based on given training examples which
minimize the representation error with a sparseness constraint. A
novel test image is then projected onto the span of the atoms in
each learned dictionary. The residual vectors along with the
coefficients are then used for recognition. Applications to
illumination robust face recognition and automatic target
recognition are presented
Mapping Trabecular Bone Fabric Tensor by in Vivo Magnetic Resonance Imaging
The mechanical competence of bone depends upon its quantity, structural arrangement, and chemical composition. Assessment of these factors is important for the evaluation of bone integrity, particularly as the skeleton remodels according to external (e.g. mechanical loading) and internal (e.g. hormonal changes) stimuli. Micro magnetic resonance imaging (µMRI) has emerged as a non-invasive and non-ionizing method well-suited for the repeated measurements necessary for monitoring changes in bone integrity. However, in vivo image-based directional dependence of trabecular bone (TB) has not been linked to mechanical competence or fracture risk despite the existence of convincing ex vivo evidence. The objective of this dissertation research was to develop a means of capturing the directional dependence of TB by assessing a fabric tensor on the basis of in vivo µMRI. To accomplish this objective, a novel approach for calculating the TB fabric tensor based on the spatial autocorrelation function was developed and evaluated in the presence of common limitations to in vivo µMRI. Comparisons were made to the standard technique of mean-intercept-length (MIL). Relative to MIL, ACF was identified as computationally faster by over an order of magnitude and more robust within the range of the resolutions and SNRs achievable in vivo. The potential for improved sensitivity afforded by isotropic resolution was also investigated in an improved µMR imaging protocol at 3T. Measures of reproducibility and reliability indicate the potential of images with isotropic resolution to provide enhanced sensitivity to orientation-dependent measures of TB, however overall reproducibility suffered from the sacrifice in SNR. Finally, the image-derived TB fabric tensor was validated through its relationship with TB mechanical competence in specimen and in vivo µMR images. The inclusion of trabecular bone fabric measures significantly improved the bone volume fraction-based prediction of elastic constants calculated by micro-finite element analysis. This research established a method for detecting TB fabric tensor in vivo and identified the directional dependence of TB as an important determinant of TB mechanical competence
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
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