831 research outputs found
A closed-form solution to estimate uncertainty in non-rigid structure from motion
Semi-Definite Programming (SDP) with low-rank prior has been widely applied
in Non-Rigid Structure from Motion (NRSfM). Based on a low-rank constraint, it
avoids the inherent ambiguity of basis number selection in conventional
base-shape or base-trajectory methods. Despite the efficiency in deformable
shape reconstruction, it remains unclear how to assess the uncertainty of the
recovered shape from the SDP process. In this paper, we present a statistical
inference on the element-wise uncertainty quantification of the estimated
deforming 3D shape points in the case of the exact low-rank SDP problem. A
closed-form uncertainty quantification method is proposed and tested. Moreover,
we extend the exact low-rank uncertainty quantification to the approximate
low-rank scenario with a numerical optimal rank selection method, which enables
solving practical application in SDP based NRSfM scenario. The proposed method
provides an independent module to the SDP method and only requires the
statistic information of the input 2D tracked points. Extensive experiments
prove that the output 3D points have identical normal distribution to the 2D
trackings, the proposed method and quantify the uncertainty accurately, and
supports that it has desirable effects on routinely SDP low-rank based NRSfM
solver.Comment: 9 pages, 2 figure
3D + t Morphological Processing: Applications to Embryogenesis Image Analysis
We propose to directly process 3D + t image sequences with mathematical morphology operators, using a new classi?cation of the 3D+t structuring elements. Several methods (?ltering, tracking, segmentation) dedicated to the analysis of 3D + t datasets of zebra?sh embryogenesis are introduced and validated through a synthetic dataset. Then, we illustrate the application of these methods to the analysis of datasets of zebra?sh early development acquired with various microscopy techniques. This processing paradigm produces spatio-temporal coherent results as it bene?ts from the intrinsic redundancy of the temporal dimension, and minimizes the needs for human intervention in semi-automatic algorithms
High-Performance 3D Compressive Sensing MRI Reconstruction Using Many-Core Architectures
Compressive sensing (CS) describes how sparse
signals can be accurately reconstructed from many fewer samples
than required by the Nyquist criterion. Since MRI scan duration
is proportional to the number of acquired samples, CS has been
gaining significant attention in MRI. However, the computationally
intensive nature of CS reconstructions has precluded their
use in routine clinical practice. In this work, we investigate how
different throughput-oriented architectures can benefit one CS
algorithm and what levels of acceleration are feasible on different
modern platforms. We demonstrate that a CUDA-based code
running on an NVIDIA Tesla C2050 GPU can reconstruct a
256 × 160 × 80 volume from an 8-channel acquisition in 19 seconds,
which is in itself a significant improvement over the state of the art. We then
show that Intel's Knights Ferry can perform the same 3D MRI
reconstruction in only 12 seconds, bringing CS methods even
closer to clinical viability
Phase Retrieval via Matrix Completion
This paper develops a novel framework for phase retrieval, a problem which
arises in X-ray crystallography, diffraction imaging, astronomical imaging and
many other applications. Our approach combines multiple structured
illuminations together with ideas from convex programming to recover the phase
from intensity measurements, typically from the modulus of the diffracted wave.
We demonstrate empirically that any complex-valued object can be recovered from
the knowledge of the magnitude of just a few diffracted patterns by solving a
simple convex optimization problem inspired by the recent literature on matrix
completion. More importantly, we also demonstrate that our noise-aware
algorithms are stable in the sense that the reconstruction degrades gracefully
as the signal-to-noise ratio decreases. Finally, we introduce some theory
showing that one can design very simple structured illumination patterns such
that three diffracted figures uniquely determine the phase of the object we
wish to recover
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