The blood vessels and nerve trees consist of tubular objects interconnected into a complex tree- or web-like structure that has a range of structural scale 5 <svg style="vertical-align:-3.56265pt;width:9.5625px;" id="M1" height="12.175" version="1.1" viewBox="0 0 9.5625 12.175" width="9.5625" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D707" d="M538 96q-38 -45 -84 -76.5t-71 -31.5q-44 0 -15 117q12 49 18 89h-2q-99 -128 -163 -178q-36 -28 -70 -28q-26 0 -44 38h-2q-16 -69 -16 -129q0 -43 11 -75.5t24 -42.5l1 -6q-7 -12 -24.5 -23t-37.5 -11q-40 0 -40 76q0 52 35 202l94 407l78 24l5 -5q-32 -122 -72 -310&#xA;q-7 -33 0 -55t25 -22q36 0 105.5 75t107.5 145l32 146l75 26h10q-50 -197 -78 -347q-7 -38 6 -38q7 0 31 17t47 39z" /></g></svg>m diameter capillaries to 3 cm aorta. This large-scale range presents two major problems; one is just making the measurements, and the other is the exponential increase of component numbers with decreasing scale. With the remarkable increase in the volume imaged by, and resolution of, modern day 3D imagers, it is almost impossible to make manual tracking of the complex multiscale parameters from those large image data sets. In addition, the manual tracking is quite subjective and unreliable. We propose a solution for automation of an adaptive nonsupervised system for tracking tubular objects based on multiscale framework and use of Hessian-based object shape detector incorporating National Library of Medicine Insight Segmentation and Registration Toolkit (ITK) image processing libraries.

Oleksandr P. Dzyubak

Erik L. Ritman

Automation of Hessian-Based Tubularity Measure Response Function in 3D Biomedical Images


		We develop a new formulation, mathematically elegant, to detect critical points of 3D scalar images. It is based on a topological number, which is the generalization to three dimensions of the 2D winding number. We illustrate our method by considering three different biomedical applications, namely, detection and counting of ovarian follicles and neuronal cells and estimation of cardiac motion from tagged MR images. Qualitative and quantitative evaluation emphasizes the reliability of the results.

Alessandro Becciu

Andrea Fuster

Mark Pottek

Bart van den Heuvel

Bart ter Haar Romeny

Hans van Assen

3D Winding Number: Theory and Application to Medical Imaging

Nonrigid image registration is widely used to estimate
tissue deformations in highly deformable anatomies. Among
the existing methods, nonparametric registration algorithms
such as optical flow, or Demons, usually have the advantage of
being fast and easy to use. Recently, a diffeomorphic version
of the Demons algorithm was proposed. This provides the
advantage of producing invertible displacement fields, which
is a necessary condition for these to be physical. However,
such methods are based on the matching of intensities and
are not suitable for registering images with different contrast
enhancement. In such cases, a registration method based on the
local phase like the Morphons has to be used. In this paper, a
diffeomorphic version of the Morphons registration method is
proposed and compared to conventional Morphons, Demons,
and diffeomorphic Demons. The method is validated in the
context of radiotherapy for lung cancer patients on several
4D respiratory-correlated CT scans of the thorax with and without
variable contrast enhancement.

Guillaume Janssens

Laurent Jacques

Jonathan Orban de Xivry

Xavier Geets

Benoit Macq

Diffeomorphic Registration of Images with Variable Contrast Enhancement

Dynamic PET, in contrast to static PET, can identify temporal variations in the radiotracer concentration. Mathematical modeling of the tissue of interest in dynamic PET can be simplified using compartment models as a linear system where the time activity curve of a specific tissue is the convolution of the tracer concentration in the plasma and the impulse response of the tissue containing kinetic parameters. Since the arterial sampling of blood to acquire the value of tracer concentration is invasive, blind methods to estimate both blood input function and kinetic parameters have recently drawn attention. Several methods have been developed, but the effect of accuracy of the estimated blood function on the estimation of the kinetic parameters is not studied. In this paper, we present a method to compute the error in the kinetic parameter estimates caused by the error in the blood input function. Computer simulations show that analytical expressions we derive are sufficiently close to results obtained from numerical methods. Our findings are important to observe the effect of the blood function on kinetic parameter estimation, but also useful to evaluate various blind methods and observe the dependence of kinetic parameter estimates to certain parts of the blood function.

Yafang Cheng

&#304;mam &#350;amil Yetik

Propagation of Blood Function Errors to the Estimates of Kinetic Parameters with Dynamic PET

This paper provides 
                  auxiliary results for our general scheme of 
                  computed tomography.  In 3D 
                  parallel-beam geometry, we first demonstrate 
                  that the inverse Fourier transform in different 
                  coordinate systems leads to different 
                  reconstruction formulas and explain why the 
                  Radon formula cannot directly work with 
                  truncated projection data.  Also, we introduce a 
                  gamma coordinate system, analyze its properties, compute the Jacobian of the coordinate transform, and define weight functions for the inverse Fourier transform assuming a simple scanning model. Then, we generate Orlov's theorem and a weighted Radon formula from the inverse Fourier transform in the new system. Furthermore, we present the motion equation of the frequency plane and the conditions for sharp points of the instantaneous rotation axis. Our analysis on the motion of the frequency plane is related to the Frenet-Serret theorem in the differential geometry.

Yuchuan Wei

Hengyong Yu

Ge Wang

Inverse Fourier Transform in the Gamma Coordinate System

Bioluminescence tomography (BLT) is a promising tool for studying physiological and pathological processes at cellular and molecular levels. In most clinical or preclinical practices, fine discretization is needed for recovering sources with acceptable resolution when solving BLT with finite element method (FEM). Nevertheless, uniformly fine meshes would cause large dataset and overfine meshes might aggravate the ill-posedness of BLT. Additionally, accurately quantitative information of density and power has not been simultaneously obtained so far. In this paper, we present a novel multilevel sparse reconstruction method based on adaptive FEM framework. In this method, permissible source region gradually reduces with adaptive local mesh refinement. By using sparse reconstruction with <svg style="vertical-align:-3.13504pt;width:11.1875px;" id="M1" height="14.475" version="1.1" viewBox="0 0 11.1875 14.475" width="11.1875" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(1.25,0,0,-1.25,0,14.475)"><g transform="translate(72,-60.42)"><text transform="matrix(1,0,0,-1,-71.95,63.6)"><tspan style="font-size: 12.50px; " x="0" y="0">𝑙</tspan></text><text transform="matrix(1,0,0,-1,-67.97,60.47)"><tspan style="font-size: 8.75px; " x="0" y="0">1</tspan></text></g></g></svg> regularization on multilevel adaptive meshes, simultaneous recovery of density and power as well as accurate source location can be achieved. Experimental results for heterogeneous phantom and mouse atlas model demonstrate its effectiveness and potentiality in the application of quantitative BLT.

Xiaowei He

Yanbin Hou

Duofang Chen

Yuchuan Jiang

Man Shen

Junting Liu

Qitan Zhang

Jie Tian

Sparse Regularization-Based Reconstruction for Bioluminescence Tomography Using a Multilevel Adaptive Finite Element Method

To maximize the time-integrated X-ray flux from multiple X-ray sources and shorten the data acquisition process, a promising way is to allow overlapped projections from multiple sources being simultaneously on without involving the source multiplexing technology. The most challenging task in this configuration is to perform image reconstruction effectively and efficiently from overlapped projections. Inspired by the single-source simultaneous algebraic reconstruction technique (SART), we hereby develop a multisource SART-type reconstruction algorithm regularized by a sparsity-oriented constraint in the soft-threshold filtering framework to reconstruct images from overlapped projections. Our numerical simulation results verify the correctness of the proposed algorithm and demonstrate the advantage of image reconstruction from overlapped projections.

Changguo Ji

SART-Type Image Reconstruction from Overlapped Projections

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<p><em>International Journal of Biomedical Imaging</em> aims to promote research and development of biomedical imaging by publishing high-quality research articles and reviews in this rapidly growing interdisciplinary field.</p>


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International Journal of Biomedical Imaging - Table of contents 2011

International Journal of Biomedical Imaging | Hindawi

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International Journal of Biomedical Imaging aims to promote research and development of biomedical imaging by publishing high-quality research articles and reviews in this rapidly growing interdisciplinary field.

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International Journal of Biomedical Imaging

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International Journal of Biomedical Imaging