We present a new algorithm for automatic detection of bright tubular structures and its performance for automatic
segmentation of vessels in breast MR sequences. This problem is interesting because vessels are the main
type of false positive structures when automatically detecting lesions as regions that enhance after injection of
the contrast agent. Our algorithm is based on the eigenvalues of what we call the shape tensor. It is new in
that it does not rely on image derivatives of either first order, like methods based on the eigenvalues of the mean
structure tensor, or second order, like methods based on the eigenvalues of the Hessian. It is therefore more
precise and less sensitive to noise than those methods. In addition, the smoothing of the output which is inherent
to approaches based on the Hessian or structure tensor is avoided. The output of our filter does not present
the typical over-smoothed look of the output of the two differential filters that affects both their precision and
sensitivity. The scale selection problem appears also less difficult in our approach compared to the differential
techniques. Our algorithm is fast, needing only a few seconds per sequence. We present results of testing our
method on a large number of motion-corrected breast MR sequences. These results show that our algorithm
reliably segments vessels while leaving lesions intact. We also compare our method to the differential techniques
and show that it significantly out-performs them both in sensitivity and localization precision and that it is less
sensitive to scale selection parameters.
KEYWORDS: Reconstruction algorithms, 3D image reconstruction, Image quality, Tolerancing, 3D image processing, Magnetic resonance imaging, Image restoration, Chemical elements, 3D applications, Computer simulations
Non-uniformly sampled data in MRI applications must be interpolated onto a regular Cartesian grid to perform fast image reconstruction using FFT. The conventional method for this is gridding, which requires a density compensation function (DCF). The calculation of DCF may be time-consuming, ambiguously defined, and may not be always reusable due to changes in k-space trajectories. A recently proposed reconstruction method that eliminates the requirement of DCF is block uniform resampling (BURS) which uses singular value decomposition (SVD). However, the SVD is still computationally intensive. In this work, we present a modified BURS algorithm using conjugate gradient method (CGM) in place of direct SVD calculation. Calculation of a block of grid point values in each iteration further reduces the computational load. The new method reduces the calculation complexity while maintaining a high-quality reconstruction result. For an n-by-n matrix, the time complexity per iteration is reduced from O(n*n*n) in SVD to O(n*n) in CGM. The time can be further reduced when we stop the iteration in CGM earlier according to the norm of the residual vector. Using this method, the quality of the reconstructed image improves compared to regularized BURS. The reduced time complexity and improved reconstruction result make the new algorithm promising in dealing with large-sized images and 3D images.
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