A Alessandro Becciu

A Multi-scale Feature Based Optic Flow Method for 3D Cardiac Motion Estimation

The dynamic behavior of the cardiac muscle is strongly dependent on heart diseases. Optic flow techniques are essential tools to assess and quantify the contraction of the cardiac walls. Most of the current methods however are restricted to the analysis of 2D MR-tagging image sequences: due to the complex twisting motion combined with longitudinal shortening, a 2D approach will always suffer from through-plane motion. In this paper we investigate a new 3D aperture-problem free optic flow method to study the cardiac motion by tracking stable multi-scale features such as maxima and minima on 3D tagged MR and sine-phase image volumes. We applied harmonic filtering in the Fourier domain to measure the phase. This removes the dependency of intensity changes of the tagging pattern over time due to T1 relaxation. The regular geometry, the size-changing patterns of the MR-tags stretching and compressing along with the tissue, and the phase- and sine-phase plots represent a suitable framework to extract robustly multi-scale landmark features. Experiments were performed on real and phantom data and the results revealed the reliability of the extracted vector field. Our new 3D multi-scale optic flow method is a promising technique for analyzing true 3D cardiac motion at voxel precision, and free of through-plane artifacts present in multiple-2D data sets.

A variational approach to cardiac motion estimation based on covariant derivatives and multi-scale Helmholtz decomposition

The investigation and quantification of cardiac motion is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider a new method to track cardiac motion from magnetic resonance (MR) tagged images. Tracking is achieved by following the spatial maxima in scale-space of the MR images over time. Reconstruction of the velocity field is then carried out by minimizing an energy functional which is a Sobolev-norm expressed in covariant derivatives. These covariant derivatives are used to express prior knowledge about the velocity field in the variational framework employed. Furthermore, we propose a multi-scale Helmholtz decomposition algorithm that combines diffusion and Helmholtz decomposition in one non-singular analytic kernel operator in order to decompose the optic flow vector field in a divergence free, and rotation free part. Finally, we combine both the multi-scale Helmholtz decomposition and our vector field reconstruction (based on covariant derivatives) in a single algorithm and show the practical benefit of this approach by an experiment on real cardiac images.

3D winding number: theory and application to medical imaging

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.

Extraction of Cardiac Motion Using Scale-Space Features Points and Gauged Reconstruction

Motion estimation is an important topic in medical image analysis. The investigation and quantification of, e.g., the cardiac movement is important for assessment of cardiac abnormalities and to get an indication of response to therapy. In this paper we present a new aperture problem-free method to track cardiac motion from 2-dimensional MR tagged images and corresponding sine-phase images. Tracking is achieved by following the movement of scale-space critical points such as maxima, minima and saddles. Reconstruction of dense velocity field is carried out by minimizing an energy functional with regularization term influenced by covariant derivatives gauged by a prior assumption. MR tags deform along with the tissue, a combination of MR tagged images and sine-phase images was employed to produce a regular grid from which the scale-space critical points were retrieved. Experiments were carried out on real image data, and on artificial phantom data from which the ground truth is known. A comparison between our new method and a similar technique based on homogeneous diffusion regularization and standard derivatives shows increase in performance. Qualitative and quantitative evaluation emphasize the reliability of dense motion field allowing further analysis of deformation and torsion of the cardiac wall.

Cardiac motion estimation using covariant derivatives and helmholtz decomposition

Quantification of cardiac function is important for the assessment of abnormalities and response to therapy. We present a method to reconstruct dense cardiac motion from sparse features in tagging MRI, decomposed into solenoidal and irrotational parts using multi-scale Helmholtz decomposition. Reconstruction is based on energy minimization using covariant derivatives exploiting prior knowledge about the motion field. The method is tested on cardiac motion images. Experiments on phantom data show that both covariant derivatives and multi-scale Helmholtz decomposition improve motion field reconstruction.