Abstract: Distortion of Left Ventricle (LV) external anatomy is related to some dysfunctions, such as hypertrophy. The architecture of myocardial fibers determines LV electromechanical activation patterns as well as mechanics. Thus, their joined modelling would allow the design of specific interventions (such as peacemaker implantation and LV remodelling) and therapies (such as resynchronization). On one hand, accurate modelling of external anatomy requires either a dense sampling or a continuous infinite dimensional approach, which requires non-Euclidean statistics. On the other hand, computation of fiber models requires statistics on Riemannian spaces. Most approaches compute separate statistical models for external anatomy and fibers architecture. In this work we propose a general mathematical framework based on differential geometry concepts for computing a statistical model including, both, external and fiber anatomy. Our framework provides a continuous approach to external anatomy supporting standard statistics. We also provide a straightforward formula for the computation of the Riemannian fiber statistics. We have applied our methodology to the computation of complete anatomical atlas of canine hearts from diffusion tensor studies. The orientation of fibers over the average external geometry agrees with the segmental description of orientations reported in the literature.

Abstract: Smoothing of biomedical images should preserve gray-level transitions between adjacent tissues, while restoring contours consistent with anatomical structures. Anisotropic diffusion operators are based on image appearance discontinuities (either local or contextual) and might fail at weak inter-tissue transitions. Meanwhile, the output of block-wise and morphological operations is prone to present a block structure due to the shape and size of the considered pixel neighborhood. In this contribution, we use differential geometry concepts to define a diffusion operator that restricts to image consistent level-sets. In this manner, the final state is a non-uniform intensity image presenting homogeneous inter-tissue transitions along anatomical structures, while smoothing intra-structure texture. Experiments on different types of medical images (magnetic resonance, computerized tomography) illustrate its benefit on a further process (such as segmentation) of images.

Abstract: A good reliable approach to cardiac triggering is of utmost importance in obtaining accurate quantitative results of atherosclerotic plaque burden from the analysis of IntraVascular UltraSound. Although, in the last years, there has been an increase in research of methods for retrospective gating, there is no general consensus in a validation protocol. Many methods are based on quality assessment of longitudinal cuts appearance and those reporting quantitative numbers do not follow a standard protocol. Such heterogeneity in validation protocols makes faithful comparison across methods a difficult task. We propose a validation protocol based on the variability of the retrieved cardiac phase and explore the capability of several quality measures for quantifying such variability. An ideal detector, suitable for its application in clinical practice, should produce stable phases. That is, it should always sample the same cardiac cycle fraction. In this context, one should measure the variability (variance) of a candidate sampling with respect a ground truth (reference) sampling, since the variance would indicate how spread we are aiming a target. In order to quantify the deviation between the sampling and the ground truth, we have considered two quality scores reported in the literature: signed distance to the closest reference sample and distance to the right of each reference sample. We have also considered the residuals of the regression line of reference against candidate sampling. The performance of the measures has been explored on a set of synthetic samplings covering different cardiac cycle fractions and variabilities. From our simulations, we conclude that the metrics related to distances are sensitive to the shift considered while the residuals are robust against fraction and variabilities as far as one can establish a pair-wise correspondence between candidate and reference. We will further investigate the impact of false positive and negative detections in experimental data.

Abstract: Cardiac vessel displacement is a main artifact in IVUS sequences. It hinders visualization of the main structures in an appropriate orientation and alignment and affects extracting vessel measurements. In this paper, we present a novel approach for image sequence alignment based on spectral analysis, which removes rigid dynamics, preserving at the same time the vessel geometry. First, we suppress the translation by taking, for each frame, the center of mass of the image as origin of coordinates. In polar coordinates with such point as origin, the rotation appears as a horizontal displacement. The translation induces a phase shift in the Fourier coefficients of two consecutive polar images. We estimate the phase by adjusting a regression plane to the phases of the principal frequencies. Experiments show that the presented strategy suppress cardiac motion regardless of the acquisition device. 1.

Abstract: Optical flow is a valuable tool for motion analysis in medical imaging sequences. A reliable application requires determining the accuracy of the computed optical flow. This is a main challenge given the absence of ground truth in medical sequences. This paper presents an error analysis of Lucas-Kanade schemes in terms of intrinsic design errors and numerical stability of the algorithm. Our analysis provides a confidence measure that is naturally correlated to the accuracy of the flow field. Our experiments show the higher predictive value of our confidence measure compared to existing measures.