3D Hermite Transform Optical Flow Estimation in Left Ventricle CT Sequences Heart diseases are the most important causes of death in the world and over the years, thestudy of cardiac movement has been carried out mainly in two dimensions, however, it is important toconsider that the deformations due to the movement of the heart occur in a threedimensional space.The 3D  t analysis allows to describe most of the motions of the heart, for example, the twistingmotion that takes place on every beat cycle that allows us identifying abnormalities of the heartwalls. Therefore, it is necessary to develop algorithms that help specialists understand the cardiacmovement. In this work, we developed a new approach to determine the cardiac movement inthree dimensions using a differential optical flow approach in which we use the steered Hermitetransform (SHT) which allows us to decompose cardiac volumes taking advantage of it as a model ofthe human vision system (HVS). Our proposal was tested in complete cardiac computed tomography(CT) volumes ( 3D  t), as well as its respective left ventricular segmentation. The robustness tonoise was tested with good results. The evaluation of the results was carried out through errors inforwarding reconstruction, from the volume at time t to time t  1 using the optical flow obtained(interpolation errors). The parameters were tuned extensively. In the case of the 2D algorithm, theinterpolation errors and normalized interpolation errors are very close and below the values reportedin ground truth flows. In the case of the 3D algorithm, the results were compared with another similarmethod in 3D and the interpolation errors remained below 0.1. These results of interpolation errorsfor complete cardiac volumes and the left ventricle are shown graphically for clarity. Finally, a seriesof graphs are observed where the characteristic of contraction and dilation of the left ventricle isevident through the representation of the 3D optical flow.

Left Ventricle Motion Estimation Based on Unsupervised Recurrent Neural Network Left ventricle (LV) motion estimation plays an essential role in understanding the pathology of heart diseases and diagnosing and treatment of heart diseases. In this paper, we propose a recurrent registration network ( R2  Net) with convolutional neural networks (CNNs) to estimate the motion of left ventricle using cardiac MR image sequences. Our  R2  Net network is composed of a CNN, a function compositor, and a spatial transformer. The CNN is an asymmetric Unet architecture, which evaluates the correspondence between two images and outputs the sparse deformation field between two input images. Consecutive images are input to the CNN, and consecutive deformation fields are estimated. The compositor composites two deformation fields at adjacent time points together to generate a composited deformation field. The transformer warps the cardiac MR image at ED using the composited deformation field, and generates a deformed image. By composting successive deformation fields onebyone, the final deformation field between ED and ES is estimated. We define a loss function without ground truth and train the  R2  Net in an unsupervised way. Moreover, the bending energy is introduced to the loss function to impose the deformation field smooth and topologypreserving. Our method is evaluated using public datasets. Experimental results show that our method outperforms the stateoftheart researches in respect of several evaluation metrics.