Analysis of echocardiographic movies by variational methods

Analysis of left ventricle echocardiographic movies by vari-ational methods: a dedicated software for ECG and ECHO syn-chronizations during cardiac cycles. The image sequences elaboration, which represent our main topic, concerns the identi cation of contours of an object for segmentation and study of its movement over time. A newer dynamic approach to the well-known static variational method for the time-series medical echocardiographic images is presented, and a graphic software applications for synchronization between cardiac movement and electric signals (ECG) are developed. Many approaches have been proposed to process time-series of digital images, and it is di cult establish the most e ective one. Here we focus on PDE-based and variational methods. Standard snake models of closed curve evolution, pertaining to the Level-Set Method due to S. Osher and J. A. Sethian et al., have been implemented to characterize the internal ventricular area over time. We have applied standard nite di erence techniques for the approximation solution of the involved eikonal equations for front evolution. Well-known techniques of Gaussian regularization, such as heat equation, have highlighted the loss of de nition of ventricular edge. Thus we now present a numerical frame preprocessing technique, based on a variational model, that consists of functional minimization with a Mumford-Shah (M-S) time-dependent energy term, which is suitable to enhance ventricular edge and regularize initial data for curve evolution. This one, unlike the standard convolution with a regularizing operator, allows to compute the bright-intensity gradient of the image for velocity term of the curve evolution. We show the formulation of the standard model problem for image segmentations by curve evolution and a newer approach of pre-treating model by functional minimization. The applicability of the resolution method is discussed and an open mathematical problem for a new functional involving time-dependence are presented. Finally we describes the digital format of movies, the adaptation of single frames, the step which characterize the elaboration protocol, the quality of the results obtained with the preprocessing on a test problem. We additionaly describe the choice and implementation of reduced numerical methods in the real case and their computational cost. We compare results obtained by various preprocessing methods on identi ed areas, the curve evolution beyond the edge, ventricular area his trends over time and the evaluated Ejection Fraction. The implemented graphic application is presented, as well as the principal use of the signal-synchronizing software.

Elaborazione di sequenze di immagini con metodi variazionali.