Bilinear Models for Spatio-Temporal Point Distribution Analysis

Abstract

In this work we describe the usage of bilinear statistical models as a means of factoring the shape variability into two components attributed to inter-subject variation and to the intrinsic dynamics of the human heart. We show that it is feasible to reconstruct the shape of the heart at discrete points in the cardiac cycle. Provided we are given a small number of shape instances representing the same heart at different points in the same cycle, we can use the bilinear model to establish this.Using a temporal and a spatial alignment step in the preprocessing of the shapes, around half of the reconstruction errors were on the order of the axial image resolution of 2 mm, and over 90% was within 3.5 mm. From this, we conclude that the dynamics were indeed separated from the inter-subject variability in our dataset.

A bi-ventricular cardiac atlas built from 1000+ high resolution MR images of healthy subjects and an analysis of shape and motion

“…Apart from PCA, independent component analysis (ICA) has also been used to encode the variation of the cardiac shape (Suinesiaputra et al, 2009). Recently, Hoogendoorn et al proposed a bilinear shape model in which the inter-subject variation and inter-phase variation are encoded separately in two dimensions (Hoogendoorn et al, 2009(Hoogendoorn et al, , 2013. To utilise pre-existing statistical shape models, Pereañez et al proposed a framework of merging multimodality models by spatial normalisation and eigenspace fusion (Pereañez et al, 2014).…”

Conditional Shape Models for Cardiac Motion Estimation

“…In the current work no assumptions were made about the relation between cardiac shape and motion, in contrast to the method proposed by Hoogendoorn et al, in which shape and motion variations are explicitly decoupled [5]. Although the motion of the heart depends for a large amount on its electrophysiology, which is not apparent from its shape, we think that shape can still predict cardiac motion when both the shape and motion of the heart are affected by disease (e.g.…”

“…Such a 4D statistical model was, for instance, built by Perperidis et al for segmenting the left ventricle, right ventricle, and myocardium, but was not used for motion prediction [4]. Hoogendoorn et al built a bilinear model for the extrapolation of cardiac motion, assuming that the motion of the heart is independent of its shape [5]. We, in contrast, build statistical shape models of the shape and motion of the heart without assuming their independence and evaluate its applicability for the prediction of cardiac motion by conditioning the motion model on single time point shape information.…”

eCurves: A Temporal Shape Encoding

“…, time points) and corresponding segmentations of a 3D+t scan so that the resulting deformation maps capture local expansion or contraction of anatomical structures between time points. They have been heavily applied to anatomical shapes extracted from cardiac MRIs [11], [12], [13]. However, the registration of these encodings can bias measurements as they are complex systems that are based on simplifying assumptions and expert-based parameter tuning [14].…”