High-dimensional multimodal uncertainty estimation by manifold alignment:Application to 3D right ventricular strain computations

TL;DR

This work tackles the challenge of uncertainly in high-dimensional medical image descriptors by presenting a multimodal framework based on manifold alignment to fuse multiple descriptors into a shared latent space. Local uncertainties are modelled in this latent space via PCA-based Gaussian sampling, followed by reconstruction of high-dimensional patterns to yield spatially resolved uncertainty maps for RV 3D strain. The approach is validated on toy data and a real RV dataset, showing that uncertainties localize to anatomically challenging regions and reflect differences among strain definitions, while outperforming simple descriptor-wise standard deviation baselines. The methods are generalizable to other population analyses with heterogeneous high-dimensional descriptors and can benefit uncertainty-aware clinical interpretations of imaging-derived biomarkers.

Abstract

Confidence in the results is a key ingredient to improve the adoption of machine learning methods by clinicians. Uncertainties on the results have been considered in the literature, but mostly those originating from the learning and processing methods. Uncertainty on the data is hardly challenged, as a single sample is often considered representative enough of each subject included in the analysis. In this paper, we propose a representation learning strategy to estimate local uncertainties on a physiological descriptor (here, myocardial deformation) previously obtained from medical images by different definitions or computations. We first use manifold alignment to match the latent representations associated to different high-dimensional input descriptors. Then, we formulate plausible distributions of latent uncertainties, and finally exploit them to reconstruct uncertainties on the input high-dimensional descriptors. We demonstrate its relevance for the quantification of myocardial deformation (strain) from 3D echocardiographic image sequences of the right ventricle, for which a lack of consensus exists in its definition and which directional component to use. We used a database of 100 control subjects with right ventricle overload, for which different types of strain are available at each point of the right ventricle endocardial surface mesh. Our approach quantifies local uncertainties on myocardial deformation from different descriptors defining this physiological concept. Such uncertainties cannot be directly estimated by local statistics on such descriptors, potentially of heterogeneous types. Beyond this controlled illustrative application, our methodology has the potential to be generalized to many other population analyses considering heterogeneous high-dimensional descriptors.

Figures (10)

• Figure 1: Overview of the pipeline proposed in this paper. (a) High-dimensional descriptors (here, 3D RV strain patterns) are encoded into low-dimensional latent spaces that are locally aligned depending on neighborhood relationships between samples (Sec.\ref{['sec:ManifoldAlignment']}). (b) Remaining differences in the latent space after alignment are exploited to estimate a statistical distribution that models uncertainties (Sec.\ref{['sec:UncertaintyModelling']}). (c) Reconstructing high-dimensional samples from this distribution allows estimating high-dimensional uncertainty patterns (Sec.\ref{['sec:UncertaintyModelling']}).
• Figure 2: The three ways to compute circumferential and longitudinal directions we evaluated in this paper. (a) Long-axis computations, (b) Heat diffusion computations (the turquoise disks represent the cold point, while the apex stands as the hot point), (c) Geodesic distance computations (the white line corresponds to the geodesic joining the two purple dots).
• Figure 3: Local uncertainty quantification on a toy experiment, on the red (R) and green (G) channels of images of two objects from the COIL-100 dataset Nene:1996, of different view angles and additionally rotated between $-5^{\circ}$ and $+5^{\circ}$. (a) Samples of the two objects. The red channel dominates in both objects, being either almost uniform (soda can) or almost complementary of the green channel (toy bear). (b) Estimated uncertainties on the red and green channels, respectively, for the sample with the largest differences between the red and green latent spaces, after alignment with MML. (c) Similar display for the sample with the smallest differences.
• Figure 4: Local uncertainty quantification when noise was introduced artificially in a certain zone (illustrated on the left side of the figure), for different noise intensity levels ($\alpha \in [0,1]$) .
• Figure 5: Strain patterns from a representative subject, and corresponding uncertainties. The Long-axis (LA) is used as reference for comparison between two descriptors (with heat diffusion and geodesic computations) and all three descriptors together (center of the figure). The red and blue circles highlight zones of major differences for strain and uncertainty, respectively.