Low-Rank-Modulated Functa: Exploring the Latent Space of Implicit Neural Representations for Interpretable Ultrasound Video Analysis

Julia Wolleb; Cristiana Baloescu; Alicia Durrer; Hemant D. Tagare; Xenophon Papademetris

cs.CVMar 26, 2026

Low-Rank-Modulated Functa: Exploring the Latent Space of Implicit Neural Representations for Interpretable Ultrasound Video Analysis

Authors: Julia Wolleb, Cristiana Baloescu, Alicia Durrer, Hemant D. Tagare, Xenophon Papademetris

Organizations: Dept. of Biomedical Informatics & Data Science, Yale University, New Haven, USA · Yale Biomedical Imaging Institute, Yale University, New Haven, USA · Department of Emergency Medicine, Yale School of Medicine, New Haven, USA · Dept. of Biomedical Engineering, University of Basel, Allschwil, Switzerland ·

Abstract

Implicit neural representations (INRs) have emerged as a powerful framework for continuous image representation learning. In Functa-based approaches, each image is encoded as a latent modulation vector that conditions a shared INR, enabling strong reconstruction performance. However, the structure and interpretability of the corresponding latent spaces remain largely unexplored. In this work, we investigate the latent space of Functa-based models for ultrasound videos and propose Low-Rank-Modulated Functa (LRM-Functa), a novel architecture that enforces a low-rank adaptation of modulation vectors in the time-resolved latent space. When applied to cardiac ultrasound, the resulting latent space exhibits clearly structured periodic trajectories, facilitating visualization and interpretability of temporal patterns. The latent space can be traversed to sample novel frames, revealing smooth transitions along the cardiac cycle, and enabling direct readout of end-diastolic (ED) and end-systolic (ES) frames without additional model training. We show that LRM-Functa outperforms prior methods in unsupervised ED and ES frame detection, while compressing each video frame to as low as rank k=2 without sacrificing competitive downstream performance on ejection fraction prediction. Evaluations on out-of-distribution frame selection in a cardiac point-of-care dataset, as well as on lung ultrasound for B-line classification, demonstrate the generalizability of our approach. Overall, LRM-Functa provides a compact, interpretable, and generalizable framework for ultrasound video analysis. The code is available at https://github.com/JuliaWolleb/LRM_Functa.

Figures & tables

Figure 1: Overview of our LRM-Functa framework. A) Our approach builds on VidFuncta , where each ultrasound video is represented by a video-level modulation vector $v$ and time-resolved modulation vectors $\phi=\{\phi_{t}\}_{t=1}^{T}$ . (B) Pairwise cosine similarity of $\phi$ over time reveals a clear low-rank pattern. (C) Motivated by this observation, we constrain the latent modulation space to a low-rank subspace $\mathcal{B}_{\beta}$ . (D/E) This structured latent space enables efficient compression-reconstruction and cardiac phase analysis.

Figure 2: Proposed architecture for low-rank adaptation of the modulation vectors. Each video $\mathcal{V}$ is encoded into a video-level representation $v$ and time-resolved frame representations $\phi_{t}$ , which are projected onto a rank- $k$ subspace $\mathcal{B}_{\beta}$ to produce modulation vectors $m_{t}=v+\mathcal{B}_{\beta}\phi_{t}$ . These vectors shift the activations of a shared MLP $M_{\theta}$ , trained to reconstruct pixel intensities $\hat{z}$ at each coordinate $(x,y)$ , shown as a red cross.

Panel of Figure 3 — Figure 3: For $k=2$ , we visualize the raw trajectories $\phi_{t}$ over time. LRM-Functa o exhibits spiral-like trajectories, whereas LRM-Functa b collapses the trajectory to a line. Projecting $\phi_{t}$ onto the principal motion direction $p$ and filtering yields the 1D signal $s_{filt}$ , which enables direct interpretable identification of ED and ES frames.

Figure 5: Mean SSIM and PSNR scores on the EchoNet-Dynamic test set for all comparing methods across varying latent dimensions $k$ (x-axis shown on a log2 scale). For small $k$ , our LRM-Functa variants are the only methods to produce stable reconstructions, while for higher ranks, LRM-Functa o achieves among the highest performance.

	EchoNet, $k=2$		EchoNet, $k=512$		OOD POCUS, $k=512$
Method	ED MAE	ES MAE	ED MAE	ES MAE	ED MAE	ES MAE
Coin++	$8.29\pm 12.3$	$5.82\pm 10.8$	$4.46\pm 6.9$	$3.26\pm 5.5$	$1.83\pm 1.1$	$2.32\pm 1.4$
MedFuncta	$3.72\pm 3.8$	$3.48\pm 3.4$	$2.90\pm 3.3$	$2.17\pm 2.4$	$1.61\pm 1.3$	$1.27\pm 1.5$
VidFuncta	$3.06\pm 2.6$	$2.90\pm 2.8$	$3.08\pm 3.3$	$2.37\pm 2.4$	$\textbf{1.33}\pm\textbf{1.2}$	$1.89\pm 3.8$
Autoencoder	$2.81\pm 3.5$	$2.26\pm 2.7$	$3.82\pm 4.7$	$2.44\pm 2.6$	$3.06\pm 3.5$	$4.24\pm 2.6$
LRM-Functa b	$\textbf{2.26}\pm\textbf{2.5}$	$\textbf{1.98}\pm\textbf{2.1}$	$\textbf{2.48}\pm\textbf{2.9}$	$2.21\pm 2.2$	$1.40\pm 1.5$	$\textbf{ 1.13}\pm\textbf{1.4}$

Table 1: Mean

\pm

standard deviation for the ED and ES MAE on the EchoNet-Dynamic and the OOD POCUS test sets. All methods are unsupervised.

	Ejection fraction, $k=2$			B-line classifier [ $\times 10^{-2}$ ], $k=512$
Method	MAE	RMSE	R 2 score	Accuracy	F1 score	AUROC
Coin++	$9.15\pm 0.1$	$12.17\pm 0.2$	$0.03\pm 0.03$	77.5 $\pm$ 5.0	67.8 $\pm$ 8.7	80.9 $\pm$ 9.0
MedFuncta	$9.42\pm 0.1$	$12.94\pm 0.1$	$\text{-}0.02\pm 0.02$	81.0 $\pm$ 6.3	73.1 $\pm$ 7.7	90.1 $\pm$ 1.9
VidFuncta	$9.14\pm 0.1$	$13.09\pm 0.2$	$\text{-}0.02\pm 0.03$	83.5 $\pm$ 5.2	76.6 $\pm$ 7.3	91.9 $\pm$ 3.6
Autoencoder	$7.16\pm 0.3$	$9.79\pm 0.5$	$0.47\pm 0.06$	68.0 $\pm$ 2.1	50.2 $\pm$ 6.5	66.6 $\pm$ 5.7
LRM-Functa b	$5.70\pm 0.2$	$7.63\pm 0.3$	$\textbf{0.67}\pm\textbf{0.03}$	77.5 $\pm$ 6.4	70.9 $\pm$ 3.9	89.5 $\pm$ 2.2

Table 2: Mean

\pm

std of downstream performance on

\hat{\mathcal{V}}

, evaluated on the reconstructed EchoNet-Dynamic and LUS test sets using 5-fold cross-validation.

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Medical image representation learning builds reusable visual features for diagnosis, segmentation, retrieval, and other clinical imaging tasks.

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Ultrasound is the most widely used real-time imaging modality in clinical practice, yet per-frame video annotation remains a major bottleneck: expert labels are scarce and costly, and image appearance varies with speckle, shadowing, attenuation, and operator-dependent probe pose. This is especially limiting because clinically relevant information is often dynamic, from left-ventricular motion in echocardiography to muscle and bone kinematics in musculoskeletal imaging. Population atlases can amortize annotation cost by registering observations to a shared canonical coordinate system, but existing neural atlas methods mainly target single videos, small test-time image sets, or object-centric image collections. We introduce a cohort-scale neural atlas for ultrasound video: a single canonical chart with per-video Generative Latent Optimization embeddings, trained jointly over thousands of frames in DINOv3 feature space. Across five cardiac and musculoskeletal datasets with point landmarks and segmentation masks, our method learns coherent canonical templates and enables accurate atlas-space annotation transfer. On EchoNet-Dynamic and MSK-Bone, it supports single- and few-shot transfer with accuracy competitive with strong dense-correspondence baselines, while training in minutes on a single consumer GPU. The learned embeddings are interpretable: linear projections reveal structured cohort variation, image-decoder interpolation produces anatomically plausible intermediate frames, and test-time latent inversion reconstructs held-out frames through the atlas. These results suggest that cohort-scale neural atlases offer a practical, interpretable representation for reducing expert annotation burden in ultrasound video analysis.

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