Markerless Strain Quantification Methods

• Markerless strain quantification is a method that measures tissue deformation using inherent tissue textures and advanced algorithms without adding physical markers.
• It employs techniques such as transformer-based tracking, phase analysis, and point cloud registration to extract dense, local displacement and strain fields.
• Its applications range from biomedical research to clinical settings, enabling accurate, noninvasive, and real-time tissue and material deformation analysis.

Markerless strain quantification encompasses a spectrum of computational, imaging, and mathematical strategies that enable dense, local measurement of deformation in soft and biological tissues without the need for fiducial markers, applied speckles, or physical landmarks. These methods rely on extracting surface or volumetric texture from native tissue, or on deep feature learning, to infer the underlying displacement and strain fields. Markerless quantification offers advantages in preserving physiological conditions, simplifying experimental protocols, and enabling in situ, noninvasive strain measurement in biomedical, engineering, and surgical settings.

1. Core Principles of Markerless Strain Quantification

Markerless strain quantification directly measures deformation without artificial labels or physical markers by leveraging endogenous texture, imaging contrast, or learned representations:

• Natural Texture Tracking: Endogenous features—collagen bundles, cell patterns, or anatomical irregularities—are used as landmarks for computational tracking. Multiphoton microscopy or bright-field imaging may reveal appropriate contrast, as exemplified in soft tissue applications such as bladder contraction studies (Asadbeygi et al., 4 Jan 2026).
• Dense, Markerless Deformation Fields: Machine learning (deep convolutional networks, transformers, implicit neural representations) and classical computer vision (phase analysis, point cloud registration, nonrigid alignment using Coherent Point Drift variants) form the methodological base. These algorithms extract spatial correspondences and model local or global tissue deformation fields (Asadbeygi et al., 4 Jan 2026, Bell et al., 10 Sep 2025, Wu et al., 8 Oct 2025, Molimard, 2011, Daly et al., 30 Jun 2025).
• Strain Tensor Extraction: Once the displacement field $u(X)$ is known, mathematical formulations (finite or infinitesimal strain definitions) are applied to compute local strain tensors, including Green–Lagrange strain and principal strains, at arbitrary points within the observation domain.

2. Algorithmic Frameworks and Mathematical Formulation

2.1. Image- and Video-based Approaches

• Transformer-based Tracking (CoTracker3): Zero-shot pretrained transformer models (CoTracker3) track dense grids of virtual points by encoding both local texture and long-range context via spatial/temporal self-attention. No dataset-specific fine-tuning or speckling is required, enabling robust tracking under complex motions such as folding or buckling as seen in bladder tissue (Asadbeygi et al., 4 Jan 2026).
• Phase Analysis for Random Patterns: Phase gradients of local windowed Fourier spectra are computed using bi-triangular or Gaussian windows over zones-of-interest (ZOIs), producing direct estimates of the small-strain tensor without explicit displacement differentiation. Displacement is retrieved as the pseudo-inverse of a matrix constructed from phase vectors at multiple frequency orientations (Molimard, 2011).

2.2. 3D Point Cloud and Mesh-based Approaches

• Distance-weighted Coherent Point Drift (DW-CPD): Nonrigid 3D registration aligns segmented anatomical meshes (e.g., valve leaflet surfaces) across timepoints by GMM-based drift with additional distance-decay weighting and kernel regularization, providing dense correspondences for subsequent strain calculation (Wu et al., 8 Oct 2025).
• RGB-D/PointNet++ and Kinematic Registration: Intraoperative techniques such as SpineAlign segment and register intraoperative point clouds and preoperative meshes via deep learning and articulated kinematic models. Displacement fields are then determined by rigid and nonrigid optimization, enabling strain mapping on complex anatomical surfaces (Daly et al., 30 Jun 2025).

2.3. Implicit Neural Representations

• INR-based Continuous Displacement Modeling: A low-dimensional latent code, inferred from stack or pair of MR images, conditions a fully-connected neural network that maps spatial coordinates to a continuous displacement field across the cardiac cycle, eliminating the need for tag-line tracking or optical flow (Bell et al., 10 Sep 2025).

2.4. Strain Calculations

Universal to all frameworks, local strain is defined as follows (notation may vary by source):

• Deformation Gradient: $F = \nabla_X x = \nabla_X u + I$, where $X$ is reference and $x(X, t)$ deformed coordinate (Asadbeygi et al., 4 Jan 2026, Wu et al., 8 Oct 2025, Daly et al., 30 Jun 2025, Bell et al., 10 Sep 2025).
• Green–Lagrange Strain: $E = \frac{1}{2}(F^T F - I)$.
• Principal Strains: Obtained as the eigenvalues of $E$.
• Error Metrics: Pixel RMSE for tracking, strain RMSE and spatial standard deviation for field accuracy, shape agreement metrics (MSD, Hausdorff distance) for surface registrations.

3. Validation, Metrological Performance, and Benchmarks

Comprehensive quantitative evaluations are reported across modalities and anatomical sites:

Framework	Tracking Error	Strain Error	Validation Benchmarks
CoTracker3	RMSE ≤1.5 px	Strain RMSE ≤0.013	Synthetic images, latex dog-bone, real tissue (Asadbeygi et al., 4 Jan 2026)
DW-CPD	MSD < 0.4 mm	MAE < 0.1 (strain)	FE-validated synthetic valves, 3D echo data (Wu et al., 8 Oct 2025)
Phase Analysis	0.02–0.035 px disp.	~9% rel. uncertainty	Numerical (sinusoidal test), composite tension (Molimard, 2011)
INR-LV Motion	2.14 mm RMSE	2.86% (circ.), 6.42% (radial)	>450 subjects, manual expert ground truth (Bell et al., 10 Sep 2025)
SpineAlign	ΔRMSE ∼0.1–0.4 mm	Not directly reported	Phantom & clinical spine datasets (Daly et al., 30 Jun 2025)

These results demonstrate that markerless methods using endogenous texture or neural inference can achieve accuracy comparable to or exceeding traditional, marker-based approaches in both displacement and strain field estimation.

4. Applications and Biological/Clinical Insights

Markerless strain quantification is now essential in biomedical research and translational applications:

• Active Bladder Contraction: CoTracker3-based framework quantifies complex, anisotropic strain fields during in vitro contraction, revealing spatial heterogeneity and significant longitudinal-circumferential differences (mean Eyy ≈ –0.30 vs. Exx ≈ –0.20, p<0.01) in rat bladders (Asadbeygi et al., 4 Jan 2026).
• Valve Leaflet Strain in Echocardiography: Robust markerless mapping on 3D echo reveals biomechanical signatures associated with prolapse (median/IQR 1st principal strain >0.5 strongly correlated with billow), offering potential as an early disease biomarker (Wu et al., 8 Oct 2025).
• Myocardial Strain (CMR): INR-based methods enable continuous, high-resolution, and rapid mapping of left ventricular wall motion and global strain metrics, important for large-cohort and real-time cardiac phenotyping (Bell et al., 10 Sep 2025).
• Intraoperative Spine Deformation: Markerless pipeline using RGB-D and deep correspondence prediction provides dense strain estimation for surgical navigation and assessment, reducing the need for invasive markers (Daly et al., 30 Jun 2025).
• Experimental Mechanics: Direct phase-analysis enables high spatial resolution strain mapping in composite materials with native or applied random texture, supporting validation against interferometry and finite element methods (Molimard, 2011).

5. Methodological Limitations and Best Practices

Despite the advantages, several domain-specific and general limitations must be recognized:

• Texture Dependence: The reliability of markerless tracking is affected by the quality and uniqueness of natural texture; dropout or low contrast (e.g., in phase-based analysis) reduces accuracy (Molimard, 2011, Asadbeygi et al., 4 Jan 2026).
• Segmentation and Registration Quality: Pipeline robustness depends on segmentation accuracy (e.g., PretrainingNet IoU~0.8 for spine); errors propagate to strain fields (Daly et al., 30 Jun 2025, Wu et al., 8 Oct 2025).
• Assumptions on Strain Magnitude: Phase-based approaches assume small strain (<0.2%) to maintain phase unambiguity; large deformations demand more robust feature-tracking (e.g., transformer or point-cloud methods) (Molimard, 2011, Asadbeygi et al., 4 Jan 2026).
• Validation Protocols: Best practices include the use of synthetic deformations, phantom experiments, physiology-relevant error metrics (RMSE, MSD, HD), and calibration through known/benchmark transformations (Asadbeygi et al., 4 Jan 2026, Wu et al., 8 Oct 2025, Molimard, 2011).

6. Generalizability, Future Directions, and Open Challenges

Markerless techniques are broadly adaptable to different imaging modalities, tissues, and deformation regimes. Current and future research directions include:

• 3D and Volumetric Extensions: Stereo and multi-camera/deep multi-slice approaches for volumetric strain mapping and temporal cine matching (Asadbeygi et al., 4 Jan 2026, Bell et al., 10 Sep 2025).
• Biomechanical Integration: Incorporation of material models, tissue thickness, and biophysical regularization (e.g., incompressibility for myocardium, fiber orientation constraints) via differentiable pipelines (Bell et al., 10 Sep 2025, Wu et al., 8 Oct 2025).
• Clinical Translation: Enabling real-time intraoperative guidance, large-scale cohort phenotyping, and early pathological biomarker discovery without the confounding effects of applied markers (Daly et al., 30 Jun 2025, Wu et al., 8 Oct 2025).
• Multi-modal Data Fusion: Integration with CT, MRI, ultrafast ultrasound, and advanced optical imaging for enhanced constraint and validation.
• Standardization and Open-source Toolchains: Emphasis on reproducible, open-source pipelines for mesh triangulation, deformation measurement, and high-level error reporting, facilitating broader adoption (Asadbeygi et al., 4 Jan 2026, Wu et al., 8 Oct 2025).

This convergence of computation, imaging, and mechanics establishes markerless strain quantification as an indispensable methodology for full-field biomechanical analysis in both research and translational clinical settings.