Introduction
Our team has developed an optimised-based block matching (BM) algorithm to perform speckle tracking iteratively.
In this project, a new displacement estimation method is introduced by formulating the tracking as an optimisation problem that jointly penalises intensity disparity and motion discontinuity — making it more robust to signal decorrelation than previous approaches.
The speckle tracking algorithm combines the BM algorithm with a smoothness constraint for a neighbourhood of kernels.
The proposed technique was evaluated using both healthy and ischaemic cases.
Dataset
Example synthetic echocardiogram used for algorithm evaluation.
We used a publicly available synthetic echocardiographic dataset with known ground-truth (exact solutions) from several major vendors:
GE, Hitachi-Aloka, Esaote, Philips, Samsung, Siemens, and Toshiba.
To obtain realistic speckle texture for each vendor, scattering amplitude was sampled from 2D real clinical recordings as templates.
An electromechanical cardiac model was then used to relocate scatterers within the myocardium to simulate realistic motion.
Synthetic probe settings such as scan depth, focus depth, and beam density were defined in collaboration with vendors under NDA.
Methods
Standard Block Matching
Classic BM begins by placing a window (kernel) on one frame and searching for the most similar pattern in the next frame using a similarity metric such as Sum of Squared Differences (SSD).
Each kernel represents a cluster of speckles acting as a trackable fingerprint.
In the reference frame (time t₀), the region of interest (blue square) is defined; in the next frame (t₁), the algorithm searches for the best match.
The resulting displacement vector estimates motion between frames. Repeating this across the sequence yields a dense displacement map.
Fig. 1 — Speckle tracking using BM, showing region matching across frames.
This process repeats over the image sequence to generate a vector field across space and time.
Proposed Optimisation-Based Block Matching Approach
A new displacement estimation method formulates the tracking as an optimisation problem that jointly penalises:
- Intensity disparity between kernels
- Motion discontinuity between neighbours
This minimises the cost function and enforces a smooth, realistic motion field.
Tracking Parameters
- Kernel size: 11×11 pixels
- Spacing: 1 pixel (dense solution)
- Iterations: 20
- Regularisation parameter λ = 0.3
- Neighbourhood: 45×45 kernels
Larger λ values over-regularise motion, producing overly uniform fields; smaller values favour local variations.
A threshold for convergence was applied when additional iterations produced negligible updates.
Fig. 2 — Flowchart showing steps in the proposed optimisation-based tracking algorithm.
Results
Displacement Vector Field
The algorithm generated a dense displacement field for all vendor datasets.
Figure 3 shows an example A4C view from a healthy Siemens sequence at peak systole, alongside the corresponding ground truth.
Fig. 3 — Example A4C view from the Siemens sequence during rapid ejection (peak systole).
The optimised BM method reduces noise and discontinuities compared to standard BM, producing smoother displacement maps more consistent with physiological motion.
Fig. 4 — Boxplots of error for healthy Siemens sequences.
Displacement error distributions across all vendors show the proposed approach yields significantly lower variance and bias.
Regional and Global Strain Measurements
Using estimated displacement fields, regional (segmental) longitudinal strain values were calculated.
Fig. 6 — Top: LV segmentation regions overlaid on A4C view.
Bottom: Violin plots of error in segmental strain for healthy Siemens data.
The plots show mean (black line) and median (green line) values; boxes represent quartiles, and whiskers indicate 2.5%–97.5% percentiles.
Results confirm strong agreement with ground-truth strain values.
Observations
- The optimised BM approach provides superior motion continuity and noise resilience.
- Displacement and strain errors are consistently lower than standard BM.
- Outputs demonstrate accuracy sufficient for clinical-grade speckle tracking analysis.