Willow 4 DaVinci: The Biomechanical Physics Engine

Today, we are proud to announce the launch of Willow 4 DaVinci. With DaVinci, we are officially moving beyond the limitations of visual observation and into the world of computational physics.

We have built a system where versatility is core. It operates with equal precision from a single smartphone on the field to a multi-camera, professional setup in a controlled environment. Crucially, it is entirely non-invasive - liberated from the constraints of markers, sensors, and specialized hardware. It meets athletes where they are, requiring no change to their existing training routines. The future of biomechanics is not seen, it is calculated.

 

The Scientific Imperative to Move Beyond Visual Tracking

We architected DaVinci around a core principle we call the "Physics-First Paradigm." We don’t track the implement (or the end effector like the hand hitting a volleyball). Instead, we use a state-of-the-art pose estimation framework to model what it does best: capture the intricate kinematics of the human body. We then feed this high-fidelity human data into our proprietary physics engine, which calculates the implement's dynamics as a direct, rigid extension of the human engine. This is our key differentiator, and it is a process built on a foundation of proven mathematical principles and a revolutionary, multi-stage architecture.

The Anatomy of a Session: A Journey Through the Da Vinci Engine

To truly appreciate the depth of this system, let us follow a single, unedited training session on its journey from upload to insight. This is a symphony of distributed computing, advanced AI, and uncompromising scientific validation.

1. Ingestion & The Automated Triage 

Our process begins the moment a coach or athlete uploads an entire, unedited training session to our platform. This raw footage triggers our event-driven AWS Lambda Orchestrator. The system's first job is to act as an intelligent, automated video editor. We employ an ensemble of AI specialists to meticulously scan the entire session. One AI model, a "coach", identifies all sport-specific actions. A second, a "physicist", identifies every moment of high kinetic energy. These findings are then passed to an arbitration function (_actions_overlap) that cross-validates the two reports. This eliminates countless hours of manual video editing and provides the foundation for a truly holistic session review.

2. The Pose Estimation Swarm

With a list of validated actions, the orchestrator delegates the heavy computational work to a distributed AWS Fargate swarm. This architecture allows us to spin up a massive, parallel processing grid on demand, analyzing every action simultaneously. Inside each container, a sophisticated pose estimation framework is executed to extract a dense, time-series dataset of human kinematic landmarks, including 2D joints and 3D world_joints.

3. The Crucible: Our Proprietary Calibration Engine 

As the kinematic data streams into our schemaless/vector/knowledge graph databases, our aggregator function is triggered. It is here that one of our most significant innovations takes place: our Tiered Auto-Calibration Engine. This engine is our solution to converting relative pixel coordinates into absolute, real-world measurements.

Pro Mode Calibration

For professional, clinical, or research applications requiring absolute ground truth, Pro Mode moves beyond single-camera analysis to achieve a complete, three-dimensional environmental reconstruction. Through the interface, a user can define a complete control volume before an analysis begins. The system is designed to fuse synchronized video streams from multiple cameras, for which the user specifies key parameters such as precise height from the ground plane. The user can populate the scene with multiple known or custom calibration objects. For each object, precise spatial data (such as its distance from each camera and its distance from the subject, along with its exact physical measurements for custom items) are entered as control inputs. 

When combined with high-end motion capture cameras and precisely configured world points, the system generates a true 3D model of the athlete's movement, with data outputs suitable for elite biomechanical analysis, CAD, robotics platforms, or advanced biomechanical simulators.

Resilient Auto-Calibration

• Auto Tier 1 (Gold Standard): 3D Homography Reconstruction | Our system uses independent models and rigorous geometric checks (_synthesize_and_validate_sheet_sources) to calculate a homography matrix (_calculate_homography_from_sheet), a proven mathematical principle that corrects for all perspective distortion and yields a true, 3D-reconstructed coordinate space.
• Auto Tier 2 (Silver Standard): Statistically Hardened 2D Scaling | If no sheet is available, our engine identifies known objects and uses outlier rejection via the interquartile range (IQR) method (_harden_calibration_from_sources) and a weighted average to derive a single, highly accurate inches_per_pixel scale factor.
• Auto Tier 3 (Bronze Standard): Graceful Fallback | If no calibration is possible, our engine gracefully proceeds with a pixel-space analysis, ensuring valuable insights into motion quality and consistency are always available.

4. The Da Vinci Physics Engine: Where Math Meets Motion 

With calibrated, real-world data, we enter the heart of our platform. A foundational design philosophy of the DaVinci engine is our unwavering commitment to scientific transparency and validity. It is, to our knowledge, the only commercial physics engine in the world for video analysis that is built exclusively on 100% published, proven, and trusted biomechanical calculations and methodologies. There are no "black box" algorithms. Every insight is traceable to an established scientific principle.

To begin, the raw data is smoothed using a Savitzky-Golay filter (savgol_filter), a peer-reviewed digital signal processing algorithm that removes noise without distorting the underlying motion profile. With a clean signal, our engine performs numerical differentiation (np.gradient) - a standard calculus technique - to compute the first derivative of position (velocity), the second derivative (acceleration), and the third derivative (jerk). Simultaneously, we analyze the kinematic chain, calculating the peak angular velocity of key body segments to mathematically verify if an athlete is achieving the correct proximal-to-distal sequencing - the "whip effect" that is a cornerstone of power generation documented in decades of biomechanics research.

5. The Validation Gauntlet: The Biomechanical Fingerprint

Before data is presented, it must pass one final validation. Our Multi-Factor Outlier Rejection Filter creates a "biomechanical fingerprint" for every action in the session. Using the Median Absolute Deviation (MAD) - a statistical method highly resistant to anomalies -we calculate a robust Z-score for key metrics. This ensures we create a holistic and statistically representative picture of an athlete's true performance.

6. The Synthesis Engine & The Living Dossier

In the final stage, the complete set of validated session data is compiled into a comprehensive enrichedDataDossier. This dossier is then provided to our final, large-scale multimodal AI to synthesize this high-fidelity data into a rich, narrative-driven coaching experience. This creates more than a report; it creates a Living Dossier, a persistent data object that enables our AI to be a true conversational partner.

Our Four Pillars of Uniqueness

The Willow 4 DaVinci platform is the only solution to integrate these four essential pillars into a single, cohesive commercial offering:

1. A Foundation in State-of-the-Art Pose Estimation: We build our analysis upon a proven, industry-leading framework for capturing foundational human kinematic data.
2. Proprietary Calibration & Hierarchical Data Modeling: We have developed a revolutionary, in-house calibration technology that powers an intelligent engine capable of prioritizing true 3D reconstructed data before seamlessly falling back to a statistically hardened 2D calibrated system.
3. A Physics-First Calculation Engine: We are fundamentally a simulation tool. We don’t guess at implement performance; we calculate it with mathematical rigor. Our engine is built exclusively on 100% published and academically validated biomechanical formulas, ensuring every insight is grounded in trusted science.
4. An Interactive Generative AI Coaching Interface: We don’t just show you numbers. We feed our high-quality, validated data into a generative model that becomes a persistent, adaptive AI coach, transforming data into a valuable, ongoing dialogue.

Our Vision for the Future

While our journey begins in sports, the DaVinci engine is a foundational technology for understanding all human movement, with applications in Telemedicine, Robotics, and Immersive Gaming and much more.