REAL-TIME MONOCULAR 3D HAND DISTENCE ESTIMATION USING A QUADRATIC REGRESSION MODEL
DOI:
https://doi.org/10.51453/3093-3706/2026/1468Keywords:
3D hand Distence, computer vision, Deep Learning, 3D Distence EstimationAbstract
This research addresses the problem of estimating the distance from a user's hand to a conventional 2D monocular camera in a 3D space, aiming to optimize low-cost Human-Machine Interfaces (HMIs) and virtual reality interactions. In contrast to expensive dedicated depth sensors such as lasers, ultrasound, or RGB-D cameras, the proposed method integrates the MediaPipe Hands framework to detect 21 skeletal hand landmarks in real-time, and applies a quadratic nonlinear regression model to calculate the physical distance. To overcome geometric distortions caused by hand closure/opening gestures or wrist rotations, the pixel distance between two geometrically stable landmark pairs—namely landmarks 5–17 (representing the horizontal axis) and landmarks 9–0 (representing the vertical axis)—is extracted as the independent input variables. The final estimated distance is refined through a minimum filter to suppress tracking noise.
Empirical evaluations on a standard consumer laptop demonstrate that the model operates highly efficiently in real-time with minimal resource overhead, consuming only 176.6 MB of RAM and 20.5% of CPU. The model is evaluated across three distinct illumination environments (well-lit, dimly-lit, and outdoor) within a physical distance range of 22 cm to 117 cm. Experimental results show that the proposed model achieves outstanding accuracy at interaction distances between 50 cm and 100 cm, yielding a minimum relative error of only 0.02% at 90 cm. A rigorous comparative study with a standard linear regression model validates the superiority of the quadratic nonlinear approach in modeling the perspective-scaling characteristics of 2D monocular projection.
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