Achieving Successful 3-Dimensional Hand Tracking Using Quasi-Random Sequences

With the advent of emerging technologies in the space of human-computer interaction (HCI), a prevalent challenge has been finding methods that can accurately represent these motions in real time.  Applications using RGB-D cameras to track movements for consumer-based systems has already been employed by Microsoft in the space of tracking silhouette movements in video games as well as app navigation in the Microsoft Kinect system.  However, tracking methods must evolve in order to successfully represent the complexity of human hand motion.  The two main categories of 3D hand articulation tracking methods consist of appearance-based and model-based tracking.  Appearance-based tracking methods are efficient in the limited space of comparing the present model to a number of already defined hand configurations.  Model-based tracking methods allow the computational configuration to explore a continuous space in which the hand motions are optimized at a high dimensional space in near real time.

Figure 1 – 256 Points from a Pseudorandom Number Source (Left) Compared to a Quasi-Random Low-Discrepancy Source (Right)

If the computer tracks the human wrist with six degrees of freedom and the other joints accordingly, the ensuing dimensional analysis occurs at a high dimensional space.  A saddle joint (2 DOF) at the base of the each finger plus the additional hinge joints (1 DOF each) at the middle of the finger describes each finger with four degrees of freedom.  In turn, the problem of tracking the articulation of a single hand is performed in a dimensional space of 27.  This highly dimensional problem formulation requires an optimization technique specific to the problem that can provide a uniform coverage of the sampled space.  Quasi-random sequences are known to exhibit a more uniform coverage of a high dimensional compared to random samples taken from a uniform distribution.  The Sobol sequence, developed by Russian mathematician Ilya Sobol, describes a quasi-random low-discrepancy sequence that more evenly distributes a number of points in a higher dimensional space.  Figure 1 represents the distribution discrepancy between a pseudorandom number generation and a quasi-random low-discrepancy Sobol sequence generation.

Figure 2 – High Dimensional Design Space with Given Constraints from Preliminary Design Module in AxSTREAM™

Clearly described in the figure, it is possible to visualize how the quasi-random distribution would employ a better system for tracking hand articulations on 27-dimensional space with much fewer missteps. This particular technology will continue to evolve as the steps of the process are improved. The quasi-random sampling presents a candidate solution in the parametric space of hand configurations, and objectively creates iterations for each frame in which these points are captured. Although the commercial application of this technology still seems rather futuristic, the ability to interact with a computer system by using a number of hand gestures has seen massive improvement in the past years. This technology could potentially represent the next big advancement for upcoming interactive computer systems. Aside from the applications displayed in this article, SoftInWay has been using this technology in order to optimize the highly dimensional system seen in the preliminary design of turbomachines. The solution generator in AxSTREAM® uses a quasi-random search algorithm to successfully distribute a high dimensional system characterized by geometry limits, performance bounds, and different flow conditions. To learn more about the preliminary design module for applications in any turbomachinery platform follow the link –


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