Accuracy alone is not enough when a motion-tracking system signals a car to stop, slow down, or continue, or when it helps a doctor interpret a video of a beating heart. In such high-stakes settings, it is also crucial that the user has a clear measure of the AI-generated information’s reliability.
For his Engineering Design Day year-long capstone project, Andy Wang, a junior in the Whiting School of Engineering’s Department of Applied Mathematics and Statistics, developed a statistical methodfor determining how much confidence we should place in these kinds of results—and for making the system’s decision processes more transparent.
As computer vissions and motion-tracking systems continue to shape decisions in areas like transportation and healthcare, his work points toward a broader goal: not just smarter systems, but ones we can better understand and trust.
Wang’s research focused on optical flow—a class of computer vision techniques used to estimate motion and track objects by tracking the movement of individual pixels during a series of video frames.
Optical Flow interprets motion as it occurs over time and then makes decisions based on its assessment of movement. Its applications include detecting objects in traffic, tracking people through space, and analyzing motion in real time.
“Because optical flow is frequently used in safety-critical settings, you want not just an answer, but a sense of how much you can trust that answer,” he says.
But real-world conditions can make these kinds of predictions complicated, such as when objects are hidden from view or when images are distorted by lighting. Furthermore, many current optical flow methods rely on deep learning models that produce predictions without explaining how they were derived, making it hard to know if they should be trusted.
“You can get good estimates from optical flow, but you don’t really know where they came from,” Wang says. “That makes it hard to judge how reliable the estimates are.”
Being able to trust results matters, especially in high-stakes settings. “If a car approaches an intersection and another vehicle disappears behind a building, a traditional system may still estimate the first car’s motion even though it can no longer see it—and it may not signal that this key information is missing,” Wang explains. Similar problems can arise in medical imaging when visual distortions—like noise, shadows, or sensor imperfections—affect how motion is captured, increasing the risk of misinterpreting what is happening.
Wang solved this problem by pairing motion estimates with uncertainty estimates.
Rather than relying solely on black-box AI models, his approach builds on interpretable, mathematically grounded techniques. Wang’s method signals when motion estimates are uncertain and lets the system treat those estimates more cautiously.
To do this, Wang developed a way to recompute motion at multiple image resolutions and applies a Kalman filter—a statistical method used to refine predictions over time— across scales, passing forward both refined motion estimates and their uncertainty at each step. This lets the system calculate both how objects move and how confident the system is in these estimates—producing a confident value for each pixel and showing exactly where predictions may be less reliable. The method is fast enough for real-time use, based on transparent mathematics, and provides confidence measures alongside its predictions.
“If you don’t know when the system might be wrong, you risk acting on bad information,” Wang says, noting that without a measure of confidence, users have no way to judge how reliable a prediction is.
Advised by Mario Micheli, senior lecturer of applied mathematics and statistics, Wang is now preparing his findings for publication.