{"id":56410,"date":"2026-05-13T14:31:28","date_gmt":"2026-05-13T18:31:28","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=news&p=56410"},"modified":"2026-05-28T11:55:00","modified_gmt":"2026-05-28T15:55:00","slug":"when-math-sees-motion-can-we-trust-it","status":"publish","type":"news","link":"https:\/\/engineering.jhu.edu\/ams\/news\/when-math-sees-motion-can-we-trust-it\/","title":{"rendered":"When math sees motion, can we trust it?\u202f\u202f\u00a0"},"content":{"rendered":"

Accuracy alone is not enough when a motion-tracking\u202fsystem signals a\u202fcar to stop, slow down, or continue,\u202for\u202fwhen it\u202fhelps\u202fa doctor\u00a0interpret a\u202fvideo\u202fof a beating heart. In such high-stakes settings, it is also\u202fcrucial\u202fthat the user has a clear measure of the\u202fAI-generated\u202finformation\u2019s\u202freliability.\u202f\u202f\u202f<\/span>\u00a0<\/span><\/p>\n

For his Engineering Design Day<\/a>\u202fyear-long\u202fcapstone project,\u202fAndy Wang, a junior in the\u202f<\/span>Whiting School of Engineering\u2019s<\/span><\/a>\u202fDepartment of Applied Mathematics and Statistics,\u202fdeveloped a statistical methodfor\u202fdetermining\u202fhow much confidence we should place in these kinds of results\u2014and\u202ffor making the system\u2019s\u202fdecision processes\u202fmore transparent.\u202f<\/span>\u00a0<\/span><\/p>\n

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\u202fand trust.\u202f<\/span>\u00a0<\/span><\/p>\n

Wang\u2019s\u202fresearch focused on optical flow\u2014a\u202fclass of\u202fcomputer vision\u202ftechniques\u202fused to\u202festimate motion and\u202ftrack\u202fobjects by tracking\u202fthe movement\u202fof\u202findividual\u202fpixels\u202fduring a series of video frames.\u202f<\/span>\u00a0<\/span><\/p>\n

Optical Flow\u202finterprets\u202fmotion\u202fas it occurs over time and then\u202fmakes\u202fdecisions\u202fbased on its assessment\u202fof\u202fmovement.\u202fIts applications include\u202fdetecting\u202fobjects\u202fin\u202ftraffic, tracking\u202fpeople through space,\u202fand\u202fanalyzing motion in real\u202ftime.\u202f<\/span>\u00a0<\/span><\/p>\n

\u201cBecause\u202foptical flow\u202fis\u202ffrequently\u202fused in safety-critical settings, you want not just an answer, but a sense of how much you can trust that answer,\u201d he\u202fsays.\u202f<\/span>\u00a0<\/span><\/p>\n

But real-world conditions\u202fcan make\u202fthese kinds of\u202fpredictions\u202fcomplicated, such as when objects are hidden\u202ffrom\u202fview or\u202fwhen images are distorted by lighting. Furthermore, many current\u202foptical flow methods rely on deep learning models that produce predictions without explaining how they were derived,\u202fmaking it hard to know\u202fif\u202fthey\u202fshould\u202fbe trusted.\u202f<\/span>\u00a0<\/span><\/p>\n

\u201cYou\u202fcan\u202fget good estimates\u202ffrom optical flow, but you don\u2019t really know where they came from,\u201d Wang says.\u202f\u201cThat makes it hard to judge how reliable the estimates are.\u201d\u202f<\/span>\u00a0<\/span><\/p>\n

Being able to trust results matters, especially in high-stakes settings.\u202f\u201cIf a car approaches an intersection and another vehicle disappears behind a building, a traditional system may still estimate the\u202ffirst car\u2019s\u202fmotion even though it can no longer see it\u2014and it may not signal that this key information is missing,\u201d Wang explains.\u202fSimilar problems can arise in medical imaging when\u202fvisual distortions\u2014like noise, shadows, or sensor imperfections\u2014affect how motion is captured, increasing the risk of misinterpreting what is happening. \u202f\u202f\u202f<\/span>\u00a0<\/span><\/p>\n

Wang\u202fsolved this problem by pairing motion estimates with uncertainty estimates.\u202f<\/span>\u00a0<\/span><\/p>\n

Rather than relying solely on black-box AI models, his approach\u202fbuilds on\u202finterpretable, mathematically grounded techniques.\u202fWang\u2019s method\u202fsignals when motion estimates are uncertain\u202fand lets the system\u202ftreat those estimates more\u202fcautiously.\u202f<\/span>\u00a0<\/span><\/p>\n

To do this, Wang developed a way to recompute\u202fmotion at multiple image resolutions and\u202fapplies\u202fa Kalman\u202ffilter\u2014a\u202fstatistical method used to refine predictions over time\u2014\u202facross scales, passing forward both refined motion estimates and their uncertainty at each step. This lets the system\u202fcalculate\u202fboth how objects move and how confident the system is in these\u202festimates\u2014producing a\u202fconfident\u202fvalue for each pixel and showing exactly where predictions may be less reliable.\u202fThe method is fast enough for real-time use, based on transparent mathematics, and provides confidence measures alongside its predictions.\u202f\u202f<\/span>\u00a0<\/span><\/p>\n

\u201cIf you don\u2019t know when the system might be wrong, you risk acting on bad information,\u201d Wang says, noting\u202fthat without\u202fa measure of confidence, users have no way\u202fto judge\u202fhow reliable a prediction is.\u202f\u202f<\/span>\u00a0<\/span><\/p>\n

Advised by\u202f<\/span>Mario Micheli<\/span><\/a>, senior lecturer of applied mathematics and statistics,\u202fWang is now preparing\u202fhis findings\u202ffor publication.\u202f\u202f<\/span>\u00a0<\/span><\/p>\n","protected":false},"template":"","class_list":["post-56410","news","type-news","status-publish","hentry","news_categories-applied-mathematics","news_categories-research","news_categories-student-experience"],"acf":[],"yoast_head":"\nWhen math sees motion, can we trust it?\u202f\u202f\u00a0 | Department of Applied Mathematics and Statistics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.jhu.edu\/ams\/news\/when-math-sees-motion-can-we-trust-it\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"When math sees motion, can we trust it?\u202f\u202f\u00a0 | Department of Applied Mathematics and Statistics\" \/>\n<meta property=\"og:description\" content=\"Accuracy alone is not enough when a motion-tracking\u202fsystem signals a\u202fcar to stop, slow down, or continue,\u202for\u202fwhen it\u202fhelps\u202fa doctor\u00a0interpret a\u202fvideo\u202fof a beating heart. 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