The Robin Van Persie Problem

THE VAN PERSIE PROBLEMAnurag Misra Garuna ProductionsMENTOR: DR. AMITABHA MUKHERJEEAnurag Misra 121441Lets have a look at it!Anurag Misra Garuna ProductionsVan Persie the Header!Oh my God!!!2

Anurag Misra Garuna ProductionsHow did Van Persie actually do it?Anurag Misra Garuna ProductionsHumans are basically very complex machines.Just like machines humans also learn these incredibly difficult tasks by encountering such situations again and again, and applying it using their cognitive model4This is basically this: Anurag Misra Garuna Productions

5Applied to do something completely unknown like this Anurag Misra Garuna Productions

Or like this6How will I reproduce the Van Persie Header?Anurag Misra Garuna ProductionsOr basically how to train a machine to perform something similarto the Incredible Van Persie Goal!?7The solution lies in:

Anurag Misra Garuna ProductionsVisuomotor Learning Using ImageManifolds: Developing a neural network by taking numerous trials throw trajectories as inputs and using that neural network to predict the right trajectory8Anurag Misra Garuna ProductionsHumans like footballers basically learn by doing actions and then observing the result: the trajectory caused. They do and learn.So do machines! This is what is called Machine Learning!9Anurag Misra Garuna Productions

10Anurag Misra Garuna ProductionsSince each throw varies only on the parameters (,v), there are only two ways in which we can modify the images while remaining locally withinthe subspace of throw images11Anurag Misra Garuna ProductionsThe structure of this image manifold exactly mimics the structure of the motor parameters (the motor manifold).They can be mapped toa single joint manifold, which can be discovered using standard non-linear dimensionality reduction algorithms such as ISOMAP.

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Variations in Manifolds: according to a) angleof projection, and b) velocity. (low values in yellow)Resulting manifold obtained using a Hausdorff distance metric (Huttenlocher, Klanderman, and Rucklidge 1993):( h ( A, B ) = max aA min b B ||a b ||).i.e. Obtain a low dimensional embedding for theimages using ISOMAP 13Anurag Misra Garuna ProductionsWe solve our Van Persie Header problem by solving an easier problem known as Dart Throwing Problem, where you hit a dart at a target boardThe Dart Throwing Problem is a simple problem which we solve by the Algorithm we named as Dart Throwing Algorithm

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Remodeling the goal as (n+1)*(n+1) Dart Problem16Anurag Misra Garuna Productions

And assuming a static goalkeeper at some distance from the goal

17REFERENCES: Anurag Misra Garuna ProductionsFrom visuo-motor to languageDeepali Semwal, Sunakshi Gupta, Amitabha MukerjeeDepartment of Computer Science and EngineeringIndian Institute of Technology, KanpurHuttenlocher, D. P.; Klanderman, G. A.; and Rucklidge,W. J. 1993. Comparing images using the hausdorffdistance. IEEE PAMI 15(9):850863.

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