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Relations as Context to improve Multi-Target Tracking and Activity Recognition. Cristina Manfredotti 12, Enza Messina 1, David Fleet 2 1 DISCo, University of Milano-Bicocca 2 Computer Science Dept, University of Toronto

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 2 Relations to improve tracking

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 3 Complex activity recognition Y.Ke, R.Sukthankar, M.Hebert; Event Detection in Crowed Videos

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 4 Objectives Goals: 1.To model relations and 2.To maintain beliefs over particular relations between objects In order to simultaneously: Improve tracking with informed predictions and Identify complex activities based on observations and prior knowledge

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 5 Relational Domain Relational Domain: set of objects characterized by attributes 1 and with relations 1 between them Boat Id color position(t) velocity(t) direction(t) DecreasingVelocity(t) A SameDirection(t) distance(t) Before(t) Boat B Id color position(t) velocity(t) direction(t) DecreasingVelocity(t) SameDirection(t) distance(t) Before(t) 1 Attributes and relations are predicate in FOL.

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 6 A Parenthesis: To model uncertainty in a Relational Domain we will use Relational (Dynamic) Bayesian Networks

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 7 BN: the Alarm example

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 8 Thanks to Mark Chavira A large BN

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 9 The Alarm Relational Domain Relational Domain contains a set of objects with relations between them Objects e.g.: Relation neighbor alarm burglar toCall (the howner of the house) toHear (the alarm) neighbors attributes: capacity of hearing, attention,... alarms attributes: its volume, its sensibility,...

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 10 Alarm RBN: Alarm.Volume NeighborCalls Earthquacke Neigh.DegOfDef Neigh.NoiseAround

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 11 Closing the parenthesis... Syntax RBN: –a set of nodes, one for each variable –a directed, acyclic graph –a conditional distribution for each node given its parents This distribution must take into account the actual complexity of the nodes! Syntax RBN: –a set of nodes, one for each predicate –a directed, graph –a conditional distribution for each node given its parents,

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 12 Relational State The State of a Relational Domain is the set of the predicates that are true in the Domain. Relational state State of attributes State of relations

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 13 Dynamics The State of a Relational Domain is the set of the predicates that are true in the Domain. State evolves with time We extend a RBN to a RDBN as we are used to extend a BN to a DBN.

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 14 Inference Markov assumption and Conditional independence of data on state. bel(s t ) = ® p(z t |s t ) s p(s t |s t-1 )bel(s t-1 )ds t-1 Bayesian Filter The problem of computing: bel(s t ) = p(s t |z 1:t )

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 15 p(x t-1 |z 1:t-1 )p(x t |z 1:t-1 )p(x t |z 1:t ) Bel(x t-1 ) Bel(x t ) Transition model Sensor model t = t+1 ~ Transition model Sensor model Inference Relations in the State result in correlating the State of different objects between them p(x t-1 |z 1:t-1 )p(x t |z 1:t-1 )p(x t |z 1:t ) Bel(x t-1 ) Bel(x t ) Transition model Sensor model t = t+1

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 16 Sensor model (1 st assumption) part of the state relative to relations, s r, not directly observable p(z t |s t ) = p(z t |s a t ) observation z t independent by the relations between objects. Intuitively: Travelling Together vs Being Close

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 17 Transition model: a trick p(s t |s t-1 ) = p(s a t,s r t |s a t-1, s r t-1 ) S a t-1 S r t-1 SatSat SrtSrt Intuitive

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 18 p(s a t,s r t |s a t-1,s r t-1 )= But s r t independent by s a t-1 given s r t-1 and s a t p(s a t,s r t |s a t-1,s r t-1 ) = p(s a t |s a t-1,s r t-1 ) p(s r t |s r t-1, s a t ) bel(s t ) = p(s t |z 1:t ) = p(s a t,s r t |z 1:t ) bel(s t )=αp(z t |s a t,s r t ) s p(s a t,s r t |s a t-1,s r t-1 )bel(s t-1 )ds t-1 p(z t |s a t,s r t ) = p(z t |s a t ) Relational Inference p(s a t |s a t-1,s r t-1 ) p(s r t |s a t-1,s r t-1, s a t ) Transition model (2 nd assumption)

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 19 Conditional Probability Distribution FOPT: a Probabilistic Tree whose nodes are FOL formulas CPD relation t (x,y): relation t-1 (x,y) p(relation t (x,y)) x t, y t CPD y t : x, relation t-1 (x,y) p(y t |y t-1 ) T F p(y t |y t-1 ) p(x t |x t-1,y t-1,r t-1 )

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 20 * It is a technique that implements a recursive Bayesian Filter through a Monte Carlo simulation. The key idea is to represent the posterior pdf as a set of samples (particles) paired with weights and to filter the mesurament based on these weights.. Particle Filtering* (general case)

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 21 Relational Particle Filter

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 22 RPF: extraction X a t,(m) X r t,(m) X a t,(m) ~ p(x a t,(m) |s a t-1,s r t-1 ) X a t,(m) ~ p(x r t,(m) |s a t = x a t,(m),s r t-1 ) X r t,(m)

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 23 RPF: weighting The consistency of the probability function ensures the convergence of the algorithm. X a t,(m) X r t,(m) Weight ( ) ~p(z t |x a t ) The weighting step is done according to the attributes part of each particle only, the relational part follows.

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 24 Tracking AND activity Recognition X a t,(m) X r t,(m) X a t,(m) X r t,(m) X a t,(m) X a {t,(m)} X o {t,(m)} X r t,(m) X a t+1,(m) 1° step of sampling: prediction of the state of attributes X a t,(m) X a {t,(m)} X o {t,(m)} X r t,(m) X a t+1,(m) X a {t,(m)} X o {t,(m)} X r t+1,(m) 2° step of sampling: prediction of the state of relations Or activity prediction

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 25 Canadian Harbor: rendezvous Same speed

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 26 Canadian Harbor: Avoidance Constant speed

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 27 Exp: attributestransition

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 28 Exp: relationstransition

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 29 Exp: Results methodTP ratioTN ratio Mean Tracking Error (km) RPF0.45450.72351.8379 PF3.3906 random0.44440.4841

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 30 To conclude... Modeling Relations dynamically: –To improve multi target tracking –To recognize complex activities Inference in Dynamic Relational Domain – In theory complex BUT – Simplified by smart decomposition of the transition model non-relational sensor model Results are promising

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 31 BNs: a drawback Each node is a variable: Two different nodes If we would have 4 neighbors? We have to construct a graph with 2 more nodes.

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 32 Related works Complex tracking tasks: –Heuristics M.Isard and J. MacCormick BraMBLe, A Bayesian Multi-Blob Tracker.

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 33 Related works Complex tracking tasks: –Heuristics –Mixed-States models M.Isard and A.Blake A mixed-state condensation tracker with automatic model switching

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 34 Related works Complex tracking tasks: –Heuristics –Mixed-States models Complex activity recognition: –Stochastic grammar Free Y.A.Ivanov and A.F.Bobick Recognition of Visual Activities and Interactions by Stochastic Parsing

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C.Manfredotti, E.Messina, D.Fleet: Relations as context. Potsdam, Germany, 14° Sept.09 35 Related works Complex tracking tasks: –Heuristics, –Mixed-States models Complex activity recognition: –Stochastic grammar Free, –First Order Logic S. Tran and L. Davis, Visual Event Modeling and Recognition using Markov Logic Networks

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