## Biomedical Image Analysis: TrackingIn biological and medical imaging applications, tracking objects in motion is a critical task. This book describes the state-of-the-art in biomedical tracking techniques. We begin by detailing methods for tracking using active contours, which have been highly successful in biomedical applications. The book next covers the major probabilistic methods for tracking. Starting with the basic Bayesian model, we describe the Kalman filter and conventional tracking methods that use centroid and correlation measurements for target detection. Innovations such as the extended Kalman filter and the interacting multiple model open the door to capturing complex biological objects in motion. A salient highlight of the book is the introduction of the recently emerged particle filter, which promises to solve tracking problems that were previously intractable by conventional means. Another unique feature of Biomedical Image Analysis: Tracking is the explanation of shape-based methods for biomedical image analysis. Methods for both rigid and nonrigid objects are depicted. Each chapter in the book puts forth biomedical case studies that illustrate the methods in action. In biological and medical imaging applications, tracking objects in motion is a critical task. This book describes the state-of-the-art in biomedical tracking techniques. We begin by detailing methods for tracking using active contours, which have been highly successful in biomedical applications. The book next covers the major probabilistic methods for tracking. Starting with the basic Bayesian model, we describe the Kalman filter and conventional tracking methods that use centroid and correlation measurements for target detection. Innovations such as the extended Kalman filter and the interacting multiple model open the door to capturing complex biological objects in motion. |

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### Contents

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232 Gradient Vector Flow | 22 |

TRACKING WITH SNAKES | 25 |

241 External Force for Cell Tracking Case Study | 29 |

242 Motion Gradient Vector Flow | 30 |

Particle Filters and MultiTarget Tracking | 71 |

42 THE PARTICLE FILTER | 72 |

421 The CONDENSATION Algorithm | 74 |

422 Auxiliary Particle Filters | 75 |

43 MULTITARGET TRACKING | 77 |

431 Multiple Hypothesis Tracking | 78 |

432 Joint Probabilistic Data Association | 79 |

433 Markov Chain Monte Carlo Methods | 81 |

243 Computation of Motion Gradient Vector Flow Field | 32 |

25 CHOOSING PARAMETER VALUES | 34 |

26 DYNAMIC PROGRAMMING FOR SNAKE EVOLUTION | 38 |

27 CONCLUSIONS | 43 |

Bayesian Tracking and the Kalman Filter | 45 |

32 SEQUENTIAL BAYESIAN FILTERING | 46 |

33 KALMAN FILTER | 50 |

THE ALPHABETA FILTER | 52 |

341 AlphaBeta Filter Gains | 55 |

342 Initializing the Kalman Tracker | 57 |

343 Executing the AlphaBeta Filter | 58 |

35 THE EXTENDED KALMAN FILTER | 62 |

36 INTERACTING MULTIPLE MODELS FOR TRACKING | 64 |

37 SUMMARY | 69 |

435 Auction Algorithm | 85 |

44 CASE STUDIES | 87 |

441 Leukocyte Tracking with CONDENSATION | 88 |

442 Multiple Cell Tracking with MCMC | 93 |

45 SUMMARY | 98 |

Tracking Shapes by Sampling | 99 |

52 TRACKING RIGID SHAPES | 100 |

521 Tracking by Affine and Projective Snakes | 101 |

523 Projective Snakes for Tracking | 107 |

53 TRACKING DEFORMABLE SHAPES | 108 |

532 Sequential Bayesian Formulation | 120 |

54 SUMMARY | 125 |

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### Common terms and phrases

active contour affine parameters affine transformation alpha—beta filter annealing assume balloon force biomedical image analysis boundary cell tracking centroid compute CONDENSATION algorithm conditional independence constraint covariance delineate denotes derivative detected ellipse energy changes estimate example extended Kalman filter external force ﬁeld ﬁlter follows Gaussian GICOV given gradient descent gradient descent equation gradient vector flow image gradient implementation initial contour iteration Kalman filter Markov chain matrix MCMC methods MGVF minimization minimum Motion Gradient Vector motion model non-negative observation obtain optimal p(Zt parameter values particle filter posterior density potential surface prediction probability density problem recursion represent respect rolling leukocytes sequential Bayesian SEQUENTIAL BAYESIAN FILTERING shape shape-based shown in Fig simulated annealing snake evolution snaxel snaxel positions solution space stationary distribution step stochastic target temperature transition probabilities update variables velocity Yi)t zero

### Popular passages

Page 5 - Which of you fathers, if your son asks for a fish, will give him a snake instead? Or if he asks for an egg, will give him a scorpion? If you then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give the Holy Spirit to those who ask him!

Page 5 - The earth doth like a snake renew Her winter weeds outworn.