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Lecture 10 Causal Estimation of 3D Structure and Motion

Lecture 10 Causal Estimation of 3D Structure and Motion. VISION as a SENSOR. machine to INTERACT with the environment. NEED to estimate relative 3D MOTION. 3D SHAPE (TASK). REAL-TIME. CAUSAL processing. representation of SHAPE (only supportive of representation of motion).

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Lecture 10 Causal Estimation of 3D Structure and Motion

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  1. Lecture 10Causal Estimation of 3D Structure and Motion Invitation to 3D vision

  2. VISION as a SENSOR machine to INTERACT with the environment NEED to estimate relative 3D MOTION 3D SHAPE (TASK) REAL-TIME CAUSAL processing representation of SHAPE (only supportive of representation of motion) POINT-FEATURES Invitation to 3D vision

  3. SFM CORRESPONDENCE EASY HARD/IMPOSSIBLE TRADEOFFS LARGE BASELINE Invitation to 3D vision

  4. TRADEOFFS SFM CORRESPONDENCE LARGE BASELINE EASY HARD/IMPOSSIBLE SMALL BASELINE HARD/IMPOSSIBLE EASY Invitation to 3D vision

  5. TRADEOFFS SFM CORRESPONDENCE LARGE BASELINE EASY HARD/IMPOSSIBLE GLOBAL SMALL BASELINE LOCAL HARD/IMPOSSIBLE EASY Invitation to 3D vision

  6. WHAT DOES IT TAKE ? SFM CORRESPONDENCE LARGE BASELINE EASY HARD/IMPOSSIBLE GLOBAL SMALL BASELINE LOCAL HARD/IMPOSSIBLE EASY INTEGRATE visual information OVER TIME OCCLUSIONS! Invitation to 3D vision

  7. Setup and notation Temporal evolution: Invitation to 3D vision

  8. Given measurements of the “output” (feature point positions) Given modeling assumptions about the “input” (acceleration = noise) Estimate the “state” (3D structure, pose, velocity) Structure and motion as a filtering problem Invitation to 3D vision

  9. Model is non-linear (output map = projection) State-space is non-linear! (SE(3)) Noise: need to specify what we mean by “estimate” Even without noise: model is not observable! Difficulties … Invitation to 3D vision

  10. Equivalent class of state-space trajectories generate the same measurements Fix, e.g., the direction of 3 points, and the depth of one point (Gauge transformation) Observability Invitation to 3D vision

  11. Local coordinatization of the state space Invitation to 3D vision

  12. Now it looks very much like: And we are looking for (a point statistic of): Minimal realization Invitation to 3D vision

  13. For single rigid body/static scene, expect unimodal posterior No need to estimate entire density; point estimate suffices Robust (M-) version of EKF works well in practice … … and in real time for a few hundred feature points EFK vs. particle filter? Invitation to 3D vision

  14. Adding/removing features (subfilters) Multiple motions/outliers (M-filter, innovation tests) Tracking drift (reset with wide-baseline matching) Switching the reference features (hard! Causes unavoidable global drift) Global registration (maintain DB of lost features) In practice … Invitation to 3D vision

  15. Invitation to 3D vision

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