Goal: Fast and Robust Velocity Estimation
86
Goal: Fast and Robust Velocity Estimation P 1 P 2 P 3 P 4 Our Approach: Alignment Probability ● Spatial Distance ● Color Distance (if available) ● Probability of Occlusion Annealed Dynamic Histograms Combining 3D Shape, Color, and Motion for Robust Anytime Tracking David Held, Jesse Levinson, Sebastian Thrun, and Silvio Savarese
-
Upload
bruno-solomon -
Category
Documents
-
view
76 -
download
0
description
Combining 3D Shape, Color, and Motion for Robust Anytime Tracking. David Held, Jesse Levinson, Sebastian Thrun , and Silvio Savarese. Goal: Fast and Robust Velocity Estimation. Our Approach: Alignment Probability. P 1. P 2. Annealed Dynamic Histograms. P 4. P 3. Spatial Distance - PowerPoint PPT Presentation
Transcript of Goal: Fast and Robust Velocity Estimation
Combining 3D Shape, Color, and Motion for Robust Anytime Tracking
Goal: Fast and Robust Velocity Estimation
P1P2P3P4Our Approach: Alignment Probability
Spatial DistanceColor Distance (if available)Probability of Occlusion
Annealed Dynamic HistogramsCombining 3D Shape, Color, and Motion for Robust Anytime TrackingDavid Held, Jesse Levinson, Sebastian Thrun, and Silvio Savarese
\left p(x_t \mid z_1 \ldots z_t) = \eta \, p(z_t \mid x_t, z_{t-1}) p(x_t \mid z_1 \ldots z_{t-1})
Goal: Fast and Robust Velocity Estimation
Combining 3D Shape, Color, and Motion for Robust Anytime TrackingDavid Held, Jesse Levinson, Sebastian Thrun, and Silvio Savarese
Baseline: Centroid Kalman Filter
Local Search Poor Local Optimum!
t+1tOcclusionsActual MotionBaseline: ICP
Annealed Dynamic Histograms
Goal: Fast and Robust Velocity Estimation
P1P2P3P4Our Approach: Alignment Probability
Spatial DistanceColor Distance (if available)Probability of OcclusionCombining 3D Shape, Color, and Motion for Robust Anytime TrackingDavid Held, Jesse Levinson, Sebastian Thrun, and Silvio Savarese
Annealed Dynamic HistogramsMotivation
Quickly and robustly estimate the speed of nearby objects
Show videos - cars converging onto a lane, bikes swerving into traffic
Laser DataCamera ImagesSystem
Laser DataCamera ImagesSystem
Previous Work(Teichman, et al)
System
Laser DataCamera ImagesThis WorkVelocityEstimation
Previous Work(Teichman, et al)
Velocity Estimation
t
Velocity Estimation
t+1t
Velocity Estimation
t+1t
Velocity Estimation
t+1tVelocity Estimation
t+1tOcclusionsActual Motion
ICP Baseline
ICP Baseline
ICP BaselineTracking Probabilityvyvx?????
Local Search Poor Local Optimum!ICP Baseline
Tracking Probability
Velocity Estimation
t
Velocity Estimation
t+1t
Velocity Estimation
t+1t
Velocity Estimation
t+1t
Velocity Estimation
t+1t
Velocity Estimation
t+1t
Velocity Estimation
t+1t
Xt
Velocity Estimation
t+1t
Xt
MeasurementModelMotion ModelTracking Probability\left p(x_t \mid z_1 \ldots z_t) = \eta \, p(z_t \mid x_t, z_{t-1}) p(x_t \mid z_1 \ldots z_{t-1})
MeasurementModelMotion ModelTracking ProbabilityConstant velocity Kalman filter
MeasurementModelTracking Probability
Motion Model
MeasurementModelTracking Probability
Motion Model
MeasurementModelTracking Probability
Motion Model
MeasurementModelTracking ProbabilityMotion Model
MeasurementModelTracking ProbabilityMotion Model
MeasurementModelTracking ProbabilityMotion Model
MeasurementModelTracking ProbabilityMotion Model
MeasurementModelTracking ProbabilityMotion Model
MeasurementModelTracking ProbabilityMotion Model
MeasurementModelTracking ProbabilityMotion Model
MeasurementModelTracking ProbabilityMotion Model
MeasurementModelTracking ProbabilityMotion Model
k
MeasurementModelTracking ProbabilityMotion Model
Sensor noiseSensor resolution
k
Delta Color ValueProbabilityColor ProbabilityIncluding Color
p(z_t \mid x_t, z_{t-1}) =\eta\prod_{z_i \in z_t}p_s(z_i \mid \bar{z}_j)p_c(z_i \mid \bar{z}_j))\eta (\prod_{z_i \in z_t} \exp (-\frac{1}{2}(z_i - \bar{z}_j)^T \Sigma^{-1} (z_i - \bar{z}_j))+k)p(C)p(z_t \mid \bar{z}_j,V,C) +P(\neg C)p(z_t \mid \bar{z}_j,V,\neg C)1-p_c \exp(\frac{-r^2}{2\sigma_c^2})Including Color
p(z_t \mid x_t, z_{t-1}) =\eta\prod_{z_i \in z_t}p_s(z_i \mid \bar{z}_j)p_c(z_i \mid \bar{z}_j))\eta (\prod_{z_i \in z_t} \exp (-\frac{1}{2}(z_i - \bar{z}_j)^T \Sigma^{-1} (z_i - \bar{z}_j))+k)p(C)p(z_t \mid \bar{z}_j,V,C) +P(\neg C)p(z_t \mid \bar{z}_j,V,\neg C)1-p_c \exp(\frac{-r^2}{2\sigma_c^2})Including Color
p(z_t \mid x_t, z_{t-1}) =\eta\prod_{z_i \in z_t}p_s(z_i \mid \bar{z}_j)p_c(z_i \mid \bar{z}_j))\eta (\prod_{z_i \in z_t} \exp (-\frac{1}{2}(z_i - \bar{z}_j)^T \Sigma^{-1} (z_i - \bar{z}_j))+k)p(C)p(z_t \mid \bar{z}_j,V,C) +P(\neg C)p(z_t \mid \bar{z}_j,V,\neg C)1-p_c \exp(\frac{-r^2}{2\sigma_c^2})Including Color
p(z_t \mid x_t, z_{t-1}) =\eta\prod_{z_i \in z_t}p_s(z_i \mid \bar{z}_j)p_c(z_i \mid \bar{z}_j))\eta (\prod_{z_i \in z_t} \exp (-\frac{1}{2}(z_i - \bar{z}_j)^T \Sigma^{-1} (z_i - \bar{z}_j))+k)p(C)p(z_t \mid \bar{z}_j,V,C) +P(\neg C)p(z_t \mid \bar{z}_j,V,\neg C)1-p_c \exp(\frac{-r^2}{2\sigma_c^2})Including Color
p(z_t \mid x_t, z_{t-1}) =\eta\prod_{z_i \in z_t}p_s(z_i \mid \bar{z}_j)p_c(z_i \mid \bar{z}_j))\eta (\prod_{z_i \in z_t} \exp (-\frac{1}{2}(z_i - \bar{z}_j)^T \Sigma^{-1} (z_i - \bar{z}_j))+k)p(C)p(z_t \mid \bar{z}_j,V,C) +P(\neg C)p(z_t \mid \bar{z}_j,V,\neg C)1-p_c \exp(\frac{-r^2}{2\sigma_c^2})Including Color
Delta Color ValueProbability
p(z_t \mid x_t, z_{t-1}) =\eta\prod_{z_i \in z_t}p_s(z_i \mid \bar{z}_j)p_c(z_i \mid \bar{z}_j))\eta (\prod_{z_i \in z_t} \exp (-\frac{1}{2}(z_i - \bar{z}_j)^T \Sigma^{-1} (z_i - \bar{z}_j))+k)p(C)p(z_t \mid \bar{z}_j,V,C) +P(\neg C)p(z_t \mid \bar{z}_j,V,\neg C)1-p_c \exp(\frac{-r^2}{2\sigma_c^2})Including Color
Delta Color Value
Probabilityp(z_t \mid x_t, z_{t-1}) =\eta\prod_{z_i \in z_t}p_s(z_i \mid \bar{z}_j)p_c(z_i \mid \bar{z}_j))\eta (\prod_{z_i \in z_t} \exp (-\frac{1}{2}(z_i - \bar{z}_j)^T \Sigma^{-1} (z_i - \bar{z}_j))+k)p(C)p(z_t \mid \bar{z}_j,V,C) +P(\neg C)p(z_t \mid \bar{z}_j,V,\neg C)1-p_c \exp(\frac{-r^2}{2\sigma_c^2})Including Color
Delta Color Value
Probabilityp(z_t \mid x_t, z_{t-1}) =\eta\prod_{z_i \in z_t}p_s(z_i \mid \bar{z}_j)p_c(z_i \mid \bar{z}_j))\eta (\prod_{z_i \in z_t} \exp (-\frac{1}{2}(z_i - \bar{z}_j)^T \Sigma^{-1} (z_i - \bar{z}_j))+k)p(C)p(z_t \mid \bar{z}_j,V,C) +P(\neg C)p(z_t \mid \bar{z}_j,V,\neg C)1-p_c \exp(\frac{-r^2}{2\sigma_c^2})Probabilistic Framework3D ShapeColorTrackingMotion HistoryTracking Probability
P1P2P3P4Tracking ProbabilityvyvxDynamic DecompositionvyvxDynamic DecompositionvyvxDynamic DecompositionvyvxDynamic DecompositionvyvxDerived from minimizing KL-divergence between approximate distribution and true posteriorAnnealing
Inflate the measurement modelAnnealing
Inflate the measurement model
Annealing
Inflate the measurement model
AlgorithmFor each hypothesisCompute the probability of the alignment
MeasurementModelMotion ModelAlgorithmFor each hypothesisCompute the probability of the alignment
Finely sample high probability regions
MeasurementModelMotion ModelAlgorithmFor each hypothesisCompute the probability of the alignment
Finely sample high probability regions
Go to step 1 to compute the probability of new hypotheses
MeasurementModelMotion ModelAnnealingMore timeMore accurateAnytime Tracker
Anytime TrackerChoose runtime based on:Total runtime requirementsImportance of tracked object...
Comparisons
Comparisons
Comparisons
Kalman Filter
Kalman FilterADH Tracker(Ours)Models
Quantitative Evaluation 2
Sampling Strategies
Advantages over Radar
Conclusions3D ShapeColorTrackingMotion HistoryRobust to Occlusions, Viewpoint ChangesAdd figures and illustrations for these pointsConclusions3D ShapeColorTrackingMotion HistoryRobust to Occlusions, Viewpoint ChangesRuns in Real-timeRobust to Initialization ErrorsAdd figures and illustrations for these points
Delta Color ValueProbabilityColor ProbabilityError vs Number of Points
Error vs Distance
Error vs Number of Frames
Error vs Number of Frames
