Final Project Presentation Schedule Presentation days: April 22, 24, and 29 A single presentation is required for a team Each presentation has 12 + 3 minutes Q&A Send me an email ([email protected]) that includes: • Your name and ranking of the dates starting from the most preferred • Earlier email has higher priority in choosing the date
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Final Project Presentation Schedule
Presentation days:April 22, 24, and 29
A single presentation is required for a team
Each presentation has 12 + 3 minutes Q&A
Send me an email ([email protected]) that includes:• Your name and ranking of the dates starting from the
most preferred
• Earlier email has higher priority in choosing the date
Materials covered in the presentation
For a hands-on project
• An introduction of the background
• A brief literature review
• Methodology of your proposed method
• Experimental results if any
For a survey project
• An introduction of the background
• A discussion on the papers you reviewed
• Comparison of the methods/groups you reviewed
Motion Analysis by Optical Flow
Motion field:
• Measured on 2D images
• The projection of 3D velocity field on the image plane
Optical flow: the apparent motion of brightness patterns
• Optical flow ≠ Motion field
• Important assumptions/constraints
• Brightness constancy
• Small motion
• Constant motion in a neighborhood
Dense – estimating motion for every pixel!
Object Tracking
Tracking rigid object with rigid motion (scaling and translation)
• Global motion
• Examples: tracking vehicles, buildings, etc. from the same view angle
Tracking object with rigid/nonrigid motion
• Global motion + view change + local deformation
• Examples: tracking animals, persons, faces, etc.
Object Tracking – Motion Analysis from Multiple
Frames
Tracking vs optical flow:
• Tracking is often applied for a few specified targets in the video
• Optical flow is applied for any points on the image –dense optical flow
• Both of them need to compute the correspondence between images
Example
Object Tracking – Motion Analysis from Multiple
Frames
tth frame t+1th frame
(𝑥𝑡 , 𝑦𝑡) (𝑥𝑡+1, 𝑦𝑡+1)
𝒔𝒕
𝒐𝒕
𝒔𝒕+𝟏
𝒐𝒕+𝟏
Question:
Given 𝐬𝒕 and 𝐨𝒕+𝟏 = 𝑥𝑡+1, 𝑦𝑡+1 , how to
estimate 𝐬𝒕+𝟏?
For a point 𝑝 = (𝑥𝑡 , 𝑦𝑡) at the 𝑡𝑡ℎ time frame with a velocity of 𝑣𝑡 =
(𝑣𝑥𝑡 , 𝑣𝑦𝑡), we define a state vector 𝐬𝒕 = 𝑥𝑡 , 𝑦𝑡 , 𝑣𝑥𝑡, 𝑣𝑦𝑡𝑻
𝑣𝑡 = (𝑣𝑥𝑡 , 𝑣𝑦𝑡)p
General Strategy for Object Tracking
Predict position for next frame
Initialization Object Detection
Local search Template matching
Finalize the position
A well-known algorithm following the strategy -- Kalman filter
Tracking – General Probabilistic Formulation
Given
•𝑃(𝐬𝑡|𝐨0, ⋯ , 𝐨𝑡) - “Prior”
We should like to know
•𝑃(𝐬𝑡+1|𝐨0, ⋯ , 𝐨𝑡)- “Predictive distribution”
•𝑃(𝐬𝑡+1|𝐨0, ⋯ , 𝐨𝑡, 𝐨𝑡+1)– “Posterior”
How to compute them?
𝒔𝟎
𝒐𝟎
𝒔𝟏
𝒐𝟏
… 𝒔𝒕
𝒐𝒕
𝒔𝒕+𝟏
𝒐𝒕+𝟏
𝑃 𝐬𝑡+1 𝐨0, ⋯ , 𝐨𝑡 =
𝐬𝑡
𝑃 𝐬𝑡+1, 𝐬𝑡 𝐨0, ⋯ , 𝐨𝑡
=
𝐬𝑡
𝑃 𝐬𝑡+1 𝐬𝑡 , 𝐨0, ⋯ , 𝐨𝑡 ∗ 𝑃(𝐬𝑡|𝐨0, ⋯ , 𝐨𝑡)
Tracking – General Probabilistic Formulation
Given
•𝑃(𝐬𝑡|𝐨0, ⋯ , 𝐨𝑡) - “Prior”
We should like to know
•𝑃(𝐬𝑡+1|𝐨0, ⋯ , 𝐨𝑡)- “Predictive distribution”
•𝑃(𝐬𝑡+1|𝐨0, ⋯ , 𝐨𝑡, 𝐨𝑡+1)– “Posterior”
How to compute them?
𝒔𝟎
𝒐𝟎
𝒔𝟏
𝒐𝟏
… 𝒔𝒕
𝒐𝒕
𝒔𝒕+𝟏
𝒐𝒕+𝟏
𝑃 𝐬𝑡+1 𝐨0, ⋯ , 𝐨𝑡, 𝐨𝑡+1
=𝑃 𝐨𝑡+1 𝐬𝑡+1, 𝐨0 , ⋯ , 𝐨𝑡 ∗𝑃 𝐬𝑡+1 𝐨0, ⋯ , 𝐨𝑡
σ𝐬𝑡+1 𝑃 𝐨𝑡+1 𝐬𝑡+1, 𝐨0 , ⋯ , 𝐨𝑡 ∗𝑃 𝐬𝑡+1 𝐨0, ⋯ , 𝐨𝑡
Tracking – General Assumptions
• First-order markov
• The current state only depends on the state of the previous time step
• 𝑃 𝐬𝑡 𝐬0, ⋯ , 𝐬𝑡−1 = 𝑃 𝐬𝑡 𝐬𝑡−1
• Given the current state, the measurement at current time step is independent of the previous measurements