CS336 Midterm Review Structure of the midterm Two long questions - PowerPoint PPT Presentation

CS336 Midterm Review

Structure of the midterm Two long questions Several short question for conceptual understanding True/False and multiple choice questions

What’s going to covered on the exam? ● Poses, twists, transformations ● Image projection, multiview, flow ● Learning based approaches in depth and flow estimation ○ Make sure you understand the concepts from the papers we discussed ● Filtering methods ● Backprop-able filters ● Controls

What’s not going to be on the exam? ● Anything that requires coding, complex calculations ○ We won’t ask you to hand calculate how to integrate a twist ○ But we might ask you to write down the general formula for it ● Neural network architectures from papers ○ But we might ask you what are the assumptions, structures, prior knowledge of the problem, that are being used in designing the network structure/ data collection algo/ loss.

Review ● Exponential coordinates ● Bayesian filters ● Particle filter ● Differentiable filters ● Control ● Open for general questions

Possible meanings of rotation: Representing orientation of a frame Changing the reference frame Rotating a vector or another frame

Representations of rotation: Axis-angle Quaternion Rotation matrix Euler angles (many possible axis orders, moving axis vs stationary axis) Conversion between the representations ? Pros and cons for each representation ?

Axis-angle -> exponential coordinate Unit axis and rotation angle. This does not mean is the angular velocity and is time! Think of this product as one quantity, representing a delta motion / relative pose / pose This quantity can represent any (angular velocity, time) pair.

From rotation to homogeneous transforms Possible meanings…. Representations: Homogeneous matrix Composite one rotation representation + translation Twist

Twist Is unit twist and is the norm of twist. Norm of twist is the norm of angular part, unless angular part is zero. Then the norm of twist is the norm of translation part. This does not mean is velocity and is time!

Body velocity and spatial velocity Interpretation of v_s and v_b?

General Bayesian Filters Prior (k) Process model prediction step Posterior (k) Posterior (k-1) Belief Belief Observation model Update step

KF and EKF KF: assumes linear process model and linear observation model,Gaussian noise. Keeps distributions linear, thus updates closed-form. EKF: linearize process model and observation model around expected input. So that we can use the same closed-form update. But is only approximately correct.

Particle Filter Using samples set instead of closed-form probability distributions. Prediction step: take one sample from process model for each particle Update step: bayesian to calculate particle weights, and resample.

Back-prop KF Because an observation model for camera images will be quite complex and nonlinear. Use CNN to extract some features, and treat CNN as part of the sensor. Implement KF as a recurrent computational graph. Train to maximize log-likelihood of true state/observation w.r.t KF belief.

Back-prop particle filter Action sampler (to inject noise in dynamics model) Dynamics model (learned or coded) Observation ->new particles (for initialization and reinitialization) Observation ->particle weights ( replace bayesian) Training with maximum log-likelihood Think of particle set as mixture of Gaussians.

Control Why do we need feedback control? Joint space and task space feedback? PD control and it’s link to dissipated mass-spring? How do you compute the threshold of critical damp?