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Random Light Curtain Demo

Current instructions:

Single-click on canvas to start drawing.




Instructions

  1. Draw a polygon.
    • Single click on canvas to start drawing.
    • Single click to add edge and continue drawing.
    • Double-click to close polygon.
  2. Move/rotate/resize polygon.
    3. Draw a polygon
    Move/rotate/resize polygon
  3. Click .
  4. Click to visualize random curtains and hits.
    Note: This can be pressed anytime during the demo.
  5. Click to show and to hide analysis report.
  6. Click to start all over again!

Probabilistic Safety Guarantees using Dynamic Programming

Forward pass
Sampling a random curtain
Backward pass
Computing detection probability using DP

The light curtain constraint graph encodes the physical constraints of the light curtain device and can be used to compute feasible light curtain profiles. We extend the constraint graph to incorporate acceleration constraints of the device. We propose a mechanism to sample light curtains from the constraint graph by defining a transition probability distribution over neighboring nodes. Then, a random light curtain is simply a random walk from the leftmost to the rightmost camera ray under these transition probabilities. Importantly, we perform dynamic programming on the constraint graph to provide analytic estimates of the probability of a random curtain detecting any user-specified object!


Dynamic programming equation


For each node in the graph, we compute the detection probability of a random light curtain starting from that node and ending on the rightmost ray. The solutions to these sub-problems satisfy a recursive relationship shown by the dynamic programming equation above. This recursive expression can be used to efficiently and analytically compute the detection probability in a single backward pass through the graph.