To speed up the Observation Likelihood Model, we create a rasterized lookup table (parametrized on x, y) of the probability space.
TODO: paper does not parameterize on d\theta, but are we supposed to?
Representation
Full matrix (array of arrays)
Sparse matrix (DOK: unordered map)
Easier to represent negative indices.
Harder to optimize? (hierarchical lookups)
Higher individual lookup overhead.
tuple construction
map lookup
Model Evaluation
Approach 1
Evaluate the model at the mean of each pixel.
Approach 2
Integrate the model over the limits of each pixel.
Negative Indices
The (dx, dy) domain contains negative coordinates. How do we use/transform these coordinates in the image space if we're representing it using a matrix?
Image Space Coordinate Transform
Images generally use a left-handed coordinate system (negative cross product), but the robot uses a right-handed coordinate system. We need to transform coordinates between the two spaces.
To speed up the Observation Likelihood Model, we create a rasterized lookup table (parametrized on x, y) of the probability space.
TODO: paper does not parameterize on d\theta, but are we supposed to?
Representation
Model Evaluation
Approach 1
Evaluate the model at the mean of each pixel.
Approach 2
Integrate the model over the limits of each pixel.
Negative Indices
The (dx, dy) domain contains negative coordinates. How do we use/transform these coordinates in the image space if we're representing it using a matrix?
Image Space Coordinate Transform
Images generally use a left-handed coordinate system (negative cross product), but the robot uses a right-handed coordinate system. We need to transform coordinates between the two spaces.