Python script to visualize and plot geospatial position uncertainty in a mathematically rigorous manner. We assume that all events to be plotted are of the same type, so we are concerned with the scenario of whether event1, event2, or event3 occurred at location (x,y). Each event has a position (x,y), as well as an uncertainty associated with each coordinate (sigma_x, sigma_y).

Event locations are often reported via (latitude, longitude) as well as uncertainty in position. We adopt the frequent assumption that errors are Gaussian in nature. Positional uncertainty can be represented by a positional ellipse with width (sigma_x) and height (sigma_y) represented by uncertainty in longitude and latitude, respectively. The eye is typically drawn to large objects (which are less certain in this case), so we can partially offset this effect by scaling opacity inversely with uncertainty, as shown below:

The above plot cannot convey the joint likelihood of an event at each position. The heat map below is essentially a gaussian mixture model, and displays the joint probability that an event has occurred at a given grid square.

We can use this probability map to more accurately convey positional uncertainty by assigning the alpha channel (i.e. opacity) as the probability map. The opacity in the final image below is proportional to the probability that an event occured at that location, and more accurately conveys the true uncertainty in event location.

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geospatial_uncertainty.py

The python script generates a number of random points, computes the combined probability map, and visualizes location uncertainty by plotting the points on an image that serves as a proxy for a map.

dependencies:

cv2
numpy
matplotlib

To execute:

cd /path/to/geospatial_uncertainty_vis
# update line 15 with the correct '/path/to/geospatial_uncertainty_vis'
python geospatial_uncertainty.py
# output is akin to the plot below: