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I'd like to extract "features" of an environment scanned with a 2D LiDAR.

I tried to create a temporary occupancy map to extract "corners" with the Harris Corner Detector. However LiDAR data is noisy, it creates false corners even after applying a Gaussian filter on the map. I wonder if there are more reliable algorithms for this.

Another method I tried is to use raw data output of the LiDAR, i.e. the $(r,\theta)$ vector, and calculate its first and second derivatives and choose "abrupt changes" as landmarks. This has a major drawback, it is harder to track landmarks when LiDAR position changes since $(r,\theta)$ vectors are totally different.

I appreciate any help. Thanks.

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In general you have to assign some probability distribution to your map or cells individually and update them iteratively.

In the very simple case you can just apply a low-pass filter to each of your cells. Like that: $p[t] = a*p[t-1] + (1-a)*I(occupied)$ where I is an indicator function which is set to 1 if current lidar measurement shows that cell is occupied and to 0 otherwise.

Better way is to look at SLAM methods like FastSLAM. Which use particles and kalman filters underneath. Comparing to the case I described above, Kalman filter will produce better estimates, because it is optimal in the sense that it minimises variances thus giving you as presice estimate of a mean as possible.

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