Physics-based modeling of rain and snow effects in virtual LiDAR
A method of modeling precipitation effects in a virtual LiDAR sensor, the method includes receiving a point cloud model representing three-dimensional coordinates of objects as the objects would be sensed by a LiDAR sensor. The method further includes generating a stochastic model of rainfall or snowfall, estimating a probability that a light source from the LiDAR sensor hits a raindrop or a snowflake based on the stochastic model, and modifying the received point cloud model to include effects induced by the modeled rainfall or snowfall based on the probability that light sourced from the LiDAR sensor encounters a raindrop or a snowflake.
1 . A method of modeling precipitation effects in a virtual LiDAR sensor, the method comprising:
receiving a point cloud model representing three-dimensional coordinates of objects as the objects would be sensed by a LiDAR sensor;
generating a stochastic model of rainfall or snowfall;
estimating a probability that a light source from the LiDAR sensor hits a raindrop or a snowflake based on the stochastic model, the probability P being determined using a stochastic formulation given by:
P =(( Ar/Aro )/( V/Vo ))·( D/Do )·(π R 2 /Dm 2 ),
where Ar/Aro is a normalized drop arrival rate, V/Vo is a normalized drop velocity, D/Do is a normalized laser beam diameter, R is a droplet radius, and Dm is a length of a cubic volume in a direction parallel to the laser beam;
identifying whether the estimated probability is above a threshold; and
modifying the received point cloud model to include effects induced by the modeled rainfall or snowfall in response to the estimated probability, including performing a physics-based calculation of reflection and backscatter of incident laser light interacting with a raindrop when the estimated probability is above the threshold, the physics-based calculation comprising determining an intensity after scattering i(j,p) according to:
i ( j,p )=( R 2 /r 2 )· i 0 ·ε( j,p ) D,
where i 0 is an incident intensity, r is a distance between the droplet and a LiDAR receiver, and ε(j,p)D is a scattering coefficient defined by ε(j,p)D=f(θ, m, p), with θ being a scattering angle, m being a refraction index, and p being a path such that the modification reflects the likelihood that light sourced from the LiDAR sensor encounters a raindrop or a snowflake.
2 . The method of claim 1 , wherein the step of modifying the point cloud model further includes modeling effects of attenuation of light sourced from the LiDAR sensor or returned to the LiDAR sensor due to a raindrop or a snowflake.
3 . The method of claim 1 , wherein the step of modifying the point cloud model further includes modeling backscattering intensity from raindrops or snowflakes hit by light sourced from the LiDAR sensor.
4 . A virtual LiDAR sensor comprising a one or more modules, the one or modules configured to:
receive a point cloud model representing three-dimensional coordinates of objects as the objects would be sensed by a LiDAR sensor;
generate a stochastic model of rainfall or snowfall;
estimate a probability that a light source from the LiDAR sensor hits a raindrop or a snowflake based on the stochastic model, the probability P being determined using a stochastic formulation given by:
P =(( Ar/Aro )/( V/Vo ))·( D/Do )·(π R 2 /Dm 2 ),
where Ar/Aro is a normalized drop arrival rate, V/Vo is a normalized drop velocity, D/Do is a normalized laser beam diameter, R is a droplet radius, and Dm is a length of a cubic volume in a direction parallel to the laser beam;
identifying whether the estimated probability is above a threshold; and
modify the received point cloud model to include effects induced by the modeled rainfall or snowfall in response to the estimated probability, including performing a physics-based calculation of reflection and backscatter of incident laser light interacting with a raindrop when the estimated probability is above the threshold, the physics-based calculation comprising determining an intensity after scattering i(j,p) according to:
i ( j,p )=( R 2 /r 2 )· i 0 ·ε( j,p ) D,
where i 0 is an incident intensity, r is a distance between the droplet and a LiDAR receiver, and ε(j,p)D is a scattering coefficient defined by ε(j,p)D=f(θ, m, p), with θ being a scattering angle, m being a refraction index, and p being a path such that the modification reflects the likelihood that light sourced from the LiDAR sensor encounters a raindrop or a snowflake.
5 . The virtual LiDAR sensor of claim 4 , wherein the one or modules are further configured to modify the received point cloud model to include modeled effects of attenuation of light sourced from the LiDAR sensor or returned to the LiDAR sensor due to a raindrop or a snowflake.
6 . The virtual LiDAR sensor of claim 4 , wherein the one or modules are further configured to modify the received point cloud model to include modeled effects of backscattering intensity from raindrops or snowflakes hit by light sourced from the LiDAR sensor.
7 . A vehicle system comprising:
a vehicle;
a LiDAR sensor mounted to the vehicle, the LiDAR sensor configured to provide raw point cloud information;
a virtual LiDAR sensor configured to receive the raw point cloud information and to generate a modified point cloud that incorporates simulated effects of precipitation, the virtual LiDAR sensor further configured to:
generate a stochastic model of rainfall or snowfall;
estimate a probability that a light source from the LiDAR sensor hits a raindrop or a snowflake based on the stochastic model, the probability P being determined using a stochastic formulation given by:
P =(( Ar/Aro )/( V/Vo ))·( D/Do )·(π R 2 /Dm 2 ),
where Ar/Aro is a normalized drop arrival rate, V/Vo is a normalized drop velocity, D/Do is a normalized laser beam diameter, R is a droplet radius, and Dm is a length of a cubic volume in a direction parallel to the laser beam;
identifying whether the estimated probability is above a threshold; and
modify the received point cloud model to include effects induced by the modeled rainfall or snowfall in response to the estimated probability, including performing a physics-based calculation of reflection and backscatter of incident laser light interacting with a raindrop when the estimated probability is above the threshold, the physics-based calculation comprising determining an intensity after scattering i(j,p) according to:
i ( j,p )=( R 2 /r 2 )· i 0 ·ε( j,p ) D,
where i 0 is an incident intensity, r is a distance between the droplet and a LiDAR receiver, and ε(j,p)D is a scattering coefficient defined by ε(j,p)D=f(θ, m, p), with θ being a scattering angle, m being a refraction index, and p being a path, such that the modification reflects the likelihood that light sourced from the LiDAR sensor encounters a raindrop or a snowflake.
8 . The vehicle system of claim 7 , wherein the virtual LiDAR sensor is further configured to modify the received point cloud model to include modeled effects of attenuation of light sourced from the LiDAR sensor or returned to the LiDAR sensor due to a raindrop or a snowflake.
9 . The vehicle system of claim 7 , wherein the virtual LiDAR sensor is further configured to modify the received point cloud model to include modeled effects of backscattering intensity from raindrops or snowflakes hit by light sourced from the LiDAR sensor.