Multi-beam lidar intensity calibration by interpolating learned response curve
Lidar intensity calibration from multi-beam lidar sensors uses calibration panels with known reflectance. The intensity response curves of each lidar beam are learned and modeled as a function of the known reflectivity, the transmission power level, and the distance. Contrary to the lidar equation, characterization of multi-beam lidar scanners commonly used for autonomous driving applications reveals that intensity does not fall-off according to the theoretically expected inverse distance-squared. Instead, a maximum intensity response is attained at a specific distance (focal distance). While the focal distance varies across beams, it is independent of the transmission power. Outside of the focal distance, distance intensity exhibits a sharp fall off. The intensity response curve of the lidar is well-approximated by a parametric form. Learned splines as functions of distance and power level determine the most likely mapping from raw data to surface reflectance along with a measure of uncertainty.
1. A computer-implemented method of calibrating multi-beam lidar intensity, comprising:
directing multi-beam lidar at a target comprising at least two panels of different reflectance standards covering a calibration range and measuring intensity response curves of reflectance data for each beam of the multi-beam lidar reflected by the at least two panels;
evaluating the intensity response curves of the reflectance data for each beam of the multi-beam lidar to compute a learned reflectance value from an intensity response of each beam and an associated confidence defined as a measure of a probability that a range and raw intensity pair is generated from a surface with reflectance equal to the learned reflectance value; and
from the computed learned reflectance value and associated confidence, determining continuous reflectance for each beam.
2. The method of claim 1 , further comprising characterizing the intensity response of each beam to determine at least one of: a dynamic range of the beam, a feasible power and reflectance combination, a focal distance estimation of the lidar, or an ideal placement of a parametric form to capture an intensity response curve.
3. The method of claim 1 , wherein the intensity response of reflectance data is measured for valid lidar returns from the target, where valid lidar returns are valid if a raw intensity return is within a dynamic range of the beam and the lidar return's range is within predetermined distances measured from the target.
4. The method of claim 1 , further comprising reporting the determined continuous reflectance along with a measure of uncertainty, where the uncertainty is computed using confidence values from curve fitting in combination with a sharpness of a sub-reflectance parabola peak.
5. The method of claim 1 , further comprising computing for each panel of the target a curve reflectance response and a confidence as a function of range and measured raw intensity of lidar reflected by each panel, where the curve reflectance response is a learned reflectance value during calibration and the confidence is a measure of a probability that the range and measured raw intensity of lidar reflected by each panel is generated from a surface with a reflectance equal to the curve reflectance response.
6. The method of claim 1 , wherein determining the continuous reflectance for each beam comprises fitting a parabola to the learned reflectance value in a vicinity of a value with a highest probability.
7. The method of claim 1 , wherein the intensity response curves of reflectance data for each beam of the multi-beam lidar reflected by the at least two panels at power (p) takes the form:
f
p
(
i
,
r
)
=
c
r
exp
(
-
log
i
-
l
2
σ
)
,
where:
i is a raw lidar intensity at given power p;
r is a distance to the target, and
c, l, and σ are parameters of a log-normal power law to be estimated.
8. The method of claim 7 , further comprising determining a calibrated intensity as a reflectance associated with a parametric form that minimizes a deviation between the intensity response curves of the reflectance data for each beam of the multi-beam lidar and raw lidar intensity measurements where for every intensity response curve given a ground truth reflectance ρ, a cost curve C is given by:
C
p
(
ρ
;
i
,
r
)
=
f
p
ρ
(
r
)
-
i
.
9. The method of claim 8 , further comprising calculating calibrated intensity ρ*, which is an intensity associated with a lowest cost of the cost curve C, namely:
p
*
=
argmin
ρ
C
p
(
ρ
;
i
,
r
)
.
10. The method of claim 9 , further comprising determining a final calibrated intensity value as a minima of a quadratic fit using a cost in a vicinity of an optimal value of a cost curve C.
11. The method of claim 10 , further comprising calculating a measure of uncertainty of the final calibrated intensity value as a ratio between a second-best cost and a best cost of the cost curve C.
12. A lidar system, comprising:
a target comprising at least two panels of different reflectance standards covering a calibration range;
a lidar device configured to direct multi-beam lidar at the target; and
a hardware processor programmed to perform operations comprising:
evaluating intensity response curves of reflectance data measured by the lidar device for each beam of the multi-beam lidar to compute a learned reflectance value from an intensity response of each beam and an associated confidence defined as a measure of a probability that a range and raw intensity pair is generated from a surface with reflectance equal to the learned reflectance value; and
from the computed learned reflectance value and associated confidence, determining continuous reflectance for each beam.
13. The lidar system of claim 12 , the operations further comprising characterizing the intensity response of each beam to determine at least one of: a dynamic range of the beam, a feasible power and reflectance combination, a focal distance estimation of the lidar, or an ideal placement of a parametric form to capture an intensity response curve.
14. The lidar system of claim 12 , wherein the intensity response of reflectance data is measured for valid lidar returns from the target, where valid lidar returns are valid if a raw intensity return is within a dynamic range of the beam and the lidar return's range is within predetermined distances measured from the target.
15. The lidar system of claim 12 , the operations further comprising reporting the determined continuous reflectance along with a measure of uncertainty, where the uncertainty is computed using confidence values from curve fitting in combination with a sharpness of a sub-reflectance parabola peak.
16. lidar system of claim 12 , the operations further comprising computing for each panel of the target a curve reflectance response and a confidence as a function of range and measured raw intensity of lidar reflected by each panel, where the curve reflectance response is a learned reflectance value during calibration and the confidence is a measure of a probability that the range and measured raw intensity of lidar reflected by each panel is generated from a surface with a reflectance equal to the curve reflectance response.
17. The lidar system of claim 12 , wherein determining the continuous reflectance for each beam comprises fitting a parabola to the learned reflectance value in a vicinity of a value with a highest probability.
18. The lidar system of claim 12 , wherein the intensity response curves of reflectance data for each beam of the multi-beam lidar reflected by the at least two panels at power (p) takes the form:
f
p
(
i
,
r
)
=
c
r
exp
(
-
log
i
-
l
2
σ
)
,
where:
i is a raw lidar intensity at given power p;
r is a range to the target, and
c, l, and σ are parameters of a log-normal power law to be estimated.
19. The lidar system of claim 18 , the operations further comprising determining a calibrated intensity as a reflectance associated with a parametric form that minimizes a deviation between the intensity response curves of the reflectance data for each beam of the multi-beam lidar and raw lidar intensity measurements where for every intensity response curve given a ground truth reflectance ρ, a cost curve C is given by:
C
p
(
p
,
i
,
r
)
=
❘
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f
p
p
(
r
)
-
i
❘
"\[RightBracketingBar]"
,