<s>
The	O
normal	B-Algorithm
distributions	I-Algorithm
transform	I-Algorithm
(	O
NDT	O
)	O
is	O
a	O
point	B-Algorithm
cloud	I-Algorithm
registration	I-Algorithm
algorithm	O
introduced	O
by	O
Peter	O
Biber	O
and	O
Wolfgang	O
Straßer	O
in	O
2003	O
,	O
while	O
working	O
at	O
University	O
of	O
Tübingen	O
.	O
</s>
<s>
The	O
algorithm	O
registers	O
two	O
point	O
clouds	O
by	O
first	O
associating	O
a	O
piecewise	B-Algorithm
normal	O
distribution	O
to	O
the	O
first	O
point	O
cloud	O
,	O
that	O
gives	O
the	O
probability	O
of	O
sampling	O
a	O
point	O
belonging	O
to	O
the	O
cloud	O
at	O
a	O
given	O
spatial	O
coordinate	O
,	O
and	O
then	O
finding	O
a	O
transform	O
that	O
maps	O
the	O
second	O
point	O
cloud	O
to	O
the	O
first	O
by	O
maximising	O
the	O
likelihood	O
of	O
the	O
second	O
point	O
cloud	O
on	O
such	O
distribution	O
as	O
a	O
function	O
of	O
the	O
transform	O
parameters	O
.	O
</s>
<s>
Originally	O
introduced	O
for	O
2D	O
point	O
cloud	O
map	O
matching	O
in	O
simultaneous	B-Application
localization	I-Application
and	I-Application
mapping	I-Application
(	O
SLAM	O
)	O
and	O
relative	O
position	O
tracking	O
,	O
the	O
algorithm	O
was	O
extended	O
to	O
3D	O
point	O
clouds	O
and	O
has	O
wide	O
applications	O
in	O
computer	B-Application
vision	I-Application
and	O
robotics	O
.	O
</s>
<s>
The	O
loss	O
is	O
piecewise	B-Algorithm
continuous	I-Algorithm
and	O
differentiable	O
,	O
and	O
can	O
be	O
optimised	O
with	O
gradient-based	O
methods	O
(	O
in	O
the	O
original	O
formulation	O
,	O
the	O
authors	O
use	O
Newton	B-Algorithm
's	I-Algorithm
method	I-Algorithm
)	O
.	O
</s>
