IEEE Computational Intelligence Magazine - November 2023 - 71

FIGURE 5. The proposed decoder architectures: (a) a fully connected decoder, (b) a
deconvolution-based decoder, and (c) a hierarchical fully connected decoder.
subsequent transformation estimation
process, and the reconstructed source
point cloud needs to be restored multiple
times by iterating the current source
point cloud and the estimated transformation.
For each iteration i, a transformation
GðiÞ is applied to the source
point cloud, and the transformed source
point cloud and target point cloud are
used as the new inputs of CFNet. After
n iterations, all the poses in each iteration
are combined to obtain the overall
transformation Gest 2 SEð3Þ between
the original source point clouds and the
target point clouds
regression network is used to regress the
rotation and translation parameters
separately. After fusing the unique features
Fð~PÞ and FðQÞ, fully connected
layers are stacked to generate the hybrid
features Fr and Ft for rotation and translation
in feature interaction module.
The dual branch regression network is
utilized to return the rotation and translation
parameters. The rotation regression
branch takes all global features as
inputs and generates a 4D vector, which
represents the 3D rotation R in the
form of a quaternion, q 2 R4. Furthermore,
inspired by [19], instead of
directly regressing the translation vector
t 2 R3, the proposed method generates
two 3D vectors based on the translation
regression branch, representing the
coordinates ofthe two significant points
of the source and target point clouds,
and then computes the difference
between them as t. In each iteration,
the transformation fq; tg is
q ¼frðcat½Frð~PÞ; FrðQÞ; Ftð~PÞ; FtðQÞÞ;
(5aÞ
(5b)
t ¼ CQC~P;
where,
C~P ¼ftðcat½Frð~PÞ; Ftð~PÞ; FtðQÞÞ; (6aÞ
CQ ¼ftðcat½FrðQÞ; FtðQÞ; Ftð~PÞÞ: (6b)
The functionsfr andft represent rotation
and translation networks, and perform
the transformations: (256 4 ! 512 !
128 ! 64 ! 4; q 2 R4) and (256 3 !
512 ! 128 ! 64 ! 3; t 2 R3), respectively.
Furthermore, the vectors C~P and
CQ represent the salient point coordinates
ofthe transformed source point cloud and
the target point cloud, respectively.
E. Fully Connected Decoder
In contrast to the function of the
encoder, a decoder consisting of fully
connected layers is used to reconstruct
the input. Overall, the encoder generates
different features for the two point
clouds P and Q, and the decoder
restores the different features back to
the corresponding point cloud copy.
This method guarantees the success of
unsupervised learning when training a
salient feature extractor for registration
problems and provides good initial conditions
for point cloud registration. In
addition, to verify the effects of the
decoder on the encoder's ability to
extract features and on the final registration
quality, three decoder networks are
utilized: a fully connected decoder, a
deconvolution-based decoder, and a
hierarchical fully connected decoder, as
shown in Figure 5.
Specifically, after the encoder module
generates the salient features, the
decoder module restores the features
back to the point clouds. Different from
the traditional reconstruction process,
the proposed CFNet performs various
tasks on the input source point cloud
and target point cloud during the recovery
process. The reconstructed target
point cloud only needs to be restored
once, which is helpful for the
Gest ¼ GðnÞGðn 1Þ Gð1Þ:
(7)
Theoretically, the greater the number
of iterations, i.e., the larger n,the more
accurate the registration is within the
error-aware range. n is 8 in PCRNet [30]
IEEE Computational Intelligence Magazine - November 2023

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - November 2023
