IEEE Robotics & Automation Magazine - September 2023 - 73

surfaces and edges. We chose surface
reconstruction using tangent estimation
over polynomial estimation as it was
less prone to introducing curvature into
flat surfaces.
"
CL HAS BEEN SHOWN
TO IMPROVE NN PERVOXEL
FILTERING
Subsequently, we employed voxel filtering
to address the homogenization of
the local density of points. First, the
voxel filter constructs a regular 3D grid
around the point cloud. The resulting
cubes are referred to as voxels. An efficient
implementation of the algorithm
loops through the point cloud, assigning
to each point the index of the Voxel it is located within.
The resulting cloud replaces all occupied voxels with the
centroid of the voxel or the point closest to the centroid.
Although more computationally expensive, we chose the
latter option to avoid introducing spatial errors at the cost
of slightly less uniformity. Both variants improve the spatial
distribution of points by removing the local clustering.
FORMANCE AND TRAINING
EFFICIENCY AND
TAKES INSPIRATION
FROM HOW HUMANS
LEARN.
„
p 1
CL
We argue that a curriculum, which trains with increasingly
partial representations, can enhance the performance on representations
typically observed during partial shape recognition.
Global shape descriptors, such as unique signatures of
histograms (USHs) [18], ESF [19], and CLUE [5], do not offer
such routes to conditioning a network for partial shape
recognition as the training of a single k-nearest neighbor or
support vector machine classifier (used in [5]) is not an iterative
process.
CL has been shown to improve NN performance and
training efficiency [12] and takes inspiration from how
humans learn. Initially, we train the network on easy examples
before bringing the focus to more challenging tasks.
In practice, this learning approach employs a scoring function,
which assigns to each sample a score based on its difficulty,
and a pacing function, which determines when more
complex samples are introduced to learning. This study
approaches the problem by synthesizing point clouds at difficulty
stages, defined as the sparsity of any specific object's
point cloud; we start with full coverage and swap them in the
training pipeline according to a pacing function, i.e., in our
case, at predetermined epochs.
To perform CL, we require a means to create samples of
different difficulties. As the goal is to improve the accuracy of
partial point cloud recognition, we hypothesize that exposing
the network to partial representations will achieve this. Therefore,
we score the full point clouds from our visual dataset as
the " easiest " and synthesize various degrees of partial, more
sparse point clouds from them to form our " harder " samples.
Let's consider the generation of a partial point cloud from our
full point cloud P. Here, we generalize for a given P as we
apply this process to any V Vi ! or T Tj !
for training and
evaluation purposes, respectively. We
first apply a partitioning function (, )K$c
to generate K disjoint partitions of P,
Pk (i.e., there are no common elements)
such that
PP. We implemented
= ' =1 k
K
k
such a function c using k-means clustering
in Euclidean space. Given a desired
cluster size m, i.e., the average number
of points belonging to a cluster-the
number of clusters, K, can be computed
as
T Tj ! respectively.
Finally, let (, )p$x
PP , where p [, ]01!
6m /iVm @ or /,njTm6
,
@ for V Vi ! and
be a partitioning
function that can be applied to a generic
point cloud P to subsample it into
is the proportion of sampled points.
We can implement x by randomly selecting p of the subsets
Pk and combining them into the partial point cloud
P .
Random selection was made by sampling a discrete uniform
distribution without replacement; the results of this selection
process can be seen in Figure 5 for the baseball point cloud
in case of p = 0.1, p = 0.4, and p = 0.7. In this manner, we
simulate many different pseudorandom partial representations
of an object from a single point cloud. The number
of possible different representations for each object we can
generate with this method is given by the binomial coefficient
^h
Furthermore, by lowering p, we can generate
K
6@
pK
.
sparser and sparser, i.e., harder and harder, samples for the
CL pipeline.
EXPERIMENTS
The objects chosen were everyday household items inspired
by the range of items used in previous Amazon picking challenges.
A total of 10 objects were used, i.e., O||
==L 10.
(a)
(b)
(c)
FIGURE 4. An MLS and a voxel filter applied to a tactile baseball
point cloud. (a) Raw, (b) MLS, and (c) MLS and voxel.
(a)
(b)
(c)
FIGURE 5. A k-means sampling: point clouds are divided into K
disjoint partitions. A partial sample of proportion p is generated
by the union of randomly-sampled Pk subsets. Here we depict the
cases of p = 0.1, p = 0.4, and p = 0.7. (a) p = 0.1, (b) p = 0.4, and
(c) p = 0.7.
SEPTEMBER 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE
73
IEEE Robotics & Automation Magazine - September 2023

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