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Point Cloud Matching based on 3D Self-Similarity
Jing Huang
University of Southern California
Los Angeles, CA 90089
huang10@usc.edu
Suya You
University of Southern California
Los Angeles, CA 90089
suya.you@usc.edu
Abstract
Point cloud is one of the primitive representations of 3D
data nowadays. Despite that much work has been done in
2D image matching, matching 3D points achieved from dif-
ferent perspective or at different time remains to be a chal-
lenging problem. This paper proposes a 3D local descriptor
based on 3D self-similarities. We not only extend the con-
cept of 2D self-similarity [1] to the 3D space, but also estab-
lish the similarity measurement based on the combination of
geometric and photometric information. The matching pro-
cess is fully automatic i.e. needs no manually selected land
marks. The results on the LiDAR and model data sets show
that our method has robust performance on 3D data under
various transformations and noises.
1. Introduction
Matching is a process of establishing precise correspon-
dences between two or more datasets acquired, for exam-
ple, at different times, from different aspects or even from
different sensors or platforms. This paper addresses the
challenging problem of finding precise point-to-point cor-
respondences between two 3D point cloud data. This is a
key step for many tasks including multi-view scans registra-
tion, data fusion, 3D modeling, 3D object recognition and
3D data retrieval.
Figure 1 shows an example of point cloud data that were
acquired by airborne LiDAR sensor. The two point clouds
represent two LiDAR scans of the same area (downtown
Vancouver) acquired at different times and from different
viewpoints. The goal is to find precise matches for the
points in the overlapping areas of the two point clouds.
Matching of point clouds is challenging in that there are
usually enormous number of 3D points and the coordinate
system can vary in terms of translation, 3D-rotation and
scale. Point positions are generally not coincident; noises
and occlusions are common due to incomplete scans; and
objects are attached to each other and/or the ground. Fur-
thermore, many data may not contain any photometric in-
Figure 1. Two point clouds represent two LiDAR scans of the same
area captured at different times and from different aspects. The
proposed method can find precise matches for the points in the
overlapping area of the two point clouds.
formation such as intensity other than point positions.
Given the problems above, matching methods that solely
rely on photometric properties will fail and conventional
techniques or simple extensions of 2D methods are no
longer feasible. The unique nature of point clouds requires
methods and strategies different from those for 2D images.
In real applications, most point clouds are a set of ge-
ometric points representing external surfaces or shapes of
3D objects. We therefore treat the geometry as the essen-
tial information. We need a powerful descriptor as a way to
capture geometric arrangements of points, surfaces and ob-
jects. The descriptor should be invariant to translation, scal-
ing and rotation. In addition, the high dimensional structure
of 3D points must be collapsed into something manageable.
This paper presents a novel technique specifically de-
signed for matching of 3D point clouds. Particularly, our
approach is based on the concept of self-similarity. Self-
similarity is an attractive image property that has recently
found its way in matching in the form of local self-similarity
descriptors [1]. It captures the internal geometric layout of
local patterns in a level of abstraction. Locations in im-
age with self-similarity structure of a local pattern are dis-
tinguishable from locations in their neighbors, which can
greatly facilitate matching process. Several works have
demonstrated the value of self-similarity for image match-
ing and related applications [14] [15]. From a totally new
perspective, we design a descriptor that can efficiently cap-
1
ture distinctive geometric signatures embedded in point
clouds. The resulting 3D self-similarity descriptor is com-
pact and view/scale-independent, and hence can produce
highly efficient feature representation. We apply the devel-
oped descriptor to build a complete feature-based match-
ing system for high performance matching between point
clouds.
2. Related Work
2.1. 3D Matching
3D data matching has recently been widely addressed
in both computer vision and graphic communities. A va-
riety of methods have been proposed, but the approaches
based on local feature descriptors demonstrate superior per-
formance in terms of accuracy and robustness [3] [7]. In
local feature-based approach, the original data are trans-
formed into a set of distinctive local features, each repre-
senting a quasi-independent salient region within the scene.
The features are then characterized with robust descriptors
containing local surface properties that are supposedly re-
peatable and distinctive for matching. Finally, registration
methods such as the famous Iterative Closest Point (ICP)
[5], as well as its variants, could be employed to figure out
the global arrangement.
Spin image is a well-known feature descriptor for 3D
surface representation and matching [3]. One key element
of spin image generation is the oriented point, or 3D surface
point with an associated direction. Once the oriented point
is defined, the surrounding cylindrical region is compressed
to generate the spin image as the 2D histogram of number
of points lying in different distance grids. By using local
object-oriented coordinate system, the spin image descrip-
tor is view and scale independent. Several variations of spin
image have been suggested. For example, [18] proposed a
spherical spin image for 3D object recognition, which can
capture the equivalence classes of spin images derived from
linear correlation coefficients.
Heat Kernel Signature (HKS) proposed in [7] is a type of
shape descriptor targeting for matching objects under non-
rigid transformation. The idea of HKS is to make use of
the heat diffusion process on the shape to generate intrin-
sic local geometry descriptor. It is shown that HKS can
capture much of the information contained in the heat ker-
nel and characterize the shapes up to isometry. Further, [8]
improved HKS to achieve scale-invariant, and developed a
HKS local descriptor that can be used in the bag-of-features
framework for shape retrieval in the presence of a variety of
non-rigid transformations.
Many works also attempt to generalize from 2D to 3D,
such as 3D SURF [6] extended from SURF [4] and 3D
Shape context [19] extended from 2D Shape Context [2].
A detailed performance evaluation and benchmark on 3D
shape matching were reported in [11] that simulates the fea-
ture detection, description and matching stages of feature-
based matching and recognition algorithms. The bench-
mark tests the performance of shape feature detectors and
descriptors under a wide variety of conditions. We also use
the benchmark to test and evaluate our proposed approach.
Recently, the concept of self-similarity has drawn much
attention and been successfully applied for image matching
and object recognition. Shechtman and Irani [1] proposed
the first algorithm that explicitly employs self-similarity to
form a descriptor for image matching. They used the in-
tensity correlation computed in local region as resemblance
to generate the local descriptor. Later on, several exten-
sions and varieties were proposed. For example, Chat-
field et al. [14] combined a local self-similarity descrip-
tor with the bag-of-words framework for image retrieval of
deformable shape classes; Maver [15] used the local self-
similarity measurement for interest point detection; Huang
et al. [17] proposed a 2D self-similarity descriptor for mul-
timodal image matching, with different definitions of self-
similarity evaluated.
This paper extend the self-similarity framework to
matching of 3D point clouds. We develop a new 3D lo-
cal feature descriptor that can efficiently characterizes dis-
tinctive signatures of surfaces embedded in point clouds,
hence can produce high performance matching. To the best
of our knowledge, we are the first one to introduce the self-
similarity to the area of point cloud matching.
The remainder of the paper describes the details of our
proposed approach and implementations. We also present
the results of our analysis and experiments.
3. Point clouds and self-similarity
Originated from fractals and topological geometry, self-
similarity is the property held by those parts of a data or ob-
ject that resemble themselves in comparison to other parts
of the data. The resemblance can be photometric properties,
geometric properties or their combinations.
Photometric properties such as color, intensity or texture
are useful and necessary to measure the similarity between
imagery data, however, they are no longer as reliable on
point cloud data. In many situations, the data may only
contain point positions without any photometric informa-
tion. Therefore, geometric properties such as surface nor-
mals and curvatures are treated as the essential information
for point cloud data.
Particularly, we found that surface normal is the most ef-
fective geometric property that enables human visual per-
ception to distinguish local surfaces or shapes in point
clouds. Normal similarity has shown sufficiently robust to
a wide range of variations that occur within disparate ob-
ject classes. Furthermore, a point and its normal vector can
form a simple local coordinate system that can be used to
2
(a) (b) (c) (d) (e)
Figure 2. Illustration for self-similarities. Column (a) are three point clouds of the same object and (b) are their normal distributions.
There are many noises in the 2nd point cloud, which lead to quite different normals from the other two. However, the 2nd point cloud
shares similar intensity distribution as the 1st point cloud, which ensures that their self-similarity surface (c), quantized bins (d) and thus
descriptors (e) are similar to each other. On the other hand, while the intensity distribution of the 3rd point cloud is different from the
other two, it shares similar normals as the 1st point cloud (3rd row vs. 1st row in column (b)), which again ensures that their self-similarity
surface, quantized bins and descriptors are similar to each other.
generate view/scale-independent descriptor.
Curvature is another important geometric property that
should be considered in similarity measurement. The cur-
vature illustrates the changing rate of tangents. Curved sur-
faces always have varying normal, yet many natural shapes
such as sphere and cylinder preserve the curvature consis-
tency. Therefore, we incorporate the curvature in similar-
ity measurement to characterize local geometry of surface.
Since there are many possible directions of curvature in 3D,
we consider the direction in which the curvature is maxi-
mized, i.e. the principal curvature, to keep its uniqueness.
We also consider the photometric information in our al-
gorithm development to generalize the problem. We assume
the case that both the photometric and geometric informa-
tion are available in the dataset. We propose to use both the
properties as similarity measurements and combine them
under a unified framework.
4. 3D Self-similarity descriptor
Given an interest point and its local region, there are
two major steps to construct the descriptor: (1) generat-
ing the self-similarity surface using the defined similarity
measurements, and (2) quantizing the self-similarity surface
in a rotation-invariant manner. In this work, we consider
similarity measurements on surface normal, curvature, and
photometric properties. Once the similarity measurements
are defined, the local region is converted to self-similarity
surface centered at the interest point, with multiple/united
property similarity at each point. We can then construct the
3D local self-similarity descriptors to generate signatures of
surfaces embedded in the point cloud.
4.1. Generating self-similarity surface
Assume there are property functions f
1
, f
2
, . . . f
n
de-
fined on a point set X, which map any point x ∈ X to
property vectors f
1
(x), f
2
(x), . . . f
n
(x). For 2D images,
the property can be intensities, colors, gradients or textures.
In our 3D situation, the property set can further include nor-
mals and curvatures, besides intensities/colors.
For each property function f that has definition on two
points x and y, we can further induce a pointwise similar-
ity function s(x, y, f). Then, the united similarity can be
defined as the combination of the similarity functions of all
the properties. Figure 2 gives the intuition of how combined
self-similarity would work for different data.
4.1.1 Normal similarity
The normal gives the most direct description of the shape
information, especially for the surface model. One of the
most significant characteristics of the normal distribution is
the continuity, which means the normal similarity is usually
positively correlated to the distance between the two points.
However, any non-trivial shape could disturb the distribu-
3
Figure 3. Self-similarity surface of normals. The brighter a point
is, the more similar its normal is to the normal at the center point.
tion of normals, which gives the descriptive power of the
normal similarity.
We use the method described in [13] to extract the nor-
mals. Figure 2(b) are examples of normal distributions.
The property function of normal is a 3D function
f
normal
(x) = ⃗n(x). Assume that the normals are normal-
ized i.e. ∥⃗n(x)∥ = 1, we can define the normal similarity
between two points x and y as the angle between the nor-
mals, as formula 1 suggests.
s(x, y , f
normal
) = [π − cos
−1
(f
normal
(x) · f
normal
(y))]/π
= [π − cos
−1
(⃗n(x) · ⃗n(y))]/π.
(1)
It’s easy to see that when the angle is 0, the function re-
turns 1; whereas the angle is π, i.e. the normals are opposite
to each other, the function returns 0.
We should be careful that a locally stable normal estima-
tion method is needed here to ensure that the directions of
normals are consistent with each other, because flipping one
normal could lead to the opposite result of the function.
Figure 3 shows the visualization of the self-similarity
surface of normals of one key point.
4.1.2 Curvature similarity
The curvature illustrates the changing rate of tangents.
Curved surfaces always have varying normals, yet many
natural shapes such as sphere and cylinder preserve the cur-
vature consistency. Therefore, it’s worthwhile to incorpo-
rate the curvature information in the measurement of sim-
ilarity. Since there are infinite possible directions of cur-
vature in 3D, we only consider the direction in which the
curvature is maximized, i.e. the principal curvature.
The principal curvature direction can be approximated as
the eigen vector corresponding to the largest eigen value of
the covariance matrix C of normals projected on the tangent
plane. The property function of curvature is defined as a
single-value function
f
curv
(x) =
1
N
arg max(λ|det(C − λI) = 0), (2)
where N is the number of points (normals) taken into ac-
count in the neighborhood so that values are scaled to the
range from 0 to 1 (In practice this value is typically less
than 0.7). We then define the curvature similarity between
two points x and y as the absolute difference between them:
s(x, y , f
curv
) = 1 − |f
curv
(x) − f
curv
(y)|.
(3)
Again, the function returns 1 when the curvature values are
similar, and returns 0 when they are different.
4.1.3 Photometric similarity
Photometric information is an important clue for our un-
derstanding of the world. For example, when we look at a
gray image, we can infer the 3D structure through the ob-
servation of changes in intensity. Some point clouds, be-
sides point positions, also contain certain photometric infor-
mation such as intensity or any reflective values generated
by sensors. Such information is a combinational result of
geometric structure, material, lighting and even shadows.
While they are not as generally reliable as geometric in-
formation for point clouds, they can be helpful in specific
situations and we also incorporated them in the similarity
measurement. We try to use the photometric similarity to
model this complicated situation as it is invariant to lighting
to some extent, given the similar material properties.
In our current framework, the property function of pho-
tometry is a single-value function f
photometry
(x) = I(x)
where I(x) is the intensity function. With the range nor-
malized to [0, 1], we can define the photometric similarity
between two points x and y as their absolute difference:
s(x, y , f
photometry
) = 1 − |f
photometry
(x) − f
photometry
(y)|
= 1 − |I(x) − I(y)|.
(4)
4.1.4 United Similarity
Given a set of properties, we need to combine them to mea-
sure the united similarity:
s(x, y ) =
p∈PropertySet
w
p
· s(x, y, f
p
). (5)
The weights w
p
∈ [0, 1] can be experimentally determined
according to availability and contribution of each consid-
ered property. For example, when dealing with point clouds
converted from mesh models, we will let w
photometry
= 0
since there’s no intensity information in the data. Another
example is when we have known that there are many noise
points in the data, which makes the curvature estimation
unstable, we can reduce its weight accordingly. In gen-
eral cases, the equal weights or weights of 2:1:1 (with nor-
mals dominating) are good enough without prior knowl-
edge. Learning the best weights from different data sets,
however, could be an interesting topic.
4
Once the similarity measurements are defined, construc-
tion of self-similarity surface is straightforward. First, the
point cloud is converted to 3D positions with the defined
properties. Then, the self-similarity surface is constructed
by comparing each point’s united similarity to that of sur-
rounding points within a local spherical volume. The radius
of the sphere is k times the detected scale at which the prin-
cipal curvature reaches its local maxima. The choice of the
size can determine whether the algorithm is performed at
a local region or more like a global region. We found by
experiments that the performance is the best when k ≈ 4.
4.2. Forming the Descriptor
Our approach is trying to make full use of all kinds of
geometric information on the point cloud, mainly including
the normal and curvature, which can be seen as the first-
order and the second-order differential quantities. Since we
are facing discrete data, certain approximations are needed
for calculation. Such approximations have been provided
by open-source libraries such as Point Cloud Library (PCL).
The rotation invariance is achieved by using local refer-
ence system (Fig. 4) of each given key point: the origin
is placed at the key point; the z-axis is the direction of the
normal; the x-axis is the direction of the principal curvature;
and the y-axis is the cross product of z and x directions.
In order to reduce the dimension as well as bearing small
distortion of the data, we quantize the correlation space into
bins. In our experiments we have #Bin(r) = 6 radial bins,
#Bin(ϕ) = 8 bins in longitude ϕ and #Bin (θ) = 6 bins
in latitude θ, and replace the values in each cell with the
average similarity value of all points in the cell, resulting in
a descriptor of 6*8*6 = 288 dimensions (Fig. 4).
The index of each dimension can be represented by
a triple (Index (r), Index (ϕ), Index (θ)), ranging from
(0,0,0) to (5,7,5). Each index component can be calculated
in the following way:
Index (r) = ⌊#Bin (r ) ·
r
scale
⌋
Index (ϕ) = ⌊#Bin(ϕ) ·
ϕ
2π
⌋
Index (θ) = ⌊#Bin (θ ) ·
θ
π
⌋
(6)
In the final step, the descriptor is normalized by scaling
the dimensions with the maximum value to be 1.
5. Point Cloud Matching
We apply the developed descriptor to build a complete
feature-based point cloud matching system. Point clouds
often contain hundreds of millions of points, yielding a
large high dimensional feature space to search, index and
match. So selection of the most distinctive and repeatable
features for matching is a necessity.
Figure 4. Illustration of the local reference frame and quantization.
5.1. Multi-scale feature detector
Feature, or key point extraction is a necessary step be-
fore the calculation of 3D descriptor because (1) 3D data
always have too many points to calculate the descriptor on;
(2) distinctive and repeatable features will largely enhance
the accuracy of matching. There are many feature detec-
tion methods evaluated in [9]. Our approach detects salient
features with a multi-scale detector, where 3D peaks are de-
tected in both scale-space and spatial-space. Inspired by
[10], we propose to extract key points based on the local
Maxima of Principle Curvature (MoPC), which provide rel-
atively stable interest regions compared to a range of other
interest point detectors. Note that different from [20], where
the scale-invariant curvature is measured, we make use of
the variation of the curvature to extract the specific scale.
The first step is setting up several layers of different
scales. Assume the diameter of the input point cloud is d.
We choose one tenth of d as the largest scale, and one sixti-
eth of d as the minimum scale. The intermediate scales are
interpolated so that the ratios between them are constant.
Next, for each point p and scale s, we calculate the prin-
cipal curvature using points that lie within s units from p.
The calculation process is discussed in 4.1.2.
Finally, if the principal curvature value of point p at
scale s is larger than the value of the same point p at ad-
jacent scales and the value of all points within one third of s
units from p at scale s, meaning that the principal curvature
reaches local maxima across both scale and local neighbor-
hood of p, then p is added to the key point set with scale s.
Note that the same point could appear in multiple scales.
Figure 5 shows the feature points detected in the model.
5.2. Matching criteria
In case there can be multiple regions (and thus descrip-
tors) that are similar to each other, we follow the Nearest
Neighbor Distance Ratio (NNDR) method i.e. matching a
key point in cloud X to a key point in cloud Y if and only if
dist (x, y
1
)
dist (x, y
2
)
< threshold , (7)
where y
1
is the nearest neighbor of x in point cloud Y and
y
2
is the 2nd nearest neighbor of x in point cloud Y (in
5
Figure 5. Detected salient features (highlighted) with the proposed
multi-scale detector. Different sizes/colors of balls indicate differ-
ent scales at which the key points are detected. These features turn
out to be distinctive, repeatable and compact for matching.
the feature space). Balancing between the number of true
positives and false positives, the threshold is typically set to
be 0.75 in our experiments.
5.3. Outlier Removal
After a set of local matches are selected, we can per-
form outlier removal using global constraints. If it’s known
that there are only rigid body and scale transformations, a
3D RANSAC algorithm is applied to determine the trans-
formation that allow maximum number of matches to fit in.
Figure 10 (b) shows the filtered result for Fig. 10 (a). In
the future, variants of L
1
norm instead of L
2
norm could
be considered as penalty function, which has been proved
superior in optical flow methods.
6. Experimental Results and Evaluation
The proposed approach have been extensively tested and
evaluated using various datasets including both synthetic
data from standard benchmarks and our own datasets, cov-
ering a wide variety of objects and conditions. We evaluated
the effectiveness of our approach in the terms of distinctive-
ness, robustness and invariance.
6.1. SHREC data
We use the SHREC feature descriptor benchmark [11]
[12] and convert the mesh model to point cloud by keep-
ing only the vertices for our test. This benchmark includes
shapes with a variety of transformations such as holes, mi-
cro holes, scale, local scale, noise, shot noise, topology,
sampling and rasterization (Fig. 6).
Table 1 and 2 show the average normalized L
2
error of
SS-Normal descriptors and SS-Curvature descriptors at cor-
responding points detected by MoPC. Note that only the
transformations with clear ground truth are compared here
i.e. the isometry shape is used as the comparing template.
Given the set of detected features F (X) and F (Y ), the de-
scriptor quality is the calculated at corresponding points x
k
Transform.
Strength
1 ≤ 2 ≤ 3 ≤ 4 ≤ 5
Holes 0.11 0.22 0.33 0.45 0.52
Local scale 0.40 0.58 0.67 0.77 0.83
Sampling 0.31 0.46 0.57 0.67 0.81
Noise 0.58 0.65 0.70 0.74 0.77
Shot noise 0.13 0.23 0.28 0.32 0.35
Average 0.34 0.45 0.53 0.60 0.67
Table 1. Robustness of Normal Self-Similarity descriptor based on
features detected by MoPC (average L
2
distance between descrip-
tors at corresponding points). Average number of points: 518
Transform.
Strength
1 ≤ 2 ≤ 3 ≤ 4 ≤ 5
Holes 0.10 0.21 0.31 0.42 0.49
Local scale 0.38 0.56 0.65 0.75 0.81
Sampling 0.44 0.55 0.63 0.71 0.87
Noise 0.55 0.62 0.67 0.72 0.75
Shot noise 0.13 0.22 0.27 0.31 0.33
Average 0.32 0.43 0.51 0.58 0.65
Table 2. Robustness of Curvature Self-Similarity descriptor based
on features detected by MoPC (average L
2
distance between de-
scriptors at corresponding points). Average number of points: 518
(with descriptor f
k
(k = 1, 2, . . . , |F (Y )|) and y
j
(with de-
scriptor g
j
, j = 1, 2, . . . , |F (X)|):
d
kj
=
||f
k
− g
j
||
2
1
|F (X)|
2
−|F (X)|
k,j̸=k
||f
k
− g
j
||
2
,
(8)
and then sum up using (note that |F (X)| = |F (Y )| when
we only consider corresponding points):
Q =
1
|F (X)|
|F (X)|
k=1
d
kj
.
(9)
The results are competitive to the state-of-the-art methods
compared in [11] [12].
For synthetic data under rotational and scale transfor-
mations, the proposed feature detector and descriptor can
achieve nearly fully correct matches, e.g. Fig. 7 (a) and
(b). Figure 7 (c), (d) and (e) show the matching results be-
tween human point clouds from SHREC’10 [11] dataset un-
der affine transformation, with holes and after rasterization.
The feature extraction and descriptor calculation take about
1-2 minutes on typical data with around 50,000 points.
Another set of test data is from TOSCA High-resolution
[16]. Figure 8 (a) is a typical matching example using dense
self-similarity descriptor and 8 (b) is the matching example
using MoPC feature-based self-similarity descriptor. Figure
9 (a) shows the precision-recall curve for the wolf data.
6
Figure 6. SHREC benchmark dataset. The transformations are (from left to right): isometry, holes, micro holes, scale, local scale, noise,
shotnoise, topology and sampling.
(a) (b)
(c) (d) (e)
Figure 7. Matching result between human point clouds with rotation, scale, affine transformation, holes and rasterization.
(a) (b)
Figure 8. (a) is the matching result with dense SS descriptor of
different poses of a cat. (b) is the matching result with MoPC
feature-based SS descriptor of different poses of a wolf.
6.2. Lidar point clouds
Table 3 shows the comparison of different configurations
of similarity on 50 pairs of randomly sampled data in ran-
domly chopped 300m * 300m * 50m area of Richard Cor-
ridor in Vancouver. The precision is the ratio between the
number of correctly identified matches (TP) and all matches
(TP + FP). The running time is about 15s per pair.
We also perform experiments on different point clouds
of the same region. Figure 9 (b) shows the precision-recall
curve for 3D Self-similarity descriptor working on data
chopped out from the LiDAR data (600m * 600m * 60m,
100,000 points) of Richard Corridor in Vancouver.
0 0.05 0.1 0.15 0.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Recall
Precision
(a)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Recall
Precision
(b)
Figure 9. (a) is the precision-recall curve for the 3D Self-
similarity descriptor between two wolf models from TOSCA-
HighResolution Data. (b) is the precision-recall curve for the 3D
Self-similarity descriptor on Vancouver Richard Corridor data.
Property Precision
Normal 55%
Curvature 49%
Photometry 49%
Normal+Curvature+Photometry 51%
Table 3. Evaluation of matching results with different configura-
tions (weights) of united self-similarity. Pure normal similarity
performs the best overall, but curvature/photometry similarity can
do better for specific data.
7
(a) (b)
Figure 10. Matching result of aerial LiDAR out of two scans of the Richard Corridor area in Vancouver. (b) is the filtered result of (a).
In real applications there are tremendous data that might
spread across large scales. Our framework can also deal
with large scale data by divide-and-conquer since we only
require local information to calculate the descriptors. Fig-
ure 10 shows the matching result of aerial LiDAR out of
two scans of the Richard Corridor area in Vancouver.
7. Conclusion
In this paper we have extended the 2D self-similarity
descriptor to the 3D spatial space. The new feature-based
3D descriptor is invariant to scale and orientation change.
The new descriptor achieves competitive results on 3D point
cloud data from public dataset TOSCA as well as aerial Li-
DAR data. Since meshes or surfaces can be sampled and
transformed into the point cloud or voxel representations,
the method can be easily adapted to the matching models to
point clouds, or models to models. We are currently work-
ing on the matching propagation and shape retrieval scheme
based on our descriptor.
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