IEEE Robotics & Automation Magazine - December 2015 - 118

computing the angle between the normal of the central point
and its neighbors: a point yielding big angle values along several directions will typically denote a corner in 3-D. Two variants of such a detector are also available, one detecting
corners in the intensity domain (" Harris2D), the other
jointly exploiting the intensity as well as the 3-D domain
(" Harris6D). As for most 3-D keypoint detectors [18], a
nonmaxima suppression (NMS) stage is applied to retrieve
only local maxima of the saliency measure evaluated at each
point by the detector.
Other 3-D keypoint detector approaches were specifically
designed for the 3-D or 2.5-D domain. This is the case of intrinsic shape signature (ISS) [19], which is based on the eigenvalue decomposition (EVD) of the 3 # 3 scatter matrix
computed between each point and all neighbors within a

spherical support. Nondistinctive points are rejected by
thresholding the ratios of the three eigenvalues. The smallest
eigenvalue is used as the keypoint saliency, which is subject
to the NMS stage. Thus, keypoints retained by this method
exhibit a distinct variance of the point coordinates along one
direction with respect to the other two. As an example, Listing 8 shows how to compute keypoints using ISS.
Another recent interest point detector is normal aligned
radial feature (NARF) [20], a method specifically designed to
extract salient keypoints on range images. It focuses on detecting points along object depth borders. In particular, a subset of border points is selected such that they exhibit
substantially different dominant directions of the surface in
the local neighborhood, so that they can be stable and repeatable with respect to viewpoint changes (" NarfKeypoint).
For more details on other relevant proposals in the field,
as well as for a recent performance evaluation, we refer the
reader to [18].

Listing 8. Keypoint estimation (intrinsic shape
signatures).

Describing Keypoints-Feature Descriptors
For each detected keypoint, a descriptor is computed to
determine correspondences between the two point clouds.
A local descriptor is a compact representation of a point's
local neighborhood. In contrast to global descriptors describing a complete object or point cloud, local descriptors
try to resemble shape and appearance only in a local
neighborhood around a point, and are suitable for representing it in terms of matching. Among the approaches
currently available in the literature, we provide a brief outline of the main solutions available in the PCL for the registration of 3-D clouds. Apart from the outlined
descriptors, the PCL includes several other methods. We
refer the interested reader to [21], a survey focused on the
3-D descriptors available in the PCL (including related
code snippets), and to [22], focusing on a performance
evaluation of PCL 3-D descriptors.
The spin image descriptor [23] rotates a plane section
around the normal of the keypoint. The plane section accumulates the number of points of the cloud intersected over
a 2-D histogram while doing a complete spin around the
normal [see Figure 7(a)]. One advantage of this approach is

ISSKeypoint3D iss_detector;
iss_detector.setSalientRadius (salient_
radius);
iss_detector.setNonMaxRadius (non_max_
radius);
iss_detector.setInputCloud (input_cloud);
PontCloud::Ptr keypoints
(PontCloud());
iss_detector.compute (*keypoints);

pi

Invalid
Correspondences

Empty Space
qj

Valid
Correspondences

Figure 6. An example of transformation validation. If two surfaces
match locally, we need to make sure that their empty space
also matches and that there is no additional depth information
in the overlap region of any of the clouds that does not have
correspondences in the other cloud.

n(p)
V = (Pt-Ps) # U
ns = U
Ps
p

a

z
Pt-Ps

W=U#V

(a)

nt

V

Pt

U
i

W
(b)

(c)

(d)

Figure 7. Functional principles of feature descriptors. (a) The spin image descriptor spins a plane section around the keypoint normal
to compute its 2-D histogram. (b) The local reference frame and the three angles, a, z, and i computed by FPFH at each point pair.
(c) The 3-D spherical grid deployed by 3DSC. Two grid sectors, yielding each a bin in the 3-D histogram, are depicted in green and red,
respectively. (d) The 3-D grid deployed by SHOT, which is repeatably oriented by the local reference frame denoted by the blue arrows.

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