Image Processing Reference
In-Depth Information
The principle of the algorithm is as follows. If ε is the probability of choosing a sample that
produces a poor estimate (outlier), then 1 - ε is the probability of geting a good sample (inli-
ers). This means that the probability of catching s good samples becomes (1 - ε) s . For k trials,
the probability of failure becomes (1 - (1 - ε) s ) k . If ρ is the desired probability of success, given
for Equation (1) :
3.2 Region Growing Segmentation
The Region Growing algorithm is based on the idea that some features in local data do not
change greatly regarding those features measured for a given sample, called seed. Therefore,
regions can be “grown” if neighboring data remain homogeneous given certain constraints,
commonly the spatial closeness of the data, although other features can also be included. In
our work, we choose to enrich the spatial closeness with features that are based in local sur-
face orientation and curvature, both approximated at each point in the cloud. The algorithm
can be summarized as follows:
• Points are sorted according to their curvature.
• The point that has the minimum value of curvature is chosen as a seed and the region
growth begins from that point (flat areas have less curvature).
• For each seed point, a list containing its closest neighbors is extracted:
• The angle between the normal of each neighbor and the normal of the current point
(seed) is compared: if the angle is less than a certain threshold, the point is added to the
current region.
• Subsequently, every neighbor is tested for the curvature value. If the neighbor's
curvature is less than certain curvature threshold value then that point is turned into a
new seed.
• Current seeds are removed from the set of seeds, but remain marked as points belonging
to the region. This avoids double checking points.
Regions are found once the algorithm runs out of seeds. For further details regarding Re-
gion Growing please refer to [ 16 ] .
3.3 Min-Cut
According to the results of Golovinskiy and Funkhouser [ 17 ] , Min-Cut is robust to noise and
is very effective for segmenting dense point clouds of outdoor urban scans. However, it re-
quires prior knowledge of the location of the objects to be segmented, and has input parameter
(namely radius and σ ) that should be set in order to control the resulting segmentation, where
the main cues are distances and point densities, rather than colors and textures.
The principle of the algorithm is as follows:
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