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such as solid objects, marks on surfaces, shadows, and other image contours which
are often the basic elements for calibration, motion analysis and recognition, all
generate intensity edges and can be detected from chains of edge points. Edge de-
tection can be considered as a two-step process. Before edge localization it should
be taken the noise smoothing process that suppresses as much of the image noise as
possible, without destroying the true edges. In the absence of specific information
about type of noise, it is usually assumed that the noise is white and Gaussian. Af-
ter noise smoothing edges can be enhanced and localized. This process is done by
designing a filter responding to edges whose output is large at edge voxels and low
elsewhere, so that edges can be located as the local maxima in the filter's output
and deciding which local maxima in the filer's output are edges and which are just
caused by noise. This involves thinning wide edges to one voxel width and estab-
lishing the minimum value to declare a local maximum an edge (thresholding).
The Canny edge detector is at the moment the most widely used edge detection
algorithm in multimedia systems. Constructing a Canny detector requires the for-
mulation of a mathematical model of edges and noise and synthesizing the best fil-
ter once models and performance criteria are defined. Edges of intensity images
can be modelled according to their intensity values and profiles. For most practical
purposes, a few models are sufficient to cover all interesting edges. Description of
regular Canny 2D edge detector can be found in [3].
The edge detection operator returns a value for the first derivative in horizontal
and vertical direction. The depth dimension (the third dimension) can be achieved
by modifying a regular Canny 2D detector. The edge gradient of a 3D image ob-
ject G can be determined by computing the magnitude gradient components
∂
G
∂
G
∂
G
G
x
=
,
G
y
=
and
G
z
=
for each voxel v(x,y,z) and can be displayed
∂
x
∂
y
∂
z
as an image which intensity levels are proportional to the magnitude of the local
intensity changes [4]. The second step is to estimate the edge strength with
2
2
2
e
(
as well as the orientation of the edge normal.
As shown in Fig. 1, the orientation of edge normal is specified by angles
θ
and
x
,
y
,
z
)
=
G
+
G
+
G
d
x
y
z
that can be computed by equations
ϕ
G
y
tan
θ
=
(1)
G
x
and
G
+
z
tan
ϕ
=
.
()
()
(2)
2
2
G
G
x
y
Weighted summations of the voxel intensities in local neighbourhoods can be
listed as a numerical array in a form corresponding to the local image neighbour-
hood. The output of a gradient based edge detection is a binary image indicating
