Image Processing Reference

In-Depth Information

sidering the neighborhood of a pixel as a surface, its Hessian matrix can be expressed as:

(3)

where
I
xx
,
I
xy
, and
I
yy
are the second partial derivatives of pixel
I
(
x
,
y
). Thus, the x-corner detect-

or is described as:

(4)

where
λ
1
and
λ
2
are the Eigen values of
H
.

In order to avoid unnecessary computation, this operator is only applied in regions deined

by the valid vertices of triangle mesh. The real x-corner is the pixel with largest negative value

of
S
and the refined coordinates [
x
0
+
s
,
y
0
+
t
]
T
is given by:

(5)

6 Experimental Results

In this section, the detector response is evaluated considering an image database and by means

of experimental tests with two different cameras. The image database is provided by the tool-

board calibration patern, accounting 156 x-corners arranged as 12 × 13 matrix, being presen-

ted in different orientations. This set represents a common situation to most of systems where

the patern images are irst captured and calibration is performed in an of-line manner.

Figure 6
shows some examples of these images and
Table 1
summarizes the results obtained

for each one. The results are generated by applying the algorithm in each image and counting

the number of corners identified. Analyzing
Table 1
, the vast majority of points is detected.

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