A Fast Detection Method for Bottle Caps Surface Defect Based on Sparse Representation - Intelligent Computing for Sustainable Energy and Environment - page 81

Fig. 3. Relationship for the defects with sparse factors

According to (1) and (2), we have X 1 = X t + X d and X t = D t α t . Substituting
the above equations, expression (9) can be re-written as
α d =argmin α d 1 ,

st. X d − D d α d 2

ε. (10)

where ε is the error, which is caused by image noise and inaccurate alignment
between the sample and the template. From expression (10), we get α d using
the algorithm proposed in literature [10]. If we only judge the cap quality, α d
that is solved is enough. According to the previous knowledge, the positioning
defects in a 2D image need to know the defects sparse factors in both the vertical
and horizontal directions. So, α d needs also to be further calculated. Due to the
projection direction of X 2 perpendicular to the projection direction of X 1 ,the
interval is 90 atoms between the two best matching atoms. Thus, α t is gained
through α t cyclic right moving 90 units. This makes very simple and fast to
getting α t .Nextly, α d can be obtained easily, which uses the way same as that
of α d .

5 Experimental Results

The setup that is used for capturing caps surface image in this experiment is
depicted in Fig.4. A Basler Aca640/100gm high-performance machine vision
camera with Gigabit Ethernet interface (GigE Vision) is mounted above the
stage, which supports jumbo frames and is capable of reaching a frame rate
of 100Hz full frame (650

492). The experiments were carried out on an Intel
dual-core 3.0GHz PC with 4GB RAM. All the computations were performed
with MATLAB. The bottle cap images are captured by the high speed camera
which is triggered by the signal come from the sensor. To obtain a high speed
to deal with image, we read out only a part of the image sensor as large as

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