Flexible workpiece includes the materials like elasticity spline, textile fabric, and polyurethane sponge, due to the fact that processing trajectory is composed by small arc or small line segment primitives and the deformation of the flexible workpiece during the processing trajectory, making the captured image of processing trajectory not clear, the edge of processing image over local uneven gray, and also the pixels of boundaries between the processing trajectory image edge and background organizations not obvious. This paper takes corner search of processing trajectory as the cutinpoint, slope angle curve of starting and terminal point of each primitive is also designed, put forward the search algorithm that regards Daubechies (4) as wavelet operator to conduct slope angle curve for multiple scales wavelet transform, by judging whether there is a point of the curve appears wavelet transform extremum to determine whether the point is a corner point based on wavelet edge modulus maxima extract principle. Finally, proposed a decomposition/reconstruction design method of FIR filters based on wavelet transform of processing image. Eighttap transpose FIR filter is used to design the decomposition of Daubechies (4) and reconfigurable computing IP core. The IP core wavelet decomposition of the total timeconsuming increases only 5.561% in comparsion with PC. Trajectory angle relative error is 2.2%, and the average measurement time is 212.38 ms.
Flexible workpiece trajectory processing refers to the procedure of conducting all kinds of complicated image processing in workpiece which is consisted of multilayer soft material, and emerged some uneven pattern on the surface of workpiece [
Flexible workpiece includes the materials like elasticity spline, textile fabric, and polyurethane sponge; its material mode shows the physics nonlinearity or geometry nonlinearity, macroscopic property respond to low rigidity intensity, low elasticity modulus, soft mechanics property, and so on. The processing trajectory discussed in this paper refers to processing completion in flexible workpiece, with the following characteristics.
The trajectory straightness error
Straight linestraight line.
Arcarc.
Straightarc.
Flow chart of processing trajectory angle measurement.
Angle measurement of flexible workpiece processing trajectory is based on the wavelet decomposition of processing image; measure angle can be obtained by extracting processing trajectory profile, determining corner of each trajectory primitive (the start and terminal position of primitive), and drawing out the angle measurement auxiliary line. Since the processing trajectory profile can be extracted through wavelet modulus maxima [
For closed processing trajectory of geometric patterns, the place where starting, terminal points of primitive located is also the place of each corner in the trajectory; they are in the greater curvature of the trajectory image profile. As Figure
The slope curve
Piecewise linear approximation of the curve
According to extraction algorithm of wavelet edge modulus maxima, at an arbitrary point
Let
Then, the extrema ratio of two different scale factors
Therefore, corner detection procedure of processing trajectory image is expressed as follows.
Let
Structure of FIR filter with the length
Based on Figure
Figure
Structure of 8 gap FIR filter based on DSP48 Slice.
Eighttap FIR filter FSL control state machine.
Figure
Xilinx FPGA IP core verification platform.
Test picture of flexible workpiece trajectory processing.
Conduct a twostage wavelet decomposition on trajectory processing test image, with each stage including the horizontal and vertical direction wavelet decomposition, image decomposition effect, and wavelet decomposition time
Decomposition result of the first level wavelet transform.
The first stage
The second stage
Decomposition result of the first level wavelet transform.
The first stage
The second stage
From Figures
Figure
Reconstruction image Wavelet decomposition.
Timeconsuming comparison table of wavelet decomposition.
Testing times  Consuming time of two levels wavelet decomposition calculated by hardware (ms)  Consuming time of PC (ms)  

Firststage decomposition  Secondstage decomposition  
Decomposition  Matrix transpose  Summation  Decomposition  Matrix transpose  Summation  
1  34.6506  0.00000  34.6506  74.2829  21.3355  95.6184  123.4057 
2  34.6506  0.00000  34.6506  74.2827  21.3355  95.6182  123.4058 
3  34.6507  0.00000  34.6507  74.2828  21.3355  95.6183  123.4056 
4  34.6506  0.00000  34.6506  74.2828  21.3355  95.6183  123.4056 
5  34.6507  0.00000  34.6507  74.2828  21.3355  95.6183  123.4057 
6  34.6506  0.00000  34.6506  74.2828  21.3355  95.6183  123.4056 
7  34.6506  0.00000  34.6506  74.2829  21.3355  95.6184  123.4058 
8  34.6506  0.00000  34.6506  74.2827  21.3355  95.6182  123.4055 
9  34.6506  0.00000  34.6506  74.2828  21.3355  95.6183  123.4056 
10  34.6506  0.00000  34.6506  74.2826  21.3355  95.6181  123.4058 
11  34.6506  0.00000  34.6506  74.2828  21.3355  95.6183  123.4058 
 
Average value 



Let
Processing trajectory image.
Positioning results of primitive starting, terminal corner.
It can be seen that algorithm can accurately locate the position of the corner, the position where the starting, terminal points are of arc primitive
Comparison table of angle measurement.
Testing times  Angle measurement  Testing time (ms)  

Real 
Measure value (°)  Relative error  
1  32.50  33.24  2.28  212.38 
2  32.50  33.21  2.18  212.38 
3  32.50  33.23  2.25  212.38 
4  32.50  33.19  2.12  212.38 
5  32.50  33.24  2.28  212.38 
6  32.50  33.21  2.18  212.38 
7  32.50  33.19  2.12  212.38 
8  32.50  33.23  2.25  212.38 
9  32.50  33.21  2.18  212.38 
10  32.50  33.22  2.22  212.38 
 
Average value  2.2  212.38 
Measure result of trajectory angle.
According to the fact that processing trajectory is composed by small arc or small line segment primitives and the pixels of boundaries between the processing trajectory image and study a search algorithm of origin and terminal location combined with wavelet multiscal algorithm, the results show that relative error and average measure time of trajectory angle is 2.2% and 212.38 ms.
FIR filters accelerated decomposition/reconstruction design method of processing image wavelet transform is put forward. Eighttap transpose FIR filter is used to design the decomposition of Daubechies
This work is partially supported by National Natural Science Foundation of China (no. 51205069), Natural Science Foundation of Guangdong Province, China (no. S2013010013288), and Combination Project of Industryuniversity research of Huizhou city of Guangdong Province China (2011C010002008).