## 6 Experimentation and Performance Evaluation
### System Performances Analysis and Discussion  
FPGA implementation is proposed in the aim to be able to respect the real-time application performances requirements. Analysis of the hardware architecture must be done to determine the latency of the complete processing chain. In one hand, we proceed with a timing analysis using the Xilinx \"Timing analysis tool\" in order to identify and then decrease the latency of the critical paths. In addition, in the other hand, the processing algorithm should perform at least at the frame rate frequency of the camera to satisfy timing constraints.  
In our work, by taking profit from pipeline to decrease the latency, the operating frequency has been increased to 275.18 MHz. We used two standard IEEE-1394b FireWire cameras (Point Grey Research Inc., Richmond, BC, Canada). The maximum pixel clock frequency could reach 66.67 MHz, which corresponds to a pixel period of 15 ns. The maximum FPS (frames per second) of the camera is 30 FPS at a maximum resolution of 1024 \(\times\) 768. This means that between two frames, it exists a period of \(T\) = 33 ms. The system should respond during this period in order to satisfy the application constraints. The proposed XSG architecture for the pre-processing and laser spots extraction presents a total latency of 1024 \(\times\) 768 clock cycles (the resolution of the image). The 3D reconstruction module, which is designed to be looped twelve times to generate the 3D coordinates of the 12 laser pointers presents a total latency of 1200 clock cycles.  
For a maximum clock frequency our system can attain the following performances:  
1. Maximum throughput of 275 Mega-pixel per second
2. Pre-processing and laser spots extraction execution time = 2.86 ms
3. 3D reconstruction execution time = 0.00436 ms
4. Total execution time considering the pipeline = 2.86 ms  
The complete execution time of the proposed architecture can reach the value of 2.86 ms which is inferior to the 33 ms constraint related to the used camera characteristics. This permits to use more sophisticated camera with higher frame rate and resolution and to go further in the reconstruction speed and precision. In addition, the remaining time can be exploited for more treatments for the robot control. In our work, we use a prototype of twelve lasers devices inserted with the stereo cameras in order to validate the proposed 3D shape reconstruction system. More lasers could be introduced in the aim to increase the number of points representing the shape to be reconstructed. This permits to obtain a more accurate structure of the karst without any effect on the execution time, given that the detection blocks relative to the laser projection zones work in a parallel way. For example, when using a distance angle of 0.5\({}^{\circ}\) (instead of 30\({}^{\circ}\)) between neighboring lasers, the hardware architecture of the reconstruction module will take 0.26 ms (720 \(\times\) 100 \(\times\) 3.634) and the total latency will note change. With a robot navigation speed of 2 ms\({}^{-1}\), for example, the proposed system is able to generate a 3D shape every 5.72 mm. Examples of some FPGA implementations of real-time 3D reconstruction algorithms and their main characteristics are presented in Table 3.