A Self-Adaptive Parameter Optimization Algorithm in a Real-Time Parallel Image Processing System

Abstract

Aiming at the stalemate that precision, speed, robustness, and other parameters constrain each other in the parallel processed vision servo system, this paper proposed an adaptive load capacity balance strategy on the servo parameters optimization algorithm (ALBPO) to improve the computing precision and to achieve high detection ratio while not reducing the servo circle. We use load capacity functions (𝐿𝐶) to estimate the load for each processor and then make continuous self-adaptation towards a balanced status based on the fluctuated 𝐿𝐶 results; meanwhile, we pick up a proper set of target detection and location parameters according to the results of 𝐿𝐶. Compared with current load balance algorithm, the algorithm proposed in this paper is proceeded under an unknown informed status about the maximum load and the current load of the processors, which means it has great extensibility. Simulation results showed that the ALBPO algorithm has great merits on load balance performance, realizing the optimization of QoS for each processor, fulfilling the balance requirements of servo circle, precision, and robustness of the parallel processed vision servo system.

1. Introduction

Image processing often requires large-scale data, and many application fields require real-time performance. Thus, image parallel processing systems have been widely applied in the field of image processing to meet the needs of practical applications as discussed by Plaza et al. [1]. However, the actual performance of image processing is often lower than the peak performance provided by this system, implying that the design of the parallel algorithm is essential for improving system performance as discussed by Krefting et al. [2]. An efficient parallel algorithm should enable the load to achieve balance, evenly distribute tasks, and minimize the amount of communication between nodes and thus improving the performance of the parallel treatment system as discussed elsewhere [3, 4]. Therefore, the load balancing scheduling strategy is a difficult and enticing area of research in parallel processing.

In general, the load balancing scheduling strategy is divided into static and dynamic strategies. The static information of the system is used in the load balancing strategy when the load is distributed on each node, making it easy to be analyzed and implemented. However, such a load balancing strategy results in low utilization factor and performance degradation for it neglects the variations in the node load as discussed by Tantawi and Towsley [5]. On the other hand, the dynamic load balancing strategy can dynamically determine load migration according to the system load at each moment, improving system performance significantly as discussed by Ren et al. [6]. Current studies on the scheduling algorithm have been generally committed to seeking a better suboptimal scheduling algorithm. In particular, the self-adaptive load balancing scheduling strategy has been widely considered among professional researchers due to its ability for automatic adjustment in load balancing based on the information state of the system as discussed by Porter and Katz [7]. In addition, the self-adaptive load balancing scheduling strategy improves the load balancing effect through the perception of load variation. The load balancer collects load information on each node periodically and then utilizes the load information to determine the available node that can directly service the customer’s request. The most common self-adaptive load balancing scheduling strategy includes strategies based on the minimum as discussed by Baumgartner et al. [8] and average loads as discussed by Bhatelé et al. [9].

This study focuses on the parallel processing of a robotic stereoscopic vision servo system. According to the scheme of the parallel partition of system and the methodology of image processing, a self-adaptive load balancing scheduling strategy based on the load capacity (𝐿𝐶) measure is presented to achieve the optimization of the system among the servo cycle, servo accuracy, and system robustness.

2. Adaptive Load Balancing Algorithm Based on Load Capacity Measure

The 𝐿𝐶 measure is the estimate of the processor load, and it can maintain self-adaptive adjustment according to the information given by processor load fluctuation to achieve the optimal quality of service (QoS) of each processor. The basic principle of a self-adaptive load balancing algorithm based on the 𝐿𝐶 measure is that each processing node utilizes an 𝐿𝐶 measure to represent the current load status of the nodes. Moreover, the value of 𝐿𝐶 measure can undergo continuous self-adaptive adjustment according to the state of processor load fluctuation. Consequently, the system can achieve load balance depending on the suitable combination of parameters selected through the value of 𝐿𝐶.

2.1. Problem Description

The parameters of target detection and location algorithm for the control should be adjusted in the process of program run to improve the performance of a visual servo system and achieve balance among the servo cycle, servo accuracy, and system robustness.

In the adjustable target detection and location algorithm, a number of parameters can be set for the control of the performance of image processing. For example, 𝜆_𝑐 represents the interval length of the color image segmentation threshold, 𝜆_𝑔 represents the searching threshold length of the template matching projection, and 𝜆_𝑠 represents the interval length that needs to be matched in the stereo matching algorithm. The control parameters of image processing are normalized as follows to uniformly evaluate the adjustment parameters of parallel processing, as in 𝜆_𝑐=𝜆_𝑐−𝜆^𝑐_min𝜆^𝑐_max−𝜆^𝑐_min,𝜆_𝑔=𝜆_𝑔−𝜆^𝑔_min𝜆^𝑔_max−𝜆^𝑔_min,𝜆_𝑠=𝜆_𝑠−𝜆^𝑠_min𝜆^𝑠_max−𝜆^𝑠_min, (1) where 𝜆^𝑖_max is the maximum value of 𝜆_𝑖,  𝜆^𝑖_min is the minimum value of 𝜆_𝑖, and 𝑖∈{𝑐,𝑔,𝑠}.

𝑀_𝑐 was assumed to be the number of color image processing results. 𝑀_𝑔 is the number of template matching processing results. 𝑀_𝑠 is the number of first step results in stereo matching processing. The load fluctuation rate Δ_𝑗 of processor 𝑗 is defined as the degree of change in the load state parameters of system output in cases where devices do not work and the control parameters in charge of load balance are invariant. In the current study, the system load fluctuation rate Δ_𝑗 includes the fluctuation rate of color image processing Δ^𝑗_𝑐, the template matching processing Δ^𝑗_𝑔, and the stereo matching processing Δ^𝑗_𝑠. The threshold processing of the image processing algorithm used in this system satisfies the normal distribution. Therefore, 𝜆^𝑗_𝑠 has an exponential relationship to 𝑀^𝑗_𝑖, and the calculating formula of the fluctuation rate can be defined as follows: Δ^𝑗_𝑖=𝐾^𝑗_𝑖(𝑘)𝑀^𝑗_𝑖(𝑘)−𝑀^𝑗_𝑖(𝑘−1)𝑀^𝑗_𝑖(𝑘)+𝑀^𝑗_𝑖(𝑘−1), (2) where 𝐾^𝑗_𝑖(𝑘) is a scale coefficient that relates to 𝑀^𝑗_𝑖(𝑘) and the data size of processing algorithm 𝑖 and meets the condition of 𝐾^𝑗_𝑖(𝑘)=1/ln(𝑀^𝑗_𝑖(𝑘)).

In terms of the calculating formula of the fluctuation rate, Δ^𝑖_𝑗 is deemed equal to a number from −1 to 1 and only needs to be calculated by counting the number of computed results of the image processing algorithm when the processor is running in unit cycle, which is a very simple statistical process.

2.2. Load Capacity

𝐿𝐶 is a measure of the calculated amount of the current processor that can be accommodated, and it can be used to estimate the relative load status of each processing node. A smaller 𝐿𝐶_𝑗(𝑘) indicates the smaller capacity of the processor; that is, the current processor has a smaller calculating load and can contain more computations. The admission processing should be decreased when 𝐿𝐶_𝑗(𝑘) is greater than 1 because of the heavy processor load. The values of 𝐿𝐶_𝑗(𝑘) can continuously execute self-adaptive adjustment according to the situation of load fluctuation, adjustment parameters, and the status of image acquisition: 𝐿𝐶_𝑗(𝑘)=1+𝑓_𝑗state_𝑗−6,…,state_𝑗×_{𝑖∈𝑊𝑗}𝛽^𝑗_𝑖(𝑘)𝐿𝐶^𝑗_𝑖(𝑘),_{𝑖∈𝑊𝑗}𝛽^𝑗_𝑖(𝑘)=1𝛽^𝑗_𝑖(𝑘)⩾0, (3)(4) where 𝑊_𝑗 is a collection of all adjustable algorithms of image processing that can be included by processor 𝑗.

In (3), 𝑓_𝑖(state_𝑗−6,…, state_𝑗) represents a capacity evaluation function; that is, a conditions function. 𝑓_𝑖(state_𝑗−6,…, state_𝑗) can be expressed as follows: 𝑓_𝑗state_𝑗−5,…,state_𝑗=𝛾_𝑓⋅∑^𝑗_{𝑖=𝑗−5}state_𝑖⋅∑^𝑗_{𝑖=𝑗−5}state_𝑖,36 (5) where 𝛾_𝑓 is the adjustment range factor.

The capacity rate evaluation function is used for judging the capacity size of processor settings. The capacity rate evaluation function uses the sources of processor data to determine the overall increase or decrease in the load capacity rate. In other words, the processing speed is considered too slow when the processor has completed the assignments in a servo cycle and the original data of next servo cycle has been in the accepted state (state_𝑗=1), causing the servo cycle of the processor to be longer than the desired system cycle (40 ms). Therefore, the oversize setting of 𝐿𝐶 should be reduced. On the other hand, the processing speed is considered too fast and the servo cycle of processor is shorter than the desired system cycle (40 ms) when the data has not been received (represented by zero). In this situation, the settings of the total 𝐿𝐶 rate are too small and should be increased.

In (3), the initial value of algorithm 𝑖 in the specific weight 𝛽^𝑗_𝑖(𝑘) is set as 𝛽^𝑗_𝑖(0)=1/𝑚^𝑗_𝑏, where 𝑚^𝑗_𝑏 represents the number of adjustable image processing parameters that move under processor 𝑗. In other words, all reliabilities of the adjustable processing algorithms and weights in the process are deemed equal during initialization. However, the reliabilities of the adjustable algorithms are different in practical applications because the adjustment of weight parameters in each algorithm must be calculated using the other parameters following different parallel processing architectures. In this study, the adjustment of weight in a visual servo parallel processing system is executed between the color image processing and the template matching, which is primarily affected by the target’s changes in shape. As can be seen in (6), the change in rate of the target’s shape 𝜃_𝑝(𝑘) is defined as the proportion of the trace tr(𝑅(𝑘)) of rotation transformation between the current target and the template when the degrees of change in the shape of the objective are evaluated. Furthermore, the threshold value tr(𝑅_𝑚) of the trace of rotation transformation is executed when the template must be updated as follows: 𝜃_𝑝(𝑘)=3−tr(𝑅(𝑘))3−tr𝑅_𝑚. (6)

Then, the specific weight 𝛽^𝑗_𝑔(𝑘) and 𝛽^𝑗_𝑐(𝑘) can be expressed as follows: 𝛽^𝑗_𝑔(𝑘)=𝛾_𝑝𝜃_𝑝(𝑘),𝛽^𝑗_𝑐(𝑘)=1−𝛽^𝑗_𝑔(𝑘), (7) where 𝛾_𝑝 is the rotation adjustment factor and is a constant between 0 and 0.5.

2.3. Adjustment and Update Strategy

The adjustment capacity of the current capacity ^∗𝐿𝐶^𝑗_𝑖(𝑘) is based on the evaluation function of capacity, the weight of the algorithm, and the computing formulae of 𝐿𝐶 as follows: ^∗𝐿𝐶^𝑗_𝑖(𝑘)=𝐿𝐶^𝑗_𝑖(𝑘)𝛽^𝑗_𝑖(𝑘)𝐿𝐶_𝑗(𝑘)𝛽^𝑗_𝑖(𝑘−1)𝐿𝐶_𝑗(𝑘−1). (8)

The new 𝐿𝐶 can be calculated via the fluctuation ratio Δ^𝑗_𝑖 and adjustment parameters after the new state parameters are obtained. The new 𝐿𝐶 can be expressed as follows: 𝐿𝐶^𝑗_𝑖(𝑘)=1+𝛼Δ^𝑗_𝑖1+𝜆^𝑗_𝑖(𝑘)−𝜆^𝑗_𝑖(𝑘−1)^∗𝐿𝐶^𝑗_𝑖(𝑘−1), (9) where 𝛼 is the fluctuation factor, that is, constant between 0 and 1, reflects the magnitude of acutely adjusting 𝐿𝐶_𝑗(𝑘) along with load fluctuation.

The first and middle multiplicative factors on the right-hand side of (9) represent the effect of the fluctuation ratio and the effect of the variable adjustment parameter on 𝐿𝐶, respectively. The fluctuation factor 𝛼 weakens the effect of load fluctuation ratio on 𝐿𝐶 when the load of the processor is progressively varied with time.

Based on the previous theory, a function for updating control parameters can be established as follows: 𝜆^𝑗_𝑖(𝑘+1)=1−𝐿𝐶(𝑘)+𝜆^𝑗_𝑖(𝑘). (10)

Equation (10) reveals that the scale of the control parameters slowly decreases when the load capacity 𝐿𝐶^𝑗_𝑖(𝑘) approaches unity, avoiding the occurrence of the load thrashing phenomenon. The processor rapidly achieves a balance among the servo cycle, the servo precision, and system robustness because the control parameters have become capable of rapid increases due to the minimal load, thereby achieved the optimization of each processing QoS.

3. Application Characteristic of ALBPO Algorithm

3.1. Properties of ALBPO Algorithm

The entire system was assumed to contain 𝑛 parallel image processing subsystems. Without loss of generality, the single system was assumed to have 𝑚_𝑖 performance-adjustable parameters, and the performance-adjustable parameters 𝜆^𝑗_𝑖 in each algorithm 𝐹^𝑗_𝑖 should exhibit the following properties.(1)For the same image, the computational complexity of the algorithm 𝐹^𝑗_𝑖 increases when the parameters 𝜆^𝑗_𝑖 increase, improving the calculation accuracy and robustness of image processing. On the other hand, the computational complexity of algorithm 𝐹^𝑗_𝑖 decreases when the parameters 𝜆^𝑗_𝑖 decrease, reducing the calculation accuracy and robustness of image processing.(2)For the same image, portions of the computation randomly fluctuate in certain areas when the parameters 𝜆^𝑗_𝑖 are constant due to the images are corrupted with noise.(3)The parameters 𝜆^𝑗_𝑖 occur via the normalization process, and thus their values are {0,1}.

Moreover, the image parallel processing system has difficulty in accurately evaluating the processor’s maximum computation during the image parallel process.

3.2. Initial Settings of ALBPO Algorithms

The following initial settings were established according to the properties of the ALBPO algorithm.(1)The initial values of the performance-adjustable parameters 𝜆^𝑗_𝑖 in the 𝐹^𝑗_𝑖 algorithm were set such that they allow large deviations.(2)At the initial time and all prior times, 𝐿𝐶_𝑗=1, the load capacities 𝐿𝐶^𝑗_𝑖=1, and the product of adjustable capacity rate ^∗𝐿𝐶^𝑗_𝑖=1 in each algorithm 𝐹^𝑗_𝑖.(3)At the initial time and all prior times, the receiving status of each processor State_𝑘=0, and 𝑘∈{−5,−4,−3,−2,−1,0}.

4. Experimental Studies

4.1. Experimental System

This study conducted simulation experiments to verify the optimized performance of the ALBPO algorithm for visual servo adjustment parameters and to achieve balance among the servo cycle, servo accuracy, and system robustness in the parallel processing visual servo system. This problem can be attributed to the search for a set of maximum 𝜆^𝑗_𝑖, making the receiving status values of each processor frequently switch between −1 and 1. The simulation on a single processor can be verified in the property of the ALBPO algorithm that is independent in each processor. The 𝐹^𝑗_𝑖 algorithms, which run on each processor, exhibit identical properties, and thus the corresponding situation can be used to verify which processor has two performance-adjustable parameters.

The total computational amount Ω_max of the system was assumed to be known and constant to verify the performance of the ALBPO algorithm. The performance-adjustable parameter 𝜆₁ and the computational amount Ω₁ were assumed to exhibit a linear relationship, Ω₁=𝑘₁×𝜆₁. The performance-adjustable parameter 𝜆₂ and the computational amount Ω₂ were assumed to exhibit a nonlinear relationship, Ω₂=(𝑘₂+𝑘₂×𝜆₂)×𝜆₂. Both algorithms exhibit the random disturbance quantity.

4.2. Parameter Optimization Results of ALBPO Algorithm

Assume that Ω_max=400, 𝜆₁=0.25, 𝜆₂=0.5, Λ=5, 𝑘_T1=480, 𝑘_T2=240, 𝛾_𝑓=1, 𝛼=0.6, and servo cycle 𝑇=1000. Figure 1 shows the effects of the parameter optimization results of the SALB algorithm. The horizontal coordinates represent the sampling number. The vertical coordinates represent different values in the following different figures. Figure 1(a) represents the value of the state in the capacity rate evaluation function. Figures 1(b), 1(c), and 1(d) represent the number of processing results, capacity rate, and values of adjustable parameters, respectively. Figure 1(e) shows the overall capacity rate of the processor. Figures 1(h), 1(g), and 1(f) represent the number of processing results, capacity rate, and values of adjustable parameters, respectively. The first flip in state (state = −1) when the sampling size was 214 indicates that the initial data of the next servo cycle has changed and is awaiting the receiving state in the already received state, as shown in Figure 2. The subsequent state-repeated shocks indicate that the values of adjustable parameters simply satisfy the values of the maximum computational amount achieved by the processor. Moreover, Figures 1(b) and 1(f) indicate that the adjustable parameters of the ALBPO algorithms monotonically increase first and then remain unchanged, and thus, the adjustable parameters can be adjusted using the ALBPO algorithm to achieve the optimal control point. Changes in the number of the processing results also confirm the adjustment effect of the ALBPO algorithm. In addition, as can be seen in Figures 1(e), 1(c), and 1(g), the overall capacity rate of the two algorithms both changed at a very low rate during processing, denoting that the system can still be regulated when the system is initializing, even if the parameters of the artificial settings present deviations.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 1 

The monitoring data of the optimization results for the ALBPO algorithm.

Figure 2 

The optimization results for different 𝛾𝑓 and 𝛼.

4.3. Effects of Adjusting Amplitude Factor 𝛾_𝑓 and Volatility Factor 𝛼 on Optimization Results

Figure 1 shows the servo parameters optimization results of the ALBPO algorithm when 𝛾_𝑓=1 and 𝛼=0.6. The values of 𝛾_𝑓 and 𝛼 influence the optimization of the servo parameters significantly, thus properly selecting the values of 𝛾_𝑓 and 𝛼 can generate better optimization results. Therefore, investigating the connection between the servo parameters optimization results and adjusting the variations in the amplitude factor 𝛾_𝑓 and volatility factor 𝛼 are necessary. The maximum and minimum fluctuation values of the stable period of the system and the adjustment parameters in the stable state when 𝛾_𝑓 and 𝛼 are variable are shown in Table 1. Figure 2 shows the optimization results for the different values of 𝛾_𝑓 and 𝛼.

Table 1 

The effects of amplitude factor and volatility factor on system performance.

Figure 2 also shows the optimization results for different values of 𝛾_𝑓 and 𝛼. By analyzing the tabular data, the product size of 𝛾_𝑓 and 𝛼 was found to affect the stable period of the system, in addition to the fluctuation range of adjustment parameters in the steady state. The fluctuation range increased and the stable period decreased when the product of 𝛾_𝑓 and 𝛼 increased. Moreover, the fluctuation range decreased and the stable period increased when the product of 𝛾_𝑓 and 𝛼 decreased. Finally, the fluctuation range and the stable period exhibited minimal changes when the product of 𝛾_𝑓 and 𝛼 was constant.

5. Conclusions

The current study proposed a multiprocessor parallel scheduling algorithm to adjust the performance parameters of the image processing of the visual servo system. The proposed ALBPO algorithm was shown to be efficient in improving the computational accuracy and recognition rate under the condition that the visual servo system did not reduce the servo cycle. In the ALBPO algorithm, the unknown and time-varying maximum amounts of calculation of a processor were exchanged via 𝐿𝐶, and the 𝐿𝐶 measure and parameters were adjusted by adopting the fluctuation rate of load and the evaluation function of the state. Therefore, the optimization of the QoS of each processor and the coordination among the servo accuracy, servo speed, and system robustness were easily realized. The feasibility and efficiency of the ALBPO algorithm were demonstrated through a simulation study on the parallel processing scheduling algorithm.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

This work was supported by the Natural Scientific Research Innovation Foundation Project in Harbin Institute of Technology (HIT. NSRIF. 2009023), the National Basic Research Program of China under Grant no. G2011CB302605, the National Natural Science Foundation of China (NSFC) under Grants no. 61173145 and no. 61100188, and the National High Technology Research and Development Program of China under Grant no. 2011AA010705.