Equivalence of oblique and frontal illumination in perspective shape from shading

In this paper, it is shown that any oblique illumination shape-from-shading problem under perspective projection for Lambertian reflection and a single distant light source can be converted to an equivalent frontal illumination problem by a simple nonlinear intensity transformation which is equivalent to a rectification in stereo vision. Remarkably, it involves no approximation of depth. The method is evaluated on perspective shape-from-shading involving wide range of oblique angles. © 2007 IEEE.published_or_final_versio

Continuous non-revisiting genetic algorithm with random search space re-partitioning and one-gene-flip mutation

Special Session on Evolutionary Computer VisionIn continuous non-revisiting genetic algorithm (cNrGA), the solution set with different order leads to different density estimation and hence different mutation step size. As a result, the performance of cNrGA depends on the order of the evaluated solutions. In this paper, we propose to remove this dependence by a search space re-partitioning strategy. At each iteration, the strategy re-shuffles the solutions into random order. The re-ordered sequence is then used to construct a new density tree, which leads to a new space partition sets. Afterwards, instead of randomly picking a mutant within a partition, a new adaptive one-gene-flip mutation is applied. Motivated from the fact that the proposed adaptive mutation concerns only small amount of partitions, we propose a new density tree construction algorithm. This algorithm refuses to partition the sub-regions which do not contain any individual to be mutated, which simplifies the tree topology as well as speeds up the construction time. The new cNrGA integrated with the proposed re-partitioning strategy (cNrGA/RP/OGF) is examined on 19 benchmark functions at dimensions ranging from 2 to 40. The simulation results show that cNrGA/RP/OGF is significantly superior to the original cNrGA at most of the test functions. Its average performance is also better than those of six benchmark EAs. © 2010 IEEE.published_or_final_versio

Continuous non-revisiting genetic algorithm with overlapped search sub-region

In continuous non-revisiting genetic algorithm (cNrGA), search space is partitioned into sub-regions according to the distribution of evaluated solutions. The partitioned subregion serves as mutation range such that the corresponding mutation is adaptive and parameter-less. As pointed out by Chow and Yuen, the boundary condition of the mutation in cNrGA is too restricted that the exploitative power of cNrGA is reduced. In this paper, we tackle this structural problem of cNrGA by a new formulation of mutation range. When sub-region is formulated as which certain overlap exists between adjacent sub-regions, this creates a soft boundary and it allows individual move from a sub-region to another with better fitness. This modified cNrGA is named cNrGA with overlapped search sub-region (cNrGA/OL/OGF). By comparing with another work on this problem, Continuous non-revisiting genetic algorithm with randomly re-partitioned BSP tree (cNrGA/RP/OGF), it has an advantage on processing speed. The proposed algorithm is examined on 34 benchmark functions at dimensions ranging from 2 to 40. The results show that the proposed algorithm is superior to the original cNrGA, cNrGA/RP/OGF and covariance matrix adaptation evolutionary strategy (CMA-ES). © 2012 IEEE.published_or_final_versio

Applying non-revisiting genetic algorithm to traveling salesman problem

In [1], we propose non-revisiting genetic algorithm (NrGA) and apply it to a set of bench mark real valued test functions. NrGA has the advantage that it is non-revisiting, i.e. a visited point will not be visited again. This provides an automatic mechanism for diversity maintenance which does not suffer from premature convergence. Another advantage is that it supports a parameter-less adaptive mutation mechanism. In this paper, we show how NrGA can be adapted to a real world combinatorial optimization problem - the famous traveling salesman problem (TSP). Comparison with genetic algorithm (GA) (with revisits and standard mutation) is made. It is shown that NrGA gives superior performance compared to GA. Moreover, it gives the same stable performance using different types of mutation operators. Moreover, turning off GA's mutation operator but only use the NrGA inherent parameter-less adaptive mutation gives the best performance. © 2008 IEEE.published_or_final_versio

A non-revisiting genetic algorithm

Genetic Algorithm (GA) is a revisiting stochastic algorithm. In other words, a solution that has been visited before may be revisited. The fitness of the solution has to be evaluated each time. Since fitness evaluation is the most computationally intensive process in the execution of the GA, revisits should be minimized or eliminated. In this paper, a novel dynamic binary partitioning tree archive is proposed to eliminate all revisits. It works as follows: When the GA generates a solution, the tree is accessed. A leaf node is appended to the tree if the solution has not been visited before and so has no record in the tree. Otherwise, a search is initiated from the leaf node that is the duplicate to the solution to find the nearest neighbor solution in the search space that is not visited. During this process, whole sub-trees may be pruned if all the leaf nodes it contains are visited. The search naturally implements a self adaptive mutation mechanism. Hence the GA requires no other mutation parameter or mutation scheme. Experimental results reveal that this new GA is superior in performance compared with the standard GA with revisits, and the tree archive is not memory intensive. © 2007 IEEE.published_or_final_versio

Continuous non-revisiting genetic algorithm

The non-revisiting genetic algorithm (NrGA) is extended to handle continuous search space. The extended NrGA model, Continuous NrGA (cNrGA), employs the same tree-structure archive of NrGA to memorize the evaluated solutions, in which the search space is divided into non-overlapped partitions according to the distribution of the solutions. cNrGA is a bi-modulus evolutionary algorithm consisting of the genetic algorithm module (GAM) and the adaptive mutation module (AMM). When GAM generates an offspring, the offspring is sent to AMM and is mutated according to the density of the solutions stored in the memory archive. For a point in the search space with high solution-density, it infers a high probability that the point is close to the optimum and hence a near search is suggested. Alternatively, a far search is recommended for a point with low solution-density. Benefitting from the space partitioning scheme, a fast solution-density approximation is obtained. Also, the adaptive mutation scheme naturally avoid the generation of out-of-bound solutions. The performance of cNrGA is tested on 14 benchmark functions on dimensions ranging from 2 to 40. It is compared with real coded GA, differential evolution, covariance matrix adaptation evolution strategy and two improved particle swarm optimization. The simulation results show that cNrGA outperforms the other algorithms for multi-modal function optimization.published_or_final_versio

A study of operator and parameter choices in non-revisiting genetic algorithm

We study empirically the effects of operator and parameter choices on the performance of the non-revisiting genetic algorithm (NrGA). For a suite of 14 benchmark functions that include both uni-modal and multi-modal functions, it is found that NrGA is insensitive to the axis resolution of the problem, which is a good feature. From the empirical experiments, for operators, it is found that crossover is an essential operator for NrGA, and the best crossover operator is uniform crossover, while the best selection operator is elitist selection. For parameters, a small population, with a population size strictly larger than 1, should be used; the performance is monotonically increasing with crossover rate and the optimal crossover rate is 0.5. The results of this paper provide empirical guidelines for operator designs and parameter settings of NrGA. © 2009 IEEE.published_or_final_versio

A non-revisiting simulated annealing algorithm

In this article, a non-revisiting simulated annealing algorithm (NrSA) is proposed. NrSA is an integration of the non-revisiting scheme and standard simulated annealing (SA). It guarantees that every generated neighbor must not be visited before. This property leads to reduction on the computation cost on evaluating time consuming and expensive objective functions such as surface registration, optimized design and energy management of heating, ventilating and air conditioning systems. Meanwhile, the prevention on function re-evaluation also speeds up the convergence. Furthermore, due to the nature of the non-revisiting scheme, the returned non-revisited solutions from the scheme can be treated as self-adaptive solutions, such that no parametric neighbor picking scheme is involved in NrSA. Thus NrSA can be identified as a parameter-less SA. The simulation results show that NrSA is superior to adaptive SA (ASA) on both uni-modal and multi-modal functions with dimension up to 40. We also illustrate that the overhead and archive size of NrSA are insignificant, so it is practical for real world applications. © 2008 IEEE.published_or_final_versio

A non-revisiting particle swarm optimization

In this article, a non-revisiting particle swarm optimization (NrPSO) is proposed. NrPSO is an integration of the non-revisiting scheme and a standard particle swarm optimization (PSO). It guarantees that all updated positions are not evaluated before. This property leads to two advantages: 1) it undisputedly reduces the computation cost on evaluating a time consuming and expensive objective function and 2) It helps prevent premature convergence. The non-revisiting scheme acts as a self-adaptive mutation. Particles genericly switch between local search and global search. In addition, since the adaptive mutation scheme of NrPSO involves no parameter, comparing with other variants of PSO which involve at least two performance sensitive parameters, the performance of NrPSO is more reliable. The simulation results show that NrPSO outperforms four variants of PSOs on optimizing both uni-modal and multi-modal functions with dimensions up to 40. We also illustrate that the overhead and archive size of NrPSO are insignificant. Thus NrPSO is practical for real world applications. In addition, it is shown that the performance of NrPSO is insensitive to the specific chosen values of parameters. © 2008 IEEE.published_or_final_versio