Abstract

In the field of image processing, there are several problems where an efficient search of the solutions has to be performed within a complex search domain to find an optimal solution. Multi-thresholding which is a very important image segmentation technique is one of them. The multi-thresholding problem is simply an exponential combinatorial optimization process which traditionally is formulated based on complex objective function criterion which can be solved using only nondeterministic methods. Under such circumstances, there is also no unique measurement which quantitatively judges the quality of a given segmented image. Therefore, researchers are solving those issues by using Nature-Inspired Optimization Algorithms (NIOAs) as alternative methodologies for the multi-thresholding problem. This study presents an up-to-date review on all most important NIOAs employed in multi-thresholding based image segmentation domain.

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Introduction

Optimization, in general, is concerned with finding the best solutions for a given problem. Its applicability in many different disciplines makes it hard to give an exact definition. Mathematicians, for instance, are interested in finding the maxima or minima of a real function from within an allowable set of variables. In computing and engineering, the goal is to maximize the performance of a system or application with minimal runtime and resources.

Nature has evolved over billions of years, providing a rich source of inspiration. Researchers have drawn various inspirations to develop a diverse range of algorithms with different degrees of success. Such diversity and success do not mean that we should focus on developing more algorithms for the sake of algorithm developments, or even worse, for the sake of publication. We do not encourage readers to develop new algorithms such as grass, tree, tiger, penguin, snow, sky, ocean, or Hobbit algorithms. These new algorithms may only provide distractions from the solution of really challenging and truly important problems in optimization. New algorithms may be developed only if they provide truly novel ideas and really efficient techniques to solve challenging problems that are not solved by existing algorithms and methods.

Optimization

Optimization is a mathematical study, which searches for the best suited solution among a sea of possible alternatives. Be it engineering, medicine, economics or any other field the need of optimization is a commonly across all the domains. Maximising the profit or revenue, minimising the cost or resources, scheduling the work to get the optimal production are few examples which will be seen as some applications of utmost importance in the current business world.

The underlining methodology of mathematical optimization is to define an objective function which needed to be maximised or minimised depending on the problem at hand and take combinations of multiple parameters as input. Then a search will be performed to find out the combination of parameters providing the best value.

For an example, in the below figure if the surface of the graph represents the possible solutions, what the optimization algorithm should do is to take the current solution to the global optimum location.

According to the problem types, the algorithms usually try to intelligently drive the solution to the global optimums efficiently and without being trapped in local optimum locations.