Optimum Gray Level Image Thresholding using a Quantum Inspired Genetic Algorithm

Introduction

The concept of quantum computing (QC) has been originated from the discipline of quantum physics. In the upcoming twenty-second century, QC may be visualized as one of the most challenging research areas for the scholars of computer science and engineering (Mcmohan, 2008; Gonzalez, 2002). The inherent dynamism of QC has been derived from the Schrödinger equation (SE) (Talbi, 2006). QC has some physical phenomena in its own like superposition, interference, coherence & decoherence, entanglement etc., which facilitate the parallelism capability. The features of QC can be embedded into the classical algorithms via a proper coupling to construct quantum inspired algorithms. The new quantum version of classical algorithms may possess exponentially speed up as compared with the pure classical algorithms (Dey, 2011). So the reflection of the research activities have been turned into designing quantum versions of the conventional algorithms such that these would fit on the quantum computer when invented (Dey, 2011). According to Richard Feynman, the efficacy of classical computers is very low when the quantum mechanical activities are concerned. His observation postulates that the effect of quantum mechanics would compensate the said problem fully (Talbi, 2004). The parallelism potential makes QC to be superior to its counterpart in the context of time complexity (Talbi, 2006; Reiffel, 2000). The application of QC conceited its existence when applied into some complex optimization problems that need larger solution space (Han, 2002). Grover’s database search algorithm (Grover, 1998) and Shor’s quantum factoring algorithm (Shor, 1997) are two popular quantum inspired algorithm that have been already discovered.

There are some renowned soft computing approaches used in this direction so far. Heuristic search and various optimization techniques or image analysis using intensity distribution are appropriate examples in this regards (Ren, 2009; Filho, 2008; Nakiba, 2010; Bazi, 2007). Thresholding plays a very important role in image segmentation, which acquiesce a binary image. The basic purpose of image thresholding is to separate object with its background (Pal, 1993). Threshold converts a given gray scale or color image into its corresponding binary image based on a predefined threshold intensity value. The pixel intensity values greater than the threshold value are grouped into one category, called foreground (F). The remaining pixels are fallen into other category, called background (B) or vice-versa (Sahoo, 1997; Jawahar, 1997). The pixels belonging to set (F) are set to 1 (white), while the remaining pixels in the other set are set to 0 (black) (Pal, 1988; Dey, 2011).