Rigid transformation including rotation and translation can be elegantly represented by a unit dual quaternion. Thus, a non-differential model of the Helmert transformation (3D seven-parameter similarity transformation) is established based on unit dual quaternion. This paper presents a rigid iterative algorithm of the Helmert transformation using dual quaternion. One small rotation angle Helme...

In this paper we introduce hybridized fireworks algorithm for global optimization problems. We replaced Gaussian search method from the original fireworks algorithm with the search equation adopted from the firefly algorithm. To test our approach, we implemented six standard bound-constrained benchmarks and performed comparative analysis with the basic fireworks algorithm, as well as with two o...

Firefly Algorithm (FA) is a powerful swarm intelligence algorithm i spired by the flash phenomenon of the fireflies. However, it has weaknesses on optimizing high-dimensional problems. This paper presents an improved FA named Adaptive Firefly Algorithm (AFA). In the new algorithm, three strategies are proposed to improve its adaptability and overcome its weaknesses. The algorithm is tested on a...

Firefly algorithm is a swarm based metaheuristic algorithm inspired by the flashing behavior of fireflies. It is an effective and an easy to implement algorithm. It has been tested on different problems from different disciplines and found to be effective. Even though the algorithm is proposed for optimization problems with continuous variables, it has been modified and used for problems with n...

This paper presents an algorithm to average a set of quaternion observations. The average quaternion is determined by minimizing the weighted sum of the squared Frobenius norms of the corresponding attitude matrix differences, subject to the unit-norm constraint in the determined solution. Two cases are presented: one that incorporates scalar weights and one that incorporates general weights on...

The quaternion representation of color is shown here to be effective in the context of segmenting color images into regions of similar color texture. The advantage of using quaternion arithmetic is that a color can be represented and analyzed as a single entity. A lowdimensional basis for the color textures found in a given image is derived via quaternion principal component analysis (QPCA) of ...

Pattern recognition techniques have been used to automatically recognize the objects, personal identities, predict the function of protein, the category of the cancer, identify lesion, perform product inspection, and so on. In this paper we propose a novel quaternion-based discriminant method. This method represents and classifies color images in a simple and mathematically tractable way. The p...