Colour analysis is a crucial step in image-based fire detection algorithms. Many of the proposed fire detection algorithms in a still image are prone to false alarms caused by objects with a colour similar to fire. To design a colour-based system with a better false alarm rate, a new colour-differentiating conversion matrix, efficient on images of high colour complexity, is proposed. The elements of this conversion matrix are obtained by performing K-medoids clustering and Particle Swarm Optimisation procedures on a fire sample image with a background of high fire-colour similarity. The proposed conversion matrix is then used to construct two new fire colour detection frameworks. The first detection method is a two-stage non-linear image transformation framework, while the second is a direct transformation of an image with the proposed conversion matrix. A performance comparison of the proposed methods with alternate methods in the literature was carried out. Experimental results indicate that the linear image transformation method outperforms other methods regarding false alarm rate while the non-linear two-stage image transformation method has the best performance on the F-score metric and provides a better trade-off between missed detection and false alarm rate.