为了快速准确地进行锅炉煤燃烧火焰图像的分割,提出了基于倒数交叉熵的多阈值分割方法,以弥补现有Shannon交叉熵方法因涉及对数运算而存在无定义值和零值的缺陷,并提升算法运算速度.首先定义了倒数交叉熵,导出了最小倒数交叉熵单阈值选取公式,证明了倒数交叉熵在灰度均匀分布时和Shannon交叉熵等价;然后将此推广到多阈值选取,给出最小倒数交叉熵多阈值选取的改进粒子群优化算法,实现对多个阈值快速精确地寻优;最后针对火焰图像进行了大量的实验.结果表明,与基于改进粒子群优化的最大Shannon熵、灰度熵、Otsu、Shannon交叉熵等方法相比,该方法能够更为准确地对火焰图像进行多阈值分割,而且计算速度比Shannon交叉熵方法大大加快.
In order to segment the boiler combustion flame image quickly and accurately, a multiple-threshold selection method based on reciprocal cross entropy was proposed. It can compensate for the defect of undefined value and zero value involved in the logarithm calculation in the existing threshold selection method using Shannon cross entropy and improve the computational speed. Firstly the reciprocal cross entropy was defined and the single-threshold selection formulae using minimum reciprocal cross entropy were derived. The equivalence between the reciprocal cross entropy and Shannon cross entropy under the uniform distribution of gray level in the image was proved. Then it was generalized to the multiple-threshold selection, and the minimum multiple-threshold selection method using the reciprocal cross entropy based on improved particle swarm optimization algorithm was given in order to find the mul- tiple thresholds quickly and accurately. Finally, a large number of experiments were done on the flame images. The results show that, compared with the existing methods such as maximum Shannon entropy method, gray entropy method, maximum between-cluster variance (Otsu)method and Shannon cross entropy method based on improved particle swarm optimization, the proposed method has obvious superiority. It can segment the flame images more accurately using multiple thresholds, with greater computational speed than Shannon cross entropy method.