利用混沌布谷鸟优化的二维Renyi灰度熵图像阈值选取

为了进一步降低现有的Renyi熵阈值法的计算复杂度，提出了基于混沌布谷鸟算法和二维Renyi灰度熵的阈值选取。首先，引入一维Renyi灰度熵阈值选取公式，建立基于像素灰度和邻域梯度的二维直方图，推导出基于该直方图的二维Renyi灰度熵阈值选取公式，通过快速递推公式来减少阈值准则函数的计算量；最后，采用混沌布谷鸟算法搜索最优阈值来完成图像分割。结果表明，与二维Arimoto熵法、基于粒子群的二维Renyi熵法、基于混沌粒子群的二维Tsallis灰度熵法、基于布谷鸟算法的二维Renyi灰度熵法相比，所提出的方法能够准确实现图像分割，且运算速度有所提升。

Two-dimensional Renyi-gray-entropy image threshold selection based on chaotic cuckoo search optimization

To further reduce the computational complexity of existing thresholding methods based on Renyi’s entropy, in this paper, we propose a method for threshold selection based on 2-D Renyi-gray-entropy image threshold selection and chaotic cuckoo search optimization. First, we derive the formula for a 1-D Renyi-gray-entropy threshold selection. Then, we build a 2-D histogram based on the grayscale and gray-gradient and derive a formula for 2-D Renyi-gray-entropy threshold selection based on this histogram. We use fast recursive algorithms to eliminate redundant computation in the threshold-selection criterion function. Finally, to achieve image segmentation, we search for the optimal threshold using the chaotic cuckoo search algorithm. The experimental results show that, compared with 2-D Arimoto-entropy thresholding method, the 2-D Renyi-entropy thresholding method based on particle swarm optimization, the 2-D Tsallis-gray-entropy thresholding method using chaotic particle swarm, and the 2-D Renyi-gray-entropy thresholding method based on the cuckoo search, our proposed method can segment objects more accurately and has a higher running speed.