【作者】 陈亮；

【导师】 胡光华；

【作者基本信息】 云南大学 ， 计算数学， 2015， 硕士

【摘要】 形态学异联想记忆(Morphological Hetero-associative Memories,MHM)是一种模拟人脑联想记忆功能的数学模型。与传统的联想记忆模型相比,MHM不仅能处理二值模式还能处理实值模式,且具有良好的抗膨胀噪声或腐蚀噪声的能力,在模式识别、图像处理等领域中有广阔的应用前景和强大的生命力。虽然MHM有很多优点,但即便输入模式没有噪声,也不能够保证完全联想记忆。针对MHM的这一缺点,本文做了如下工作：首先,对二值模式的MHM进行了研究,提出了定理2。该定理给出了二值模式的MHM能够完全联想记忆的一个充分条件。根据该条件,本文利用了二值图像特征信息分别对MHM的W记忆算法和M记忆算法的输入模式进行修改,提出了两种新的联想记忆算法——BFW算法和BFM算法。最后通过实例验证了这两种算法比MHM的记忆性能更好。其次,对实值模式的MHM进行了研究,提出了实值模式的MHM能够完全联想记忆的一个充要条件,并给出了定理3。根据该条件,本文利用了灰度图像特征信息分别对MHM的W记忆算法和M记忆算法的输入模式进行修改,提出了两种新的联想记忆算法——GFW算法和GFM算法。最后通过实例验证了这两种算法比MHM的记忆性能更好。最后,本文利用GFW算法或GFM算法,提出了一种新颖的秘密图像共享算法。该算法利用GFW算法或GFM算法对假图像和秘密图像构成的图像对进行记忆得到记忆矩阵,再分别对假图像和记忆矩阵加入随机的单一噪声,生成n个含噪声的假图像和n个含噪声的记忆矩阵,并分发给n个参与者。其中任意n-1个参与者都可以通过n-1个含噪声的假图像取小或取大得到无噪声的假图像,同理n-1个参与者也可以得到无噪声的记忆矩阵。用无噪声的假图像为输入图像,通过无噪声的记忆矩阵联想得到秘密图像。最后通过实例验证了该算法是可行的。更多还原

【Abstract】 Morphological Hetero-associative Memories (MHM) is a kind of simulation mathematical model of associative memory function of human brain. Compared with the traditional associative memory model, MHM not only has capability of handling binary pattern but also can deal with the real mode, and it has good noise-tolerance to single erosive or dilative noise, as well as broad application prospects and strong vitality in pattern recognition, image processing, and so on. Although MHM has many advantages, it can’t provide perfect recall even if there is no noise in the input pattern. For the shortcoming of MHM, the following work is done in this paper.Firstly, the MHM of the binary pattern has been studied, and proposed the theorem2. The theorem gives a sufficient condition about MHM of binary pattern can provide perfect recall. According to this condition, this paper used the binary image feature information respectively to modify the input mode of W memory algorithms and M memory algorithm and proposed two new algorithms-BFW algorithm and BFM algorithm. Finally, the two algorithms have been proved that they have better memory performance than MHM by using the examples.Secondly, the MHM of the real pattern has been studied, and proposed the theorem3. The theorem gives a sufficient and necessary conditions about MHM of real pattern can provide perfect recall. According to this condition, this paper used the gray-scale image feature information respectively to modify the input mode of W memory algorithms and M memory algorithm and proposed two new algorithms-GFW algorithm and GFM algorithm. Finally, the two algorithms have been proved that they have better memory performance than MHM by using the examples.At last, in this paper, a novel secret image sharing algorithm was proposed based on GFW algorithm or GFM algorithm. This algorithm can get the memory matix by GFW or GFM algorithm recalling to false image and secret image. And then we add the random single-noise to the false image and memory matrix, so we can get n false images and n memory matrices which contain noise and distribute them to n participants. But only n-1participants can get n-1no-noise images through the n-1noise images which maximizing or minimizing. In the same way, n-1participants can get n-1memory matrices. We use no-noise false image as input image and use the no-noise memory metrix to get the secret image. Finally, the feasibility of the algorithm is varified by a practical example.更多还原