新的Cauchy-Schwarz距离函数与多模态医学图像配准

信息论测度,特别是Shannon互信息是多模态图像配准的一种重要方法,但除了互信息之外,仍然存在其它的函数来实现这一任务。对互信息、Kullback-Leibler距离和Shannon不等式之间相互关系作了分析,根据这些关系和不等式理论,提出了新的Cauchy-Schwarz距离,并将这一距离测度用于多模态医学图像的配准处理。从计算速度、噪声容忍性、测度函数图形的特点和图像窗口大小影响等几个方面,通过MR和PET医学图像的实验分析,对新的Cauchy-Schwarz距离测度和典型的Shannon信息论测度进行了分析比较。实验结果表明,新的Cauchy-Schwarz距离测度函数同样可以用于多模态图像配准,而且有着更强的噪声容忍性和更为节省的计算量。

Novel divergence measure based on Cauchy-Schwarz for multimodal medical image registration

Information theoretic similarity measures, especially mutual information, have been widely and successfully employed in multimodal image registration. Apart from these metrics, however, there are other measures which could be considered for image registration. A new similarity metrics was introduced for this task. The connections between Shannon mutual information, Kullback-Leibler divergence and Shannon inequality were analyzed. From these connections and Cauchy-Schwarz inequality, a novel generalized divergence was proposed. According to the new divergence function, a novel similarity measure based on Cauchy-Schwarz inequality for multi-modal image registration was put forward. Unlike Kullback-Leibler divergence, the new measures have some fundamental and appealing mathematical properties such as convexity, symmetry and do not require the condition of absolute continuity to be satisfied by the probability distribution involved. The performance of mutual information and normalized mutual information with the new similarity measures were compared. These measures are applied to rigid registration of clinical MR/PET images. An accurate gold standard transformation is avail able for the images. The results of tests indicated these new similarity functions have even better performance, compared with Shannon information theoretic measures.