Concave Function Measures And Medical Image Registration

Medical image registration is an active research problem in the medical image processing area.Multi-modal images give complementary information,which can be registered and fused to help clinician make a diagnosis.Some hybrid medical imaging systems can carry out image registration,but they are expensive,restricted modalities, and they can not compare images acquired at a different time point.When we analyze the differences of images acquired at a different time point,single modality image registration is considered,such as follow-up studies,for instance,for diagnosis of evolving disease processes such as MS or for assessing the outcome of therapy;or pre- and postoperatively acquired images,for instance,for validation of a surgical intervention.Medical image registration is also used to align cancer with planning target volume in accurate radiation therapy,which can increase the local control rate of cancer and decrease complications of normal tissues.With the development of image processing,computer and automation,medical image registration theory and techniques have been developed,which make automatic registration possible.So it is significant to research on automatic and modality-free medical image registration theory and techniques.Maximization of mutual information(MMI)has been extremely successful in automatically computing the registration of 3-D multimodal medical images of various organs from the image content itself.Mutual information(MI)is a basic concept from information theory,that is applied in the context of image registration to measure the amount of information that one image contains the other.The MMI registration criterion postulates that MI is maximal when the images are correctly aligned.MMI has been demonstrated to be a very general and powerful criterion,that can be applied automatically and reliably,without prior segmentation or preprocessing, on a large variety of applications.However,the methods of mutual information have unconquerable disadvantages,such as heavy cost of count,sensitivity to noise and excessive local extrema.These shortcomings restrict their broader practicable application.In the dissertation,a comprehensive analysis on medical image registration methods based on overall intensity information was accomplished.On account of the existing problems in multi-modal image registration,further discussions and investigations have been carried out.On the basis of enough analysis,detailed comparison,and adequate experiment,a novel class of practicable measures,a new data downsampling method,and a new class of MR intensity inhomogeneity correction methods were proposed.The main researches are as follows:(1)Different interpolation methods were analyzed and compared.Nearestneighbor (NN)interpolation is the simplest and quickest method,but least accurate. PV and second order GPVE interpolation are slower but accurate method.While PV interpolation yields local maxima of MI at grid-aligning positions,TRI interpolation yields local minima at these positions.This is explained by the fact that TRI interpolation blurs the reference image,making noise and other small scale structures disappear and therefore reducing histogram dispersion.At grid-aligning positions, however,no blurring is applied and the joint entropy can,therefore,be higher(and, hence,MI smaller)for grid-aligning transformations than for nonrigrid-aligning transformations.PV histogram dispersion increases again when moving away from grid-aligning positions,so PV interpolation may yield a local maximum of MI at these positions.(2)Considering the disadvantages of MI measure,a number of new registration measures were proposed.The new measures were derived by replacing the Shannon entropy function in mutual information with any strictly concave function,which were named mutual strictly concave function measures(NM_i,i=1,2,...,6).MI measure is a particular case.By comparing and analyzing MI,two f-information and five mutual strictly concave function measures,the following conclusions are drawn: Mutual strictly concave function measures whose power is greater than 1,NM₂,NM₄, and NM₅,increase stable region and decrease registration time,which is very valuable to real-time registration;Mutual strictly concave function measures whose power is smaller than 1,NM₃ and NM₆,are unfit for align medical image,because they have many local extrema that may result in wrong registration and they consume more time than NM₂,NM₄,and NM₅;Mutual strictly convex function measure may also be used to align medical images,and its minimum corresponds to correct registration.(3)According to Jensen inequality and Schur concave function,Jensen-Schur measures were proposed,which enlarged the definition of mutual strictly concave function measures and whose independent variable was a vector.Jensen-Rényi measure is a particular case of Jensen-Schur measures.When weight vector,ω,is uniform weight,Jensen-Schur measures are improper to register.Whenωis the probability density function of reference image,the new constructed measures JS₂, JS₃ and JS_w outperform JR,MI and NMI in the computational speed, convergence performance and noise immunity.(4)According to a simple Schur concave function and the definitions of Jensen-Schur measure,generalized divergence measure and f-information measure, six new measures were constructed.The Schur function with special concave characteristics can filter the small probability distribution caused by noise, interpolation and so on.The characters of six new measures,mutual information and normalized mutual information were analyzed and compared by applying them to rigid registration.The results of tests show that JS^βand D^βmeasures outperform other measures in convergence performance and noise immunity,and they are time saving in comparison with mutual information and normalized mutual information measures.The parameterαaffects the performance of measures.(5)The conventional downsampling methods are divided into two classes: uniform subsampling and nonuniform subsampling.The former can stable the intensity pdf,but can not consider important edge information;the latter is reverse.A new downsampling method based on intensity probability distribution and gradient information of floating image was proposed,which was named as pdgs downsampling method.Pdgs method can stable intensity pdf and sample enough point in floating image.The measure function curves and convergence were compared by applying five subsampling methods to the rigid registration of brain images.The results of tests show that the new downsampling method outperforms other downsampling methods in less extrema and convergence performance of the normalized mutual information.(6)Intensity inhomogeneity does harm to image registration,so it need to be removed before MR image registration.In the intensity inhomogeneity correction of MR image,since entropy minimization method did not consider space information,a better correction method based on joint information minimization was proposed, which integrated image intensity features with additional spatial image features.The space features referred to intensity derivatives.The joint entropy between image intensities and corresponding derivatives in a corrupted image is greater than that in an uncorrupted one,and it is calculated by using the joint probability distribution of image intensities and corresponding derivatives.The results on simulated brain images and clinical brain MR images show that joint information minimization method between intensities and their second derivatives is good.It can largely decrease the overlap between white matter and gray matter.So this method is a generic method,requires no preprocessing,no parameter setting,and is proved to be feasible and efficient.