InitRech 2015/2016, sujet 13

Summary

Female pelvic disorder such as the organ prolapse becomes a very common problem as a woman ages.About 20 to 30% women suffer from the severe degree of prolapse and more than 60% of women who are over 60 years are affected by this pathology.These problems are connected to the mobility of female pelvic system.In this system, a meaningful analysis of medical images usually decides the physicain's diagnosis.However, a human perception or a medical experience cannot be avoided and these two factors may cause the variability in the diagnoses.In this paper, people introduced a new method that can be classified as a model-to-image correlation approach to avoid these problems.The method performs fast semi-automatic detection of the bladder,vagina and rectum from magnetic resonance images for geometries reconstruction and further study of the mobilities.

Fisrt of all,people propsed a semi-automatic method to do the detection of the oragns.This step is an important and preliminary step for the further studies and modelling.Then they used a peridodic B-splines and offsets algorithm to create thick surfaces of hollow pelvic organs.This modelling was a step between segmentation and physical modelling.To achieve the surface modelling of patient specifc organ geometries,two steps were needed:segmentation and geometric modelling.People used some algorithms to acomplish these two goals.Despite their success, these methods were all pixel-based approach,which means that they could not provide directely smooth and accurate contour.Hence another modelling method called 'model-to-image' was carried out.

Two main steps were demanded for this method:initialisation of a fine model and deformation of the model.At first,a powerful B-spline functions for buliding the snake model(active contour) were introduced.But because of its demand for good initialisation of models which were not easy to create and for good positions of points,this method could not produce the results that people desired.Thus people introduced a new B-spline-like method.

As model-based approach was widely used for medical image processing,in this paper people introduced a new model-to-image approach.The idea was to combine the method of 'Active Contour' with the 'Virtual Image' approach.People used a cost function to find the best correlation between the virtual images and the real ones.In the end,this method became an energy minimisation problem.

To do the optimisation procedure,four important parts were demanded:

• input data(3D static and 2D dynamic MR images of the patient)
• a mathematical model with variables to be optimised(B-spline Model section)
• a cost function,which links the model to the input data
• an optimiser to minimise the cost function

Main Contribution

The proposed approach can be formulated as an optimisation procedure in the view of computation.Hence, 4 major parts are needed: 1.input data(3D static and 2D dynamic MR images) 2.a mathematical model with variables to be optimised(B-spline Model) 3.a cost function that links the model to the input data(Cost Function Formulation) 4.an optimiser that finds the optimal values of the parameters to minimise the cost function(Optimisation) First of all, we are going to introduce the MRI and Correlation method.This method consists of two types of images,static images and dynamic images.Static images can provide 3D information(sagittal,axial and coronal) while dynamic images are a temporal sequence of 2D images.In the study,the 2D dynamic images are obtained in the same midline sagittal plane of the patient as 3D images.We were mostly interested in segmentations of 3 organs(bladder,vagina and rectum) because both 2D sagittal static and dynamic MR images used these organ segmantations.For the registration procedure of a multi-scale optimisation,we needed two steps:an affine transformation of the model for the coarse registration and a B-spline deformation for the finer registration.To model the geometries of these three organs, the 2D B-spline of 3-degree method is used.In this method, we used a uniformly spaced knot vector to define the basis functions of p-degree.We could also define a span of the B-spline curve by each interval between two degrees.And then each organ can be presented by a parametric B-spline curve and each position on the curve can be calculated.The first and last control point of each curve are attached to form a closed curve.Thus,the model is analytical.As to the affine transformation step,a matrix of mapping was used.To link the model to the input data, we created an appropriate cost function.To calculate,a virtual image is generated from the model that finds the best correlation with the real image.With both the width value and the grey levels, we could detect the real images.As for the registration part,optimisation is the step which can connect the cost function(energy) and the model.