Differences

This shows you the differences between two versions of the page.

@@ Line 1: / Line 1: @@
+Assessing the Accuracy of Non-Rigid Registration
+Non-rigid registration (NRR) of both pairs and groups of images has in
+recent years increasingly been used as a basis for medical image analysis.
+The problem is highly under-constrained and a host of algorithms that have
+become available will, given a set of images to be registered, in general
+produce different results. We present two methods for assessing the
+performance of non-rigid registration algorithms, compare them on a
+registration of a set of 38 MR brain images and show them to provide a
+robust evaluation of registration success.
+The first of the proposed methods assesses registration as the spatial
+overlap, defined using Tanimoto's formulation [Ref], of corresponding
+regions in the registered images. The correspondence is defined by labels of
+distinct image regions (in this case brain tissue classes), produced by
+manual mark-up of the original images (ground truth labels). A correctly
+registered image set, will exhibit high relative overlap between
+corresponding brain structures in different images and the other way around.
+The second method assesses registration as the quality of a generative,
+statistical appearance model, constructed from registered images. The idea
+is that a correct registration produces a true dense correspondence between
+the images resulting in a better statistical appearance model of the images.
+Registration is then evaluated through specificity and generalisation
+ability of the model, or the ability of the model to i) generate realistic
+examples of the modelled entity and ii) represent well both seen and unseen
+examples of the modelled class. In practice these are evaluated by using
+generative properties of the model to produce a large number of synthetic
+examples (in this case brain images) that are then compared to real examples
+in the original set using some pre-defined image distance measure. Minimum
+distances of synthetic examples to examples in the original set and vice
+versa, give model specificity and generalisation respectively. Image
+distance is measured as a mean shuffle distance, or minimum euclidian
+distance between a pixel in one image and a corresponding neighbourhood of
+pixels in the other.
+To test the validity of the proposed methods, the brain images were
+annotated with 6 tissue classes including gray, white matter and CSF that
+provided the ground truth for image correspondence. Initially, the images
+were brought into alignment using an NRR algorithm based on the MDL
+optimisation [Ref us IPMI say]. A test set of different registrations was
+then created by applying random perturbation to each image in the registered
+set using diffeomorphic clamped-plate splines. By choosing a different
+perturbation seed for each image and gradually increasing the magnitude of
+the perturbations a series of image sets of progressively worse spatial
+correspondence and thus registration quality was obtained. By measuring the
+quality of the registraton at each step the proposed registration assessment
+measures can be validated.
+Overall, the above approach was applied 10 times using 10 different
+perturbation seeds to ensure that both methods are consistent and results
+unbiased. Results of the proposed measures for increasing registration
+perturbation are shown in Figure 1, note that Generalisation and Specificity
+plotted for different shuffle neighbourhood radious are in error form, i.e.
+they increase with decreasing performance. All metrics are generally
+well-behaved and show a monotonic decrease in registration performance. Such
+results directly validate the model based metrics which are shown be in
+agreement with the ground truth embodied in the region overlap based
+measure.
+<Graphics file: ./Graphics/1.eps>
+Figure 1: Behaviour of proposed metrics with increasing registration
+perturbation: a) Generalisation, b) Specificity and c) Tantimoto overlap
+Finally, in order to obtain a quantitative comparison of the proposed
+algorithms we explore sensitivity of the proposed metrics, where the
+slighter the difference which can be detected reliably, the more sensitive
+the method. Sensitivity is in this case defined as the rate of change in the
+measure for a given perturbation range - normalised by the average
+uncertainty in the measurement over that range:
+where X is... (TODO). Sensitivity is evaluated for all three of the proposed
+metrics and shown in Figure 2 with errors bars based on both an
+inter-instantiation error and a measure-specific error. The Specificity
+measure is the most sensitive for any radius of the shuffle distance
+followed by the overlap metric and Generalisation, with shuffle radii of 1.5
+and 2.1 (equivalent to 3x3 and 5x5 neighbourhoods) giving optimal
+sensitivity.
+Figure 2: Sensitivity of the proposed metrics
+The results shown in this abstract indicate that registration performance
+can be evaluated reliably both in the cases when ground truth information is
+available and when it is not. In particular, the methods based on generative
+statistical model evaluation are shown to be in agreement with the ground
+truth expressed throught the true image region overlap metric based on the
+Tantimoto formulation. Proposed metrics are also shown to have sufficient
+sensitivity to detect very subtle changes in registration performance, on
+the level of perturbations measured in fractions of a pixel.

Schestowitz Wiki

User Tools

Site Tools

Differences

Page Tools