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Images can contain objects that have poorly defined or partially occluded boundaries and structure. In these situations, where image evidence is inadequate and confusing, models can help to resolve ambiguities and organise evidence by adding explicit information about the objects to be identified. The modelling of shape is an important and useful method to constrain image search. Statistical shape models are able to describe allowable variability and can be trained on sets of examples [see Fellowship Project: Flexible Models for Computer Vision]. Many shape modelling techniques make use of points that are consistently present and distinguishable across a set of example images. These points are called landmarks. Modelling the variation of landmark points over a training set is a powerful technique in image analysis, and has been applied successfully in many areas. However, some objects cannot easily be described in this way, e.g. microscopic structures such as cells. Objects such as this often have no fixed form or consistent features that can be used as landmark points. Because of this, alternative shape modelling techniques describing overall shape are required. Nerve capillaries provide an example of a type of object that is not suitable to be modelled using landmarks. The image above shows a typical capillary image with the basement membrane boundary overlayed. A model-free interpretation of these images does not give adequate results due to the poor-contrast and vagueness of the boundary regions and ambiguities in local image evidence. A model would provide explicit shape information to constrain search in order to overcome these problems. However, the objects in these images have no intrinsic orientation, either in structure or camera alignment, and no fixed form. Also, the overall shape of the capillaries varies irregularly throughout the set of images. These features make it difficult to identify enough suitable points to apply a landmark based modelling technique, and therefore some other form of shape model is required to aid segmentation. Previous approaches to segment these images using data-driven methods (snakes) have been partially successful but, due to the under-constrained nature of the problem, they are prone to fail in areas of poor or confusing local image evidence. In particular, snakes can become 'caught' on areas of image evidence that are not globally consistent with a good solution. An initial approach to improve on data-driven methods is being made using a trainable shape model based on Fourier descriptors [Staib and Duncan, 1992]. Capillary boundaries are described by parameters which are calculated from a harmonic Fourier decomposition of shape. The image above shows the capillary basement membrane boundary that has been reconstructed from 32 shape parameters which were generated from the first 8 Fourier harmonics. The level of detail to which the boundaries are modelled can be increased by calculating a greater number of harmonics during decomposition. Standard statistical analysis is then carried out on these parameters to describe the types of variability that are encountered within the training set. This shape model can be used to constrain a data-driven search for examples of capillaries in new images by generating a probability for each candidate boundary. This probability can be used to favour solutions that are consistent with local image evidence and that are also within the set of likely deformations. The shape information contained within the model adds further constraints to the problem allowing a more accurate segmentation to be achieved. L.H. Staib and J.S. Duncan, ``Boundary Finding with Parametrically Deformable Models,'' IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, pp. 1061-1075, 1992. Funding for this project was provided by the EPSRC. Mike Rogers: mike.rodgers@man.ac.uk Research Courses Clinical Radiology Industrial liaison Contact Us Join Us Search Home Contact
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