Adding Curvature to Minimum Description Length Shape Models

The Minimum Description Length (MDL) approach to shape modelling seeks a compact description of a set of shapes in terms of the coordinates of marks on the shapes. It has been shown that the mark positions resulting from this optimisation to a large extent solve the so-called point correspondence problem: How to select points on shapes defined as curves so that the points correspond across a data set. However, this MDL approach does not capture important shape characteristics related to the curvature of the curves, and occasionally it places marks in obvious conflict with the human notion of point correspondence. This paper shows how the MDL approach can be fine-tuned by adding a term to the cost function expressing the mismatch of curvature features across the data set. The method is illustrated on silhouettes of adult heads. The MDL method is able to solve the point correspondence problem and a classification of the heads into male and female improves dramatically when using the MDL-generated marks

Statistical Shape Modelling for the Levator Ani

Defective pelvic organ support due to injuries of the levator ani is a common problem in women and its intervention requires a thorough understanding of the structure. Three-dimensional surfaces of the levator ani have proved to be a promising method of studying this. In this paper, we propose to build a statistical shape model (SSM) of the levator ani and describe a segmentation technique based on a limited number of control points with the SSM. The SSM was achieved by the use of harmonic shape embedding with the MDL objective function to optimise parameterisation while segmentation was performed by fitting the model to a user defined set of control points. The value of the technique was demonstrated with data acquired from a group of 11 asymptomatic subjects.Accepted versio

Multilevel principal component analysis (mPCA) in shape analysis: a feasibility study in medical and dental imaging

Background and objective Methods used in image processing should reflect any multilevel structures inherent in the image dataset or they run the risk of functioning inadequately. We wish to test the feasibility of multilevel principal components analysis (PCA) to build active shape models (ASMs) for cases relevant to medical and dental imaging. Methods Multilevel PCA was used to carry out model fitting to sets of landmark points and it was compared to the results of “standard” (single-level) PCA. Proof of principle was tested by applying mPCA to model basic peri-oral expressions (happy, neutral, sad) approximated to the junction between the mouth/lips. Monte Carlo simulations were used to create this data which allowed exploration of practical implementation issues such as the number of landmark points, number of images, and number of groups (i.e., “expressions” for this example). To further test the robustness of the method, mPCA was subsequently applied to a dental imaging dataset utilising landmark points (placed by different clinicians) along the boundary of mandibular cortical bone in panoramic radiographs of the face. Results Changes of expression that varied between groups were modelled correctly at one level of the model and changes in lip width that varied within groups at another for the Monte Carlo dataset. Extreme cases in the test dataset were modelled adequately by mPCA but not by standard PCA. Similarly, variations in the shape of the cortical bone were modelled by one level of mPCA and variations between the experts at another for the panoramic radiographs dataset. Results for mPCA were found to be comparable to those of standard PCA for point-to-point errors via miss-one-out testing for this dataset. These errors reduce with increasing number of eigenvectors/values retained, as expected. Conclusions We have shown that mPCA can be used in shape models for dental and medical image processing. mPCA was found to provide more control and flexibility when compared to standard “single-level” PCA. Specifically, mPCA is preferable to “standard” PCA when multiple levels occur naturally in the dataset

A hierarchical curve-based approach to the analysis of manifold data

One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Stereophotogrammetry and laser scanning are two widely available sources of this kind of data. A standardised surface representation is required to provide a meaningful correspondence across different images as a basis for statistical analysis. Point locations with anatomical definitions, referred to as landmarks, have been the traditional approach. Landmarks can also be taken as the starting point for more general surface representations, often using templates which are warped on to an observed surface by matching landmark positions and subsequent local adjustment of the surface. The aim of the present paper is to provide a new approach which places anatomical curves at the heart of the surface representation and its analysis. Curves provide intermediate structures which capture the principal features of the manifold (surface) of interest through its ridges and valleys. As landmarks are often available these are used as anchoring points, but surface curvature information is the principal guide in estimating the curve locations. The surface patches between these curves are relatively flat and can be represented in a standardised manner by appropriate surface transects to give a complete surface model. This new approach does not require the use of a template, reference sample or any external information to guide the method and, when compared with a surface based approach, the estimation of curves is shown to have improved performance. In addition, examples involving applications to mussel shells and human faces show that the analysis of curve information can deliver more targeted and effective insight than the use of full surface information