thereforeFshapeis calculated based on the first 7 eigenvalues.
C.5.2.5 Parameter Estimation
Finding the optimal relation between the prior and the observation model de-pends on the data and the application. A sort of objective function is needed to determine the parameters of the model. In this application,x the data is used to build a shape model and therefore an obvious choice of objective function is linked to the optimality of the shape model. In figure C.7 it is seen that the shape model is optimal with respect toFshapeatα= 0.2.
The parameters could also be chosen with respect to the mesh quality measure or the approximation error defined in section C.5.2.3. In figure C.7 box plots of the mesh quality and approximation error as function ofαare shown. It is seen that α= 1.0 would be optimal with respect to the mesh quality, thus reducing the Markov model to a pure prior model. On the other hand the improvement in mesh quality fromα= 0.2 toα= 1.0 is so small that choosingα= 0.2 could be argued to optimise both the shape model and the mesh properties.
ar-C.6 Conclusion 145
0.0 0.2 0.4 0.6 0.8 1.0
0.0420.0440.0460.0480.050
α
Approximation Error
(a)
0.0 0.2 0.4 0.6 0.8 1.0
45.8045.8545.9045.9546.00
α
Shapemodel Compactness
(b)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.040.060.080.10
α
Approximation Error
(c)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
15202530
α
Mesh Quality
(d)
Figure C.7: a) The average surface approximation error Fapp over all training shape. b) Shape model optimality with respect to Fshape. c) Box-plot of the surface approximation errorsFapp. d) Box-plot of the mesh qualityFtri.
ticle. The regularisation also improves the approximation of the training shapes by making the resulting dense meshes more homogeneous.
In the proposed method, the parameters of the model are chosen globally, mean-ing that the weightmean-ing of the prior and the observation model is the same over the entire surface. It is possible that a model with site-specific weightingαi would provide even better results. The site-specific weighting could be learned from a training set based on multiple expectation-maximisation parameter analysis.
This is, however, out of the scope of this article.
Acknowledgements
The work was supported by the Academy of Technical Sciences by grant num-ber EF915. The authors also thank Søren Laugesen and Claus Nielsen from Research Centre Eriksholm, Oticon A/S for guidance and data. The Visual-ization Toolkit (http://www.vtk.org/) was used as software platform and for visualisations.
Appendix D
Using a Shape Model in the Design of Hearing Aids
Rasmus R. Paulsen, Claus Nielsen, Søren Laugesen, and Rasmus Larsen
Abstract
Today the design of custom completely-in-the-canal hearing aids is a manual process and therefore there is a variation in the quality of the finished hearing aids. Especially the placement of the so-called faceplate on the hearing aid strongly influences the size and shape of the hearing aid. Since the future hearing aid production will be less manual there is a need for algorithms that mimic the craftsmanship of skilled operators. In this paper it is described how a statistical shape model of the ear canal can be used to predict the placement of the faceplate on a hearing aid made for a given ear canal. The shape model is a point distribution model built using a training set of shapes with manually placed landmarks. An interpolation method is used to generate dense landmark correspondence over the training set prior to building the shape model. Faceplates have also been placed on the training shapes by a skilled operator. These faceplate planes are aligned to the average shape from the shape model and an average faceplate plane is calculated. Given a surface representation of a new ear canal, the shape model is fitted using a combination of the iterative closest point algorithm and the active shape model approach. The average faceplate from the training set can now be placed on the new ear canal using the position of the fitted shape model.
A leave-one-out study shows that the algorithm is able to produce results comparable to a human operator.
D.1 Introduction
Today the production of custom completely-in-the-canal (CIC) hearing aids is a manual process. For a CIC hearing aid, all components reside in a custom-made shell that sits in the ear of the user. The shell is cast in a hard acrylic material based on an ear impression and then ground down to the desired size.
The shell is then glued together with the so-called faceplate in which the battery compartment and the microphone are mounted from the factory. The remaining internal components of the hearing aid: the loudspeaker, the amplifier and the ventilation tube are positioned inside the shell. All these processes are done by hand and this induces a variation in the quality of the final products. See [55]
for a more thorough introduction to CIC hearing aids. An actual faceplate and the corresponding CAD model can be seen in figure D.1.
Figure D.1: The faceplate used in the Oticon Adapto CIC hearing aid.
In Fig. D.2 two CIC hearing aids made for the same ear canal are seen. It is seen that the left CIC is smaller than the one to the right. The size difference is mainly due to the placement of the faceplate. The placement of the faceplate also influences the visual appearance of the finished CIC in the ear. These two hearing aids come from the Eriksholm clinic and are made following the standard procedure. Since they are not made for any special purposes, they reflect the standard variance seen in the shapes of final CIC hearing aids. Even though a large part of the elderly population suffers from hearing loss there is a social stigma associated with having a hearing aid. One way to alleviate that problem is to convince people that it is acceptable to wear a hearing aid.
Another way is to design hearing aids to be as discreet as possible.
Manufacturers of hearing aids have made initial testing of rapid prototyping of hearing aid shells using laser scans of ear impressions [254, 210]. In this process the hearing aid is designed using a custom computer aided design program. This means that the quality of the final product is still dependent of the intuition and
D.1 Introduction 149 skills of the human operator. Thus, an automatic method capable of mimicking the craftsmanship of the best skilled operators would be useful in the design process.
In this paper it is described how a statistical shape model of the human ear canal is used to predict the placement of the faceplate on a custom CIC hearing aid. The input data consists of expert placements of faceplates and the goal is to generate a system that is able to mimic the expert placements based on the assumption that the expert placements are related to the anatomy of the ear canals.
Figure D.2: Two CIC hearing aids made for the same ear canal. It is seen that the left CIC is smaller than the one to the right. The size difference is mainly due to the placement of the faceplate. It is seen that the visual appearance of the hearing aid in the ear is strongly influenced by the size.
The statistical modelling of shapes has in recent years been heavily influenced by the development of learning based models. A fairly sophisticated learning based deformable template model is the Active Shape Model developed by Cootes et al. in 1995, which uses principal component analysis of the shape space [61].
This method has previously been used to build a full 3D statistical shape model of the human ear canal [201]. The model is based on a set of 29 laser scanned ear impressions. Anatomical landmarks were placed on the surfaces of this training set and an interpolation method was used to generate a dense surface descrip-tion. The method is similar to the methods described in [184] and [143]. The method has later been extended to include a Markov Random Field restoration step to remove artifacts arising due to a closest point correspondence step used in the original method [127, 199]. A thorough description of the anatomy of the human ear canal can be found in [17].