This section will discuss important future developments of the registration and nor- malization process, the local shape characterization measures, and how the measures could be implemented within a dimensional assessment framework.
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7.9.1 Registration and Normalization
Future generalization of the registration and normalization process to capture variation across an entire surface (rather than rectangular grids which only capture part of the surface within a specified area), and surfaces that are not nominally at, will require different treatment to that proposed in this thesis. In applications such as computer vision, a different approach to the registration of deformable objects such as sheet metal assemblies known as non-rigid point set registration is often used (Zitova and Flusser, 2003). These approaches involve a combination of spatial feature detection (such as edges and corners), and constrained point set mapping, and could allow for registration of entire surfaces. These techniques were not applied in this thesis as there are several issues that need to be addressed before they can be effectively implemented for this approach, such as questions over accuracy of the method (due to the small deformations that need to be captured), required quality of scan data, and processing time, which were deemed beyond the scope of this thesis. The normalization process for surfaces that are not nominally at also presents many issues, such as the need to map the nominally curved surface into a 2.5D representation. This could be achieved using established methods (Sheffer and de Sturler, 2001), however, it is again beyond the scope of this thesis.
7.9.2 Curvature-based methods
Once the registration and normalization issues have been addressed, the curvature en- ergy and thresholds approaches are easily adaptable to any surface, as the approaches are scale, translation, and rotation invariant. This means that irrespective of the ori- entation of the surfaces or local features, the same curvature based assessment will result. Key areas of refinement required for the future use of these methods however is surface denoising, the curvature calculation method, and computational speed. Curva- ture calculations are very sensitive to noise, so effective denoising is an important step for the accurate implementation of such methods. The curvature calculation method used in this chapter where a biquadratic is fit to a local area is one of the more popu- lar approaches, however, there are other methods that could be explored to check for suitability for this application. Magid et al. (2007) provide an overview of a range of approaches for curvature calculation. Perhaps the biggest issue to address is that of computational speed. In order for the approach to be more practically implementable, particularly in a fast paced manufacturing environment, the curvature measures must be quickly accessible. The advent of less expensive and more powerful multi-core com- puters could be a solution, as surface curvature calculations lend themselves well to multi-threading approaches.
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7.9.3 Multi-scale surface analysis
In this chapter, the average power of the continuous wavelet transform of a series of lengthwise cross-sections at specified scales was used to identify the presence of local features of interest on a surface. One advantage of this approach is that as only a few select scales are required, the computational burden is relatively low. Usually when applying the CWT for signal analysis, calculation of the transform across a large range of scales is required which can be computationally expensive; the discrete wavelet transform has therefore often been chosen in favour of the CWT due to computational advantages. The discrete wavelet transform however can only compute at particular scales (2n) due to a down-sampling process. This makes it di cult to match the appropriate scale to the size of the local features of interest using the DWT, which is why it was not selected for this application. The CWT approach presented in this chapter also holds a few benefits over the curvature-based methods. For one, the CWT approach is well suited to dealing with noise, whereas the curvature-based methods can suffer considerably in the presence of noise. Furthermore, the CWT approach is more computationally forgiving than the curvature-based approaches.
For future use, the CWT approach can be readily developed to allow for a more general local characterisation of free form surfaces. For one, cross-sections in other directions could be used, such as in the width-wise and diagonal directions as done with the discrete wavelet transform. This would enable scale features in other directions to be captured as well. As the CWT approach is not rotation invariant (ie, the scale of features found on a surface is largely dependant on the orientation of the cross section), taking the cross sections at a number of angles could be an important method for reducing the sensitivity of the approach to orientation. Another key extension to the method is to ensure that the same effective size of features is being investigated. This can be achieved by adjusting the wavelet scale according to the length of the signal. This is especially suited to dealing with non-rectangular surfaces, where cross- sectional lengths could change. Other user defined wavelets could also be proposed to more closely match the exact type of local features of interest. Overall, the CWT method proposed for local shape characterization provides a powerful and potentially very practical approach for describing localized features in manufactured shapes.
7.9.4 A view to surface classi cation
This chapter has proposed a shape characterization vector that can provide discrimi- nation between differing manifestations of local shape varication. Now that a way of describing local variation has been developed, the next key stage in a quality assessment framework is to develop a relationship between the local shape vector and customer perceptions of quality, which is far from a trivial task. A common approach in pattern
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recognition is to use a labelled training data set with which to train a classifier. This could involve a customer defining or ranking a set of manufactured shapes based on some criteria, and then testing to see if a classifier built around the local shape charac- terization measures can replicate the customer definitions of quality. This process will be disused in more detail in the following chapter.
7.10
Conclusion
This chapter presents a novel approach for the description of the nature in which a manufactured surface locally deviates from its nominal design. A multi-tiered approach is suggested:
• Surface curvature energy, which is the integral of the curvature squared across a surface, provides an overall measure of the curvature of a surface, and can therefore distinguish between translated and highly distorted parts.
• The continuous wavelet transform is used to decompose the surface into scale components. Average energy values are then used to rank surfaces in terms of different scale components present in surfaces.
• Curvature based thresholds are then used to extract curvature defined features of interest.
Each shape characterization tier addresses a limitation of the previous measure, and in combination with each other, the measures provide a diverse mix of features with which to discriminate between different types of local deviations of a manufactured surface from its nominal design. Now that a numerical local shape characterization approach has been developed, the next key step is to develop a mapping between these features and customer quality perceptions of an end product. The next chapter will therefore firstly proceed to discuss how the local shape characterization approach can be integrated within a shape quality framework for the classification, assessment, and section of optimal processes for dimensional control. The next chapter will then summarise the key contributions of this thesis along with avenues of future research.
Chapter 8
Conclusion
8.1
Introduction
This chapter initially provides a conceptual framework for the implementation and integration of the various tools and techniques presented throughout this thesis for the purpose of dimensional control of sheet metal assembly variation. It will then proceed to review the major contributions of this thesis, and finally discuss future avenues of research that would extend the application of the work proposed by this thesis.