The accelerating advancement in surface-imaging technology has led to promising possibilities with respect to monitoring patient positioning during radiation therapy without the use of radiographic imaging. The aim of this chapter is to introduce theoretical aspects and key computational techniques utilized in estimating positioning errors and analysing the patient's surface during radiation treatment. In particular, we provide an overview of current surface-imaging technologies. Next, we introduce quantitative approaches for mathematical reconstruction of a patient's surface using non-uniform rational B-spline (NURBS) modelling and subsequently characterizing of the local shapes of the patient's surface based on differential geometry. In addition, an iterative closest point (ICP) registration algorithm, which is a basic technique for estimating positioning errors, is explained. We hope that the topics covered in this chapter will be assistive in understanding the current applications in the field and will create launching points for the development of novel solutions.
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