## 3 Experimental Methods  
The experimental component of this work is divided into two sections: the first section applies the proposed method to a toy problem with a defined solution while the second investigates the use of the method on an real dataset with unknown ground truth values. Each of these individual experiments utilise a common framework for considering regression labelling tasks. The first aspect of this framework is to divide the annotators into three distinct groups. The first group, the _expert_ group, represents those who are the most experienced in completing the specific task and also take the most care to produce high-quality labels; members of this group are both incentivised and entrusted to take care in their work. It is also expected that, for datasets or annotation tasks where very-high-quality labels are required, such as those in medical device development, additional mechanisms and controls should be in place to ensure the quality of the _expert_ annotators. The following group, the _crowd-sourced_ annotators, are the next proficient and include members who are typically incentivised by the completion of the task alone; it is expectedthat some members of this group may perform similarly to _expert_ annotators, while others' performances will vary. While this group is called _crowd-sourced_, it may also include soon-to-be experts or experts in training, such as graduate medical students or trainee sub-specialists. Finally, the _adversarial_ group represents those who are either not paying any attention or are actively attempting to sabotage the results by entering incorrect results. This can occur when sourcing labels from crowds if adequate protections are not established or incentive structures do not promote high-quality labels. The incentive structure of crowdsourced work systems such as Mechanical Turk encourages workers to complete tasks as quickly as possible, which can lead to either rushed or simply invalid annotations. In most cases, labelling projects often require a careful selection of incentives to assist in gathering high-quality labels. These three distinct groups of annotators were selected following our previous experience in labelling projects and specifically our work described in [13], where we selected an _expert_ group of annotators and observed the presence of the _crowd-sourced_ and _adversarial_ groups during data collection. The observation of the _adversarial_ group also leads to additional controls being used in [13] to prevent and remove clearly erroneous data. With these three groups of annotators defined, it is clearly ideal to have a high number of _expert_ annotators only as this will provide the best chance of a high-quality dataset. While this is certainly true, it may not be practically achievable as other constraints like available time and cost may be realised, hence the probable need for the _crowd-sourced_ group. It is also obvious that, where possible, _adversarial_ annotators should be prevented or excluded from the study, but there are certainly some situations where they may be difficult to identify of exclude at the start of the study. The second component of the framework is to consider that, for most regression problems, it can be presumed that there exists some canonical ground truth value \(Y_{G}\) for each distinct point or landmark in the dataset that can be modelled. In some circumstances, consistently identifying \(Y_{G}\) may be easily achieved, while, in others, identifying \(Y_{G}\) may not be possible. This is particularly possible in situations where there is a high degree of subjectivity in the task (such as facial landmarking in the second experiment of this study) or where critical information is missing, e.g., the feature of interest in the image is obscured and cannot be easily seen.