Denoising plays a vital role in freeform structured surface metrology. Traditional techniques, such as Gaussian and partial differential equation-based diffusion filters, often involve a time-consuming calibration process, particularly for complex surfaces. The main challenge lies in automating the denoising operation while accurately preserving features for varied surface textures. To address this challenge, an automatic approach PI-DnCNN based on small sample learning is presented in this paper. Denoising convolutional neural network (DnCNN) is employed as the basic architecture of this approach, due to its effectiveness in tackling mix-level Gaussian noise and adapting to small training datasets. Acknowledging the constraints of limited datasets, a novel physics-informed denoising loss function marrying filtering techniques is proposed to improve model performance. Additionally, a hybrid data augmentation strategy is developed to enhance the recognition of complex components. The paper also reports a set of experiments to demonstrate the presented approach in terms of performance over conventional techniques, enhancements with limited sample sizes, and applicability in general image denoising. The experiment results suggest that the presented approach consistently achieves higher average scores compared to traditional filters and emerges superior compared to the conventional DnCNN loss across different dataset sizes. In addition, the proposed loss also shows effectiveness in general image denoising, which suggests the robustness and universality of the approach.

In this paper a metrology-oriented specification schema is proposed to enrich the specification semantics with sufficient metrological information. It is designed particularly for applications where non-traditional measurement methods are applied; and it can also identify any redundancies, inconsistencies or incompletenesses of a specification. The proposed schema is based on category theoretical semantics which uses category theory as the foundation to model the semantics. A set of verification operations that derived from the measurement process was firstly formalised using the categorical semantics. Then a set of full faithful functors were constructed to map the set of verification operations to a set of specification operations. A set of simplification rules was then developed to deduce all of the necessary specification objects which are independent to each other. Then the residual specification objects provide a compact structure of the specification. Three test cases were conducted to validate the proposed schema. An industrial computed tomography (CT) measurement process for an impeller manufacturing using selective laser sintering (SLS) technique, was modelled and a set of independent specification elements was then deduced. The other two test cases for checking redundancy and incompleteness on general ISO specifications were carried out. The results show that the proposed schema works for proposing semantic enriched specification that are characterised by non-traditional measurement methods and for testing redundancy and incompleteness of specifications based on geometrical product specifications and verification (GPS) standards system.