Parametric and Non-parametric modelling

Up until now, we believe our readers got a clear explanation of reverse engineering. Let us give walkthrough — Reverse engineering is the process of extracting design information after studying a physical product, with the intent to reproduce the product, or to create another object that can interact with it.

In the past, designers resorted to physical measurement of the product to redraw its geometry. Today, designers use 3D scanners to capture measurements. The scanned data is then imported to CAD where the design can be analyzed, processed, manipulated and refined. Two key aspects that fall in place when focusing on reverse engineering process are:

Parametric Model/Modeling

A parametric model captures all its information about the data within its parameters. All you need to know for predicting a future data value from the current state of the model is just its parameters.
The parameters are usually finite in dimensions. For a parametric model to predict new data, knowing just the parameters is enough. A parametric model is one where we assume the ‘shape’ of the data, and therefore only have to estimate the coefficients of the model.

Non-parametric Model/Modeling

A non parametric model can capture more subtle aspects of the data. It allows more information to pass from the current set of data that is attached to the model at the current state, to be able to predict any future data.
The parameters are usually said to be infinite in dimensions. Hence, it can express the characteristics in the data much better than parametric models. For a non parametric model, predicting future data is based on not just the parameters but also in the current state of data that has been observed. A non-parametric model is one where we do not assume the ‘shape’ of the data, and we have to estimate the most suitable form of the model, along with the coefficients.