NON PARAMETRIC MODELS

Non parametric models are digital representations of objects or systems that do not rely on a fixed set of parameters to define their shape or behavior. Instead they use flexible and adaptive representations that can capture complex geometries and relationships.

There are several types of non-parametric models and they are as follows; point cloud, mesh, voxe-based and implicit models.

Point cloud models represents objects and scenes as asset of 3D points often obtained from 3D scanning or photogrammetry.

Mesh models represents objects or scenes as a network of vertices, edges and faces. They are often used in computer graphics and simulations.

Vogel based models represents objects or scenes as 3D grid of voxels. They are often used in medical imaging and scientific visualizations.

Implicit models represent objects or scenes as a mathematical function that defines the surface or boundary of the objects.

The advantages of non-parametric models are as follows; non parametric models can capture complex geometries and relationships that may be difficult to represent using parametric models. Non parametric models can provide highly accurate representations of complex objects or scenes. Non parametric models can be more robust to noise and outliers in the data. Non parametric models can capture complex patterns and relationships in the data.

The disadvantages of non-parametric models are as follows; non parametric models can be computationally intensive to create and analyze. Non parametric models often require large amounts of data to capture complex geometries and relationships. Non parametric models can be difficult to edit or modify especially if the underlying data is complex. Non parametric models do not provide the same level of parametric control as parametric models.

The applications of non-parametric models is widespread in the following industries; non parametric models are used  to represent complex objects or scenes captured through 3D scanning. Non parametric models are used to represent complex anatomical structures in medical imaging. Non parametric models are used to create realistic models of complex objects or scenes in computer graphics. Non parametric models are used to represent complex scientific data such as fluid dynamics or climate models.

The future of non-parametric models is based on the advances and developments in the following technologies; advances in computer power, improved data acquisition, integration with artificial intelligence and machine learning will enable more accurate, detailed and efficient analysis and interpretation of non-parametric models. Non parametric models will become increasingly adopted in various industries including engineering, architecture, product design etc.

SOURCES:

• Geometric modeling by Michael E. Mortenson.
• Computational geometry: Algorithms and applications by Mark de Berg, Otfried Cheong and Marc van Kreveld.
• Geometric modeling for computer graphics by Gerald Farin and Dianne Hansford.
• Computer aided geometric design by Gerald Farin.
• Geometric modeling for engineering applications by Gerald Farin.

 

 

NB: popular non parametric software are as follows; python, tensor flow, blender, maya,3dmax, cloud compare, mesh lab, paraview, mat lab. Julia etc.