Affine transformations of 3D objects represented with neural networks

An experiment is conducted to prove that multilayer feed-forward neural networks are capable of representing most classes of 3D objects, used in computer graphics. Furthermore, simple affine transformations were applied on those objects showing that modeling is possible using this type of representation. One network is used per one volumetric description of a 3D object. The neural network employed, is a function that takes as inputs 3D coordinates in object space and produces as output a value that indicates if the point belongs to the object or not. The representation method is tested by repeated evaluations of the network for points inside the object space. Objects that have a simple analytical form, e.g. a sphere or a cube, are represented by specifying the networks' parameters manually. For objects with more complicated shapes we generate training examples. These training examples consist of points on the objects' surface and points lying on inclosed and enclosing surfaces. The algorithm for generating the training data, is a simple heuristic that uses the surface normal to determine whether a point in the vicinity of the surface belongs to the inside or the outside of the object. The network is finally trained on the generated examples, using the back propagation technique. The experimental results prove that this representation method is accurate and compact. Feedforward neural networks being hardware implementable offer the ability for a faster representation. This paper is the second step, on a series of ideas, towards creating a real time 3D renderer based entirely on neural networks.