Transfer Functions in Artificial Neural Networks - A Simulation-Based Tutorial

Artificial neural networks are based on computational units that resemble basic information processing properties of biological neurons in an abstract and simplified manner. Generally, these formal neurons model an input-output behaviour as it is also often used to characterize biological neurons. The neuron is treated as a black box; spatial extension and temporal dynamics present in biological neurons are most often neglected. Even though artificial neurons are simplified, they can show a variety of input-output relations, depending on the transfer functions they apply. This unit on transfer functions provides an overview of different transfer functions and offers a simulation that visualizes the input-output behaviour of an artificial neuron depending on the specific combination of transfer functions.

Cosine Lobe Based Relighting from Gradient Illumination Photographs

We present an image-based method for relighting a scene by analytically fitting cosine lobes to the reflectance function at each pixel, based on gradient illumination photographs. Realistic relighting results for many materials are obtained using a single per-pixel cosine lobe obtained from just two color photographs: one under uniform white illumination and the other under colored gradient illumination. For materials with wavelength-dependent scattering, a better fit can be obtained using independent cosine lobes for the red, green, and blue channels, obtained from three achromatic gradient illumination conditions instead of the colored gradient condition. We explore two cosine lobe reflectance functions, both of which allow an analytic fit to the gradient conditions. One is non-zero over half the sphere of lighting directions, which works well for diffuse and specular materials, but fails for materials with broader scattering such as fur. The other is non-zero everywhere, which works well for broadly scattering materials and still produces visually plausible results for diffuse and specular materials. We also perform an approximate diffuse/specular separation of the reflectance, and estimate scene geometry from the recovered photometric normals to produce hard shadows cast by the geometry, while still reconstructing the input photographs exactly.