Computing the polar decomposition with applications
SIAM Journal on Scientific and Statistical Computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Geometric computation for machine vision
Geometric computation for machine vision
Neural Networks for Optimization and Signal Processing
Neural Networks for Optimization and Signal Processing
Analysis of 3-D Rotation Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The neural solids are novel neural networks devised for solving optimization problems. They are dual to Hopfield networks, but with a quartic energy function. These solids are open architectures, in the sense that different choices of the basic elements and interfacings solve different optimization problems. The basic element is the neural resonator (triangle for the three dimensional case), composed of resonant neurons underlying a self-organizing learning. This module is able to solve elementary optimization problems such as the search for the nearest orthonormal matrix to a given one. Then, an example of a more complex solid, the neural decomposer, whose architecture is composed of neural resonators and their mutual connections, is given. This solid can solve more complex optimization problems such as the decomposition of the essential matrix, which is a very important technique in computer vision.